Fidelity-Based Ant Colony Algorithm with Q-learning of Quantum System

NASA Astrophysics Data System (ADS)

Liao, Qin; Guo, Ying; Tu, Yifeng; Zhang, Hang

2018-03-01

Quantum ant colony algorithm (ACA) has potential applications in quantum information processing, such as solutions of traveling salesman problem, zero-one knapsack problem, robot route planning problem, and so on. To shorten the search time of the ACA, we suggest the fidelity-based ant colony algorithm (FACA) for the control of quantum system. Motivated by structure of the Q-learning algorithm, we demonstrate the combination of a FACA with the Q-learning algorithm and suggest the design of a fidelity-based ant colony algorithm with the Q-learning to improve the performance of the FACA in a spin-1/2 quantum system. The numeric simulation results show that the FACA with the Q-learning can efficiently avoid trapping into local optimal policies and increase the speed of convergence process of quantum system.

Fidelity-Based Ant Colony Algorithm with Q-learning of Quantum System

NASA Astrophysics Data System (ADS)

Liao, Qin; Guo, Ying; Tu, Yifeng; Zhang, Hang

2017-12-01

Quantum ant colony algorithm (ACA) has potential applications in quantum information processing, such as solutions of traveling salesman problem, zero-one knapsack problem, robot route planning problem, and so on. To shorten the search time of the ACA, we suggest the fidelity-based ant colony algorithm (FACA) for the control of quantum system. Motivated by structure of the Q-learning algorithm, we demonstrate the combination of a FACA with the Q-learning algorithm and suggest the design of a fidelity-based ant colony algorithm with the Q-learning to improve the performance of the FACA in a spin-1/2 quantum system. The numeric simulation results show that the FACA with the Q-learning can efficiently avoid trapping into local optimal policies and increase the speed of convergence process of quantum system.

Adding control to arbitrary unknown quantum operations

PubMed Central

Zhou, Xiao-Qi; Ralph, Timothy C.; Kalasuwan, Pruet; Zhang, Mian; Peruzzo, Alberto; Lanyon, Benjamin P.; O'Brien, Jeremy L.

2011-01-01

Although quantum computers promise significant advantages, the complexity of quantum algorithms remains a major technological obstacle. We have developed and demonstrated an architecture-independent technique that simplifies adding control qubits to arbitrary quantum operations—a requirement in many quantum algorithms, simulations and metrology. The technique, which is independent of how the operation is done, does not require knowledge of what the operation is, and largely separates the problems of how to implement a quantum operation in the laboratory and how to add a control. Here, we demonstrate an entanglement-based version in a photonic system, realizing a range of different two-qubit gates with high fidelity. PMID:21811242

Control aspects of quantum computing using pure and mixed states.

PubMed

Schulte-Herbrüggen, Thomas; Marx, Raimund; Fahmy, Amr; Kauffman, Louis; Lomonaco, Samuel; Khaneja, Navin; Glaser, Steffen J

2012-10-13

Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems.

Control aspects of quantum computing using pure and mixed states

PubMed Central

Schulte-Herbrüggen, Thomas; Marx, Raimund; Fahmy, Amr; Kauffman, Louis; Lomonaco, Samuel; Khaneja, Navin; Glaser, Steffen J.

2012-01-01

Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems. PMID:22946034

Closed-loop and robust control of quantum systems.

PubMed

Chen, Chunlin; Wang, Lin-Cheng; Wang, Yuanlong

2013-01-01

For most practical quantum control systems, it is important and difficult to attain robustness and reliability due to unavoidable uncertainties in the system dynamics or models. Three kinds of typical approaches (e.g., closed-loop learning control, feedback control, and robust control) have been proved to be effective to solve these problems. This work presents a self-contained survey on the closed-loop and robust control of quantum systems, as well as a brief introduction to a selection of basic theories and methods in this research area, to provide interested readers with a general idea for further studies. In the area of closed-loop learning control of quantum systems, we survey and introduce such learning control methods as gradient-based methods, genetic algorithms (GA), and reinforcement learning (RL) methods from a unified point of view of exploring the quantum control landscapes. For the feedback control approach, the paper surveys three control strategies including Lyapunov control, measurement-based control, and coherent-feedback control. Then such topics in the field of quantum robust control as H(∞) control, sliding mode control, quantum risk-sensitive control, and quantum ensemble control are reviewed. The paper concludes with a perspective of future research directions that are likely to attract more attention.

Quantum learning of classical stochastic processes: The completely positive realization problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Monràs, Alex; Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543; Winter, Andreas

2016-01-15

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece inmore » the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print http://arxiv.org/abs/1303.3771 (2013)].« less

Connection between optimal control theory and adiabatic-passage techniques in quantum systems

NASA Astrophysics Data System (ADS)

Assémat, E.; Sugny, D.

2012-08-01

This work explores the relationship between optimal control theory and adiabatic passage techniques in quantum systems. The study is based on a geometric analysis of the Hamiltonian dynamics constructed from Pontryagin's maximum principle. In a three-level quantum system, we show that the stimulated Raman adiabatic passage technique can be associated to a peculiar Hamiltonian singularity. One deduces that the adiabatic pulse is solution of the optimal control problem only for a specific cost functional. This analysis is extended to the case of a four-level quantum system.

Sum-of-squares-based fuzzy controller design using quantum-inspired evolutionary algorithm

NASA Astrophysics Data System (ADS)

Yu, Gwo-Ruey; Huang, Yu-Chia; Cheng, Chih-Yung

2016-07-01

In the field of fuzzy control, control gains are obtained by solving stabilisation conditions in linear-matrix-inequality-based Takagi-Sugeno fuzzy control method and sum-of-squares-based polynomial fuzzy control method. However, the optimal performance requirements are not considered under those stabilisation conditions. In order to handle specific performance problems, this paper proposes a novel design procedure with regard to polynomial fuzzy controllers using quantum-inspired evolutionary algorithms. The first contribution of this paper is a combination of polynomial fuzzy control and quantum-inspired evolutionary algorithms to undertake an optimal performance controller design. The second contribution is the proposed stability condition derived from the polynomial Lyapunov function. The proposed design approach is dissimilar to the traditional approach, in which control gains are obtained by solving the stabilisation conditions. The first step of the controller design uses the quantum-inspired evolutionary algorithms to determine the control gains with the best performance. Then, the stability of the closed-loop system is analysed under the proposed stability conditions. To illustrate effectiveness and validity, the problem of balancing and the up-swing of an inverted pendulum on a cart is used.

Quantum Sensors for the Generating Functional of Interacting Quantum Field Theories

NASA Astrophysics Data System (ADS)

Bermudez, A.; Aarts, G.; Müller, M.

2017-10-01

Difficult problems described in terms of interacting quantum fields evolving in real time or out of equilibrium abound in condensed-matter and high-energy physics. Addressing such problems via controlled experiments in atomic, molecular, and optical physics would be a breakthrough in the field of quantum simulations. In this work, we present a quantum-sensing protocol to measure the generating functional of an interacting quantum field theory and, with it, all the relevant information about its in- or out-of-equilibrium phenomena. Our protocol can be understood as a collective interferometric scheme based on a generalization of the notion of Schwinger sources in quantum field theories, which make it possible to probe the generating functional. We show that our scheme can be realized in crystals of trapped ions acting as analog quantum simulators of self-interacting scalar quantum field theories.

Superadiabatic driving of a three-level quantum system

NASA Astrophysics Data System (ADS)

Theisen, M.; Petiziol, F.; Carretta, S.; Santini, P.; Wimberger, S.

2017-07-01

We study superadiabatic quantum control of a three-level quantum system whose energy spectrum exhibits multiple avoided crossings. In particular, we investigate the possibility of treating the full control task in terms of independent two-level Landau-Zener problems. We first show that the time profiles of the elements of the full control Hamiltonian are characterized by peaks centered around the crossing times. These peaks decay algebraically for large times. In principle, such a power-law scaling invalidates the hypothesis of perfect separability. Nonetheless, we address the problem from a pragmatic point of view by studying the fidelity obtained through separate control as a function of the intercrossing separation. This procedure may be a good approach to achieve approximate adiabatic driving of a specific instantaneous eigenstate in realistic implementations.

Closed-Loop and Robust Control of Quantum Systems

PubMed Central

Wang, Lin-Cheng

2013-01-01

For most practical quantum control systems, it is important and difficult to attain robustness and reliability due to unavoidable uncertainties in the system dynamics or models. Three kinds of typical approaches (e.g., closed-loop learning control, feedback control, and robust control) have been proved to be effective to solve these problems. This work presents a self-contained survey on the closed-loop and robust control of quantum systems, as well as a brief introduction to a selection of basic theories and methods in this research area, to provide interested readers with a general idea for further studies. In the area of closed-loop learning control of quantum systems, we survey and introduce such learning control methods as gradient-based methods, genetic algorithms (GA), and reinforcement learning (RL) methods from a unified point of view of exploring the quantum control landscapes. For the feedback control approach, the paper surveys three control strategies including Lyapunov control, measurement-based control, and coherent-feedback control. Then such topics in the field of quantum robust control as H ∞ control, sliding mode control, quantum risk-sensitive control, and quantum ensemble control are reviewed. The paper concludes with a perspective of future research directions that are likely to attract more attention. PMID:23997680

Hybrid Toffoli gate on photons and quantum spins

PubMed Central

Luo, Ming-Xing; Ma, Song-Ya; Chen, Xiu-Bo; Wang, Xiaojun

2015-01-01

Quantum computation offers potential advantages in solving a number of interesting and difficult problems. Several controlled logic gates, the elemental building blocks of quantum computer, have been realized with various physical systems. A general technique was recently proposed that significantly reduces the realization complexity of multiple-control logic gates by harnessing multi-level information carriers. We present implementations of a key quantum circuit: the three-qubit Toffoli gate. By exploring the optical selection rules of one-sided optical microcavities, a Toffoli gate may be realized on all combinations of photon and quantum spins in the QD-cavity. The three general controlled-NOT gates are involved using an auxiliary photon with two degrees of freedom. Our results show that photons and quantum spins may be used alternatively in quantum information processing. PMID:26568078

Hybrid Toffoli gate on photons and quantum spins.

PubMed

Luo, Ming-Xing; Ma, Song-Ya; Chen, Xiu-Bo; Wang, Xiaojun

2015-11-16

Quantum computation offers potential advantages in solving a number of interesting and difficult problems. Several controlled logic gates, the elemental building blocks of quantum computer, have been realized with various physical systems. A general technique was recently proposed that significantly reduces the realization complexity of multiple-control logic gates by harnessing multi-level information carriers. We present implementations of a key quantum circuit: the three-qubit Toffoli gate. By exploring the optical selection rules of one-sided optical microcavities, a Toffoli gate may be realized on all combinations of photon and quantum spins in the QD-cavity. The three general controlled-NOT gates are involved using an auxiliary photon with two degrees of freedom. Our results show that photons and quantum spins may be used alternatively in quantum information processing.

Thermalization and prethermalization in isolated quantum systems: a theoretical overview

NASA Astrophysics Data System (ADS)

Mori, Takashi; Ikeda, Tatsuhiko N.; Kaminishi, Eriko; Ueda, Masahito

2018-06-01

The approach to thermal equilibrium, or thermalization, in isolated quantum systems is among the most fundamental problems in statistical physics. Recent theoretical studies have revealed that thermalization in isolated quantum systems has several remarkable features, which emerge from quantum entanglement and are quite distinct from those in classical systems. Experimentally, well isolated and highly controllable ultracold quantum gases offer an ideal testbed to study the nonequilibrium dynamics in isolated quantum systems, promoting intensive recent theoretical endeavors on this fundamental subject. Besides thermalization, many isolated quantum systems show intriguing behavior in relaxation processes, especially prethermalization. Prethermalization occurs when there is a clear separation of relevant time scales and has several different physical origins depending on individual systems. In this review, we overview theoretical approaches to the problems of thermalization and prethermalization.

Controlled Bidirectional Quantum Secure Direct Communication

PubMed Central

Chou, Yao-Hsin; Lin, Yu-Ting; Zeng, Guo-Jyun; Lin, Fang-Jhu; Chen, Chi-Yuan

2014-01-01

We propose a novel protocol for controlled bidirectional quantum secure communication based on a nonlocal swap gate scheme. Our proposed protocol would be applied to a system in which a controller (supervisor/Charlie) controls the bidirectional communication with quantum information or secret messages between legitimate users (Alice and Bob). In this system, the legitimate users must obtain permission from the controller in order to exchange their respective quantum information or secret messages simultaneously; the controller is unable to obtain any quantum information or secret messages from the decoding process. Moreover, the presence of the controller also avoids the problem of one legitimate user receiving the quantum information or secret message before the other, and then refusing to help the other user decode the quantum information or secret message. Our proposed protocol is aimed at protecting against external and participant attacks on such a system, and the cost of transmitting quantum bits using our protocol is less than that achieved in other studies. Based on the nonlocal swap gate scheme, the legitimate users exchange their quantum information or secret messages without transmission in a public channel, thus protecting against eavesdroppers stealing the secret messages. PMID:25006596

Experimental fault-tolerant universal quantum gates with solid-state spins under ambient conditions

PubMed Central

Rong, Xing; Geng, Jianpei; Shi, Fazhan; Liu, Ying; Xu, Kebiao; Ma, Wenchao; Kong, Fei; Jiang, Zhen; Wu, Yang; Du, Jiangfeng

2015-01-01

Quantum computation provides great speedup over its classical counterpart for certain problems. One of the key challenges for quantum computation is to realize precise control of the quantum system in the presence of noise. Control of the spin-qubits in solids with the accuracy required by fault-tolerant quantum computation under ambient conditions remains elusive. Here, we quantitatively characterize the source of noise during quantum gate operation and demonstrate strategies to suppress the effect of these. A universal set of logic gates in a nitrogen-vacancy centre in diamond are reported with an average single-qubit gate fidelity of 0.999952 and two-qubit gate fidelity of 0.992. These high control fidelities have been achieved at room temperature in naturally abundant 13C diamond via composite pulses and an optimized control method. PMID:26602456

Implementing controlled-unitary operations over the butterfly network

NASA Astrophysics Data System (ADS)

Soeda, Akihito; Kinjo, Yoshiyuki; Turner, Peter S.; Murao, Mio

2014-12-01

We introduce a multiparty quantum computation task over a network in a situation where the capacities of both the quantum and classical communication channels of the network are limited and a bottleneck occurs. Using a resource setting introduced by Hayashi [1], we present an efficient protocol for performing controlled-unitary operations between two input nodes and two output nodes over the butterfly network, one of the most fundamental networks exhibiting the bottleneck problem. This result opens the possibility of developing a theory of quantum network coding for multiparty quantum computation, whereas the conventional network coding only treats multiparty quantum communication.

Implementing controlled-unitary operations over the butterfly network

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soeda, Akihito; Kinjo, Yoshiyuki; Turner, Peter S.

2014-12-04

We introduce a multiparty quantum computation task over a network in a situation where the capacities of both the quantum and classical communication channels of the network are limited and a bottleneck occurs. Using a resource setting introduced by Hayashi [1], we present an efficient protocol for performing controlled-unitary operations between two input nodes and two output nodes over the butterfly network, one of the most fundamental networks exhibiting the bottleneck problem. This result opens the possibility of developing a theory of quantum network coding for multiparty quantum computation, whereas the conventional network coding only treats multiparty quantum communication.

Spin Glass a Bridge Between Quantum Computation and Statistical Mechanics

NASA Astrophysics Data System (ADS)

Ohzeki, Masayuki

2013-09-01

In this chapter, we show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Interestingly, the theoretical limitation of the surface code, accuracy threshold, to restore the quantum state has a close connection with the problem on the phase transition in a special model known as spin glasses, which is one of the most active researches in statistical mechanics. The phase transition in spin glasses is an intractable problem, since we must strive many-body system with complicated interactions with change of their signs depending on the distance between spins. Fortunately, recent progress in spin-glass theory enables us to predict the precise location of the critical point, at which the phase transition occurs. It means that statistical mechanics is available for revealing one of the most interesting parts in quantum information processing. We show how to import the special tool in statistical mechanics into the problem on the accuracy threshold in quantum computation. Second, we show another interesting technique to employ quantum nature, quantum annealing. The purpose of quantum annealing is to search for the most favored solution of a multivariable function, namely optimization problem. The most typical instance is the traveling salesman problem to find the minimum tour while visiting all the cities. In quantum annealing, we introduce quantum fluctuation to drive a particular system with the artificial Hamiltonian, in which the ground state represents the optimal solution of the specific problem we desire to solve. Induction of the quantum fluctuation gives rise to the quantum tunneling effect, which allows nontrivial hopping from state to state. We then sketch a strategy to control the quantum fluctuation efficiently reaching the ground state. Such a generic framework is called quantum annealing. The most typical instance is quantum adiabatic computation based on the adiabatic theorem. The quantum adiabatic computation as discussed in the other chapter, unfortunately, has a crucial bottleneck for a part of the optimization problems. We here introduce several recent trials to overcome such a weakpoint by use of developments in statistical mechanics. Through both of the topics, we would shed light on the birth of the interdisciplinary field between quantum mechanics and statistical mechanics.

Enhancing quantum annealing performance for the molecular similarity problem

NASA Astrophysics Data System (ADS)

Hernandez, Maritza; Aramon, Maliheh

2017-05-01

Quantum annealing is a promising technique which leverages quantum mechanics to solve hard optimization problems. Considerable progress has been made in the development of a physical quantum annealer, motivating the study of methods to enhance the efficiency of such a solver. In this work, we present a quantum annealing approach to measure similarity among molecular structures. Implementing real-world problems on a quantum annealer is challenging due to hardware limitations such as sparse connectivity, intrinsic control error, and limited precision. In order to overcome the limited connectivity, a problem must be reformulated using minor-embedding techniques. Using a real data set, we investigate the performance of a quantum annealer in solving the molecular similarity problem. We provide experimental evidence that common practices for embedding can be replaced by new alternatives which mitigate some of the hardware limitations and enhance its performance. Common practices for embedding include minimizing either the number of qubits or the chain length and determining the strength of ferromagnetic couplers empirically. We show that current criteria for selecting an embedding do not improve the hardware's performance for the molecular similarity problem. Furthermore, we use a theoretical approach to determine the strength of ferromagnetic couplers. Such an approach removes the computational burden of the current empirical approaches and also results in hardware solutions that can benefit from simple local classical improvement. Although our results are limited to the problems considered here, they can be generalized to guide future benchmarking studies.

Robust quantum control using smooth pulses and topological winding

NASA Astrophysics Data System (ADS)

Barnes, Edwin; Wang, Xin

2015-03-01

Perhaps the greatest challenge in achieving control of microscopic quantum systems is the decoherence induced by the environment, a problem which pervades experimental quantum physics and is particularly severe in the context of solid state quantum computing and nanoscale quantum devices because of the inherently strong coupling to the surrounding material. We present an analytical approach to constructing intrinsically robust driving fields which automatically cancel the leading-order noise-induced errors in a qubit's evolution exactly. We address two of the most common types of non-Markovian noise that arise in qubits: slow fluctuations of the qubit energy splitting and fluctuations in the driving field itself. We demonstrate our method by constructing robust quantum gates for several types of spin qubits, including phosphorous donors in silicon and nitrogen-vacancy centers in diamond. Our results constitute an important step toward achieving robust generic control of quantum systems, bringing their novel applications closer to realization. Work supported by LPS-CMTC.

Quantum Ensemble Classification: A Sampling-Based Learning Control Approach.

PubMed

Chen, Chunlin; Dong, Daoyi; Qi, Bo; Petersen, Ian R; Rabitz, Herschel

2017-06-01

Quantum ensemble classification (QEC) has significant applications in discrimination of atoms (or molecules), separation of isotopes, and quantum information extraction. However, quantum mechanics forbids deterministic discrimination among nonorthogonal states. The classification of inhomogeneous quantum ensembles is very challenging, since there exist variations in the parameters characterizing the members within different classes. In this paper, we recast QEC as a supervised quantum learning problem. A systematic classification methodology is presented by using a sampling-based learning control (SLC) approach for quantum discrimination. The classification task is accomplished via simultaneously steering members belonging to different classes to their corresponding target states (e.g., mutually orthogonal states). First, a new discrimination method is proposed for two similar quantum systems. Then, an SLC method is presented for QEC. Numerical results demonstrate the effectiveness of the proposed approach for the binary classification of two-level quantum ensembles and the multiclass classification of multilevel quantum ensembles.

Quantum error correction in crossbar architectures

NASA Astrophysics Data System (ADS)

Helsen, Jonas; Steudtner, Mark; Veldhorst, Menno; Wehner, Stephanie

2018-07-01

A central challenge for the scaling of quantum computing systems is the need to control all qubits in the system without a large overhead. A solution for this problem in classical computing comes in the form of so-called crossbar architectures. Recently we made a proposal for a large-scale quantum processor (Li et al arXiv:1711.03807 (2017)) to be implemented in silicon quantum dots. This system features a crossbar control architecture which limits parallel single-qubit control, but allows the scheme to overcome control scaling issues that form a major hurdle to large-scale quantum computing systems. In this work, we develop a language that makes it possible to easily map quantum circuits to crossbar systems, taking into account their architecture and control limitations. Using this language we show how to map well known quantum error correction codes such as the planar surface and color codes in this limited control setting with only a small overhead in time. We analyze the logical error behavior of this surface code mapping for estimated experimental parameters of the crossbar system and conclude that logical error suppression to a level useful for real quantum computation is feasible.

Geometrizing adiabatic quantum computation

NASA Astrophysics Data System (ADS)

Rezakhani, Ali; Kuo, Wan-Jung; Hamma, Alioscia; Lidar, Daniel; Zanardi, Paolo

2010-03-01

A time-optimal approach to adiabatic quantum computation (AQC) is formulated. The corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. We demonstrate this geometrization through some examples, where we show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance. The underlying connection with quantum phase transitions is also explored.

An Improved Protocol for Controlled Deterministic Secure Quantum Communication Using Five-Qubit Entangled State

NASA Astrophysics Data System (ADS)

Kao, Shih-Hung; Lin, Jason; Tsai, Chia-Wei; Hwang, Tzonelih

2018-03-01

In early 2009, Xiu et al. (Opt. Commun. 282(2) 333-337 2009) presented a controlled deterministic secure quantum communication (CDSQC) protocol via a newly constructed five-qubit entangled quantum state. Later, Qin et al. (Opt. Commun. 282(13), 2656-2658 2009) pointed out two security loopholes in Xiu et al.'s protocol: (1) A correlation-elicitation (CE) attack can reveal the entire secret message; (2) A leakage of partial information for the receiver is noticed. Then, Xiu et al. (Opt. Commun. 283(2), 344-347 2010) presented a revised CDSQC protocol to remedy the CE attack problem. However, the information leakage problem still remains open. This work proposes a new CDSQC protocol using the same five-qubit entangled state which can work without the above mentioned security problems. Moreover, the Trojan Horse attacks can be automatically avoided without using detecting devices in the new CDSQC.

An Improved Protocol for Controlled Deterministic Secure Quantum Communication Using Five-Qubit Entangled State

NASA Astrophysics Data System (ADS)

Kao, Shih-Hung; Lin, Jason; Tsai, Chia-Wei; Hwang, Tzonelih

2018-06-01

In early 2009, Xiu et al. (Opt. Commun. 282(2) 333-337 2009) presented a controlled deterministic secure quantum communication (CDSQC) protocol via a newly constructed five-qubit entangled quantum state. Later, Qin et al. (Opt. Commun. 282(13), 2656-2658 2009) pointed out two security loopholes in Xiu et al.'s protocol: (1) A correlation-elicitation (CE) attack can reveal the entire secret message; (2) A leakage of partial information for the receiver is noticed. Then, Xiu et al. (Opt. Commun. 283(2), 344-347 2010) presented a revised CDSQC protocol to remedy the CE attack problem. However, the information leakage problem still remains open. This work proposes a new CDSQC protocol using the same five-qubit entangled state which can work without the above mentioned security problems. Moreover, the Trojan Horse attacks can be automatically avoided without using detecting devices in the new CDSQC.

A controlled ac Stark echo for quantum memories.

PubMed

Ham, Byoung S

2017-08-09

A quantum memory protocol of controlled ac Stark echoes (CASE) based on a double rephasing photon echo scheme via controlled Rabi flopping is proposed. The double rephasing scheme of photon echoes inherently satisfies the no-population inversion requirement for quantum memories, but the resultant absorptive echo remains a fundamental problem. Herein, it is reported that the first echo in the double rephasing scheme can be dynamically controlled so that it does not affect the second echo, which is accomplished by using unbalanced ac Stark shifts. Then, the second echo is coherently controlled to be emissive via controlled coherence conversion. Finally a near perfect ultralong CASE is presented using a backward echo scheme. Compared with other methods such as dc Stark echoes, the present protocol is all-optical with advantages of wavelength-selective dynamic control of quantum processing for erasing, buffering, and channel multiplexing.

Quantum control of quasi-collision states: A protocol for hybrid fusion

NASA Astrophysics Data System (ADS)

Vilela Mendes, R.

2018-04-01

When confined to small regions quantum systems exhibit electronic and structural properties different from their free space behavior. These properties are of interest, for example, for molecular insertion, hydrogen storage and the exploration of new pathways for chemical and nuclear reactions. Here, a confined three-body problem is studied, with emphasis on the study of the “quantum scars” associated to dynamical collisions. For the particular case of nuclear reactions, it is proposed that a molecular cage might simply be used as a confining device with the collision states accessed by quantum control techniques.

Non-Abelian Bosonization and Fractional Quantum Hall Transitions

NASA Astrophysics Data System (ADS)

Hui, Aaron; Mulligan, Michael; Kim, Eun-Ah

A fully satisfying theoretical description for the quantum phase transition between fractional quantum Hall plateaus remains an outstanding problem. Experiments indicate scaling exponents that are not readily obtained in conventional theories. Using insights from duality, we describe a class of quantum critical effective theories that produce qualitatively realistic scaling exponents for the transition. We discuss the implications of our results for the physically-relevant interactions controlling this broad class of quantum critical behavior. Supported by National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1650441.

Adiabatic quantum simulation of quantum chemistry.

PubMed

Babbush, Ryan; Love, Peter J; Aspuru-Guzik, Alán

2014-10-13

We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-body, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions.

Pareto-front shape in multiobservable quantum control

NASA Astrophysics Data System (ADS)

Sun, Qiuyang; Wu, Re-Bing; Rabitz, Herschel

2017-03-01

Many scenarios in the sciences and engineering require simultaneous optimization of multiple objective functions, which are usually conflicting or competing. In such problems the Pareto front, where none of the individual objectives can be further improved without degrading some others, shows the tradeoff relations between the competing objectives. This paper analyzes the Pareto-front shape for the problem of quantum multiobservable control, i.e., optimizing the expectation values of multiple observables in the same quantum system. Analytic and numerical results demonstrate that with two commuting observables the Pareto front is a convex polygon consisting of flat segments only, while with noncommuting observables the Pareto front includes convexly curved segments. We also assess the capability of a weighted-sum method to continuously capture the points along the Pareto front. Illustrative examples with realistic physical conditions are presented, including NMR control experiments on a 1H-13C two-spin system with two commuting or noncommuting observables.

A quantum retrograde canon: complete population inversion in n 2-state systems

NASA Astrophysics Data System (ADS)

Padan, Alon; Suchowski, Haim

2018-04-01

We present a novel approach for analytically reducing a family of time-dependent multi-state quantum control problems to two-state systems. The presented method translates between {SU}(2)× {SU}(2) related n 2-state systems and two-state systems, such that the former undergo complete population inversion (CPI) if and only if the latter reach specific states. For even n, the method translates any two-state CPI scheme to a family of CPI schemes in n 2-state systems. In particular, facilitating CPI in a four-state system via real time-dependent nearest-neighbors couplings is reduced to facilitating CPI in a two-level system. Furthermore, we show that the method can be used for operator control, and provide conditions for producing several universal gates for quantum computation as an example. In addition, we indicate a basis for utilizing the method in optimal control problems.

Quantum game application to spectrum scarcity problems

NASA Astrophysics Data System (ADS)

Zabaleta, O. G.; Barrangú, J. P.; Arizmendi, C. M.

2017-01-01

Recent spectrum-sharing research has produced a strategy to address spectrum scarcity problems. This novel idea, named cognitive radio, considers that secondary users can opportunistically exploit spectrum holes left temporarily unused by primary users. This presents a competitive scenario among cognitive users, making it suitable for game theory treatment. In this work, we show that the spectrum-sharing benefits of cognitive radio can be increased by designing a medium access control based on quantum game theory. In this context, we propose a model to manage spectrum fairly and effectively, based on a multiple-users multiple-choice quantum minority game. By taking advantage of quantum entanglement and quantum interference, it is possible to reduce the probability of collision problems commonly associated with classic algorithms. Collision avoidance is an essential property for classic and quantum communications systems. In our model, two different scenarios are considered, to meet the requirements of different user strategies. The first considers sensor networks where the rational use of energy is a cornerstone; the second focuses on installations where the quality of service of the entire network is a priority.

2011 Quantum Control of Light & Matter Gordon Research Conference (July 31-August 5, 2011, Mount Holyoke College, South Hadley, MA)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thomas Weinacht

2011-08-05

Quantum control of light and matter is the quest to steer a physical process to a desirable outcome, employing constructive and destructive interference. Three basic questions address feasibility of quantum control: (1) The problem of controllability, does a control field exist for a preset initial and target state; (2) Synthesis, constructively finding the field that leads to the target; and (3) Optimal Control Theory - optimizing the field that carries out this task. These continue to be the fundamental theoretical questions to be addressed in the conference. How to realize control fields in the laboratory is an ongoing challenge. Thismore » task is very diverse viewing the emergence of control scenarios ranging from attoseconds to microseconds. How do the experimental observations reflect on the theoretical framework? The typical arena of quantum control is an open environment where much of the control is indirect. How are control scenarios realized in dissipative open systems? Can new control opportunities emerge? Can one null decoherence effects? An ideal setting for control is ultracold matter. The initial and final state can be defined more precisely. Coherent control unifies many fields of physical science. A lesson learned in one field can reflect on another. Currently quantum information processing has emerged as a primary target of control where the key issue is controlling quantum gate operation. Modern nonlinear spectroscopy has emerged as another primary field. The challenge is to unravel the dynamics of molecular systems undergoing strong interactions with the environment. Quantum optics where non-classical fields are to be generated and employed. Finally, coherent control is the basis for quantum engineering. These issues will be under the limelight of the Gordon conference on Quantum Control of Light and Matter.« less

Experimental loss-tolerant quantum coin flipping

PubMed Central

Berlín, Guido; Brassard, Gilles; Bussières, Félix; Godbout, Nicolas; Slater, Joshua A.; Tittel, Wolfgang

2011-01-01

Coin flipping is a cryptographic primitive in which two distrustful parties wish to generate a random bit to choose between two alternatives. This task is impossible to realize when it relies solely on the asynchronous exchange of classical bits: one dishonest player has complete control over the final outcome. It is only when coin flipping is supplemented with quantum communication that this problem can be alleviated, although partial bias remains. Unfortunately, practical systems are subject to loss of quantum data, which allows a cheater to force a bias that is complete or arbitrarily close to complete in all previous protocols and implementations. Here we report on the first experimental demonstration of a quantum coin-flipping protocol for which loss cannot be exploited to cheat better. By eliminating the problem of loss, which is unavoidable in any realistic setting, quantum coin flipping takes a significant step towards real-world applications of quantum communication. PMID:22127057

A surface code quantum computer in silicon

PubMed Central

Hill, Charles D.; Peretz, Eldad; Hile, Samuel J.; House, Matthew G.; Fuechsle, Martin; Rogge, Sven; Simmons, Michelle Y.; Hollenberg, Lloyd C. L.

2015-01-01

The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel—posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited. PMID:26601310

A surface code quantum computer in silicon.

PubMed

Hill, Charles D; Peretz, Eldad; Hile, Samuel J; House, Matthew G; Fuechsle, Martin; Rogge, Sven; Simmons, Michelle Y; Hollenberg, Lloyd C L

2015-10-01

The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel-posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited.

Adiabatic Quantum Simulation of Quantum Chemistry

PubMed Central

Babbush, Ryan; Love, Peter J.; Aspuru-Guzik, Alán

2014-01-01

We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-body, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions. PMID:25308187

A noise immunity controlled quantum teleportation protocol

NASA Astrophysics Data System (ADS)

Li, Dong-fen; Wang, Rui-jin; Zhang, Feng-li; Baagyere, Edward; Qin, Zhen; Xiong, Hu; Zhan, Huayi

2016-11-01

With the advent of the Internet and information and communication technology, quantum teleportation has become an important field in information security and its application areas. This is because quantum teleportation has the ability to attain a timely secret information delivery and offers unconditional security. And as such, the field of quantum teleportation has become a hot research topic in recent years. However, noise has serious effect on the safety of quantum teleportation within the aspects of information fidelity, channel capacity and information transfer. Therefore, the main purpose of this paper is to address these problems of quantum teleportation. Firstly, in order to resist collective noise, we construct a decoherence-free subspace under different noise scenarios to establish a two-dimensional fidelity quantum teleportation models. And also create quantum teleportation of multiple degree of freedom, and these models ensure the accuracy and availability of the exchange of information and in multiple degree of freedom. Secondly, for easy preparation, measurement and implementation, we use super dense coding features to build an entangled quantum secret exchange channel. To improve the channel utilization and capacity, an efficient super dense coding method based on ultra-entanglement exchange is used. Thirdly, continuous variables of the controlled quantum key distribution were designed for quantum teleportation; in addition, we perform Bell-basis measurement under the collective noise and also prepare the storage technology of quantum states to achieve one-bit key by three-photon encoding to improve its security and efficiency. We use these two methods because they conceal information, resist a third party attack and can detect eavesdropping. Our proposed methods, according to the security analysis, are able to solve the problems associated with the quantum teleportation under various noise environments.

Quantum Computation: Entangling with the Future

NASA Technical Reports Server (NTRS)

Jiang, Zhang

2017-01-01

Commercial applications of quantum computation have become viable due to the rapid progress of the field in the recent years. Efficient quantum algorithms are discovered to cope with the most challenging real-world problems that are too hard for classical computers. Manufactured quantum hardware has reached unprecedented precision and controllability, enabling fault-tolerant quantum computation. Here, I give a brief introduction on what principles in quantum mechanics promise its unparalleled computational power. I will discuss several important quantum algorithms that achieve exponential or polynomial speedup over any classical algorithm. Building a quantum computer is a daunting task, and I will talk about the criteria and various implementations of quantum computers. I conclude the talk with near-future commercial applications of a quantum computer.

Implementation of a quantum controlled-SWAP gate with photonic circuits

NASA Astrophysics Data System (ADS)

Ono, Takafumi; Okamoto, Ryo; Tanida, Masato; Hofmann, Holger F.; Takeuchi, Shigeki

2017-03-01

Quantum information science addresses how the processing and transmission of information are affected by uniquely quantum mechanical phenomena. Combination of two-qubit gates has been used to realize quantum circuits, however, scalability is becoming a critical problem. The use of three-qubit gates may simplify the structure of quantum circuits dramatically. Among them, the controlled-SWAP (Fredkin) gates are essential since they can be directly applied to important protocols, e.g., error correction, fingerprinting, and optimal cloning. Here we report a realization of the Fredkin gate for photonic qubits. We achieve a fidelity of 0.85 in the computational basis and an output state fidelity of 0.81 for a 3-photon Greenberger-Horne-Zeilinger state. The estimated process fidelity of 0.77 indicates that our Fredkin gate can be applied to various quantum tasks.

Band-selective shaped pulse for high fidelity quantum control in diamond

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chang, Yan-Chun; Xing, Jian; Liu, Gang-Qin

High fidelity quantum control of qubits is crucially important for realistic quantum computing, and it becomes more challenging when there are inevitable interactions between qubits. We introduce a band-selective shaped pulse, refocusing BURP (REBURP) pulse, to cope with the problems. The electron spin of nitrogen-vacancy centers in diamond is flipped with high fidelity by the REBURP pulse. In contrast with traditional rectangular pulses, the shaped pulse has almost equal excitation effect in a sharply edged region (in frequency domain). So the three sublevels of host {sup 14}N nuclear spin can be flipped accurately simultaneously, while unwanted excitations of other sublevelsmore » (e.g., of a nearby {sup 13}C nuclear spin) is well suppressed. Our scheme can be used for various applications such as quantum metrology, quantum sensing, and quantum information process.« less

Quantum control on entangled bipartite qubits

DOE Office of Scientific and Technical Information (OSTI.GOV)

Delgado, Francisco

2010-04-15

Ising interactions between qubits can produce distortion on entangled pairs generated for engineering purposes (e.g., for quantum computation or quantum cryptography). The presence of parasite magnetic fields destroys or alters the expected behavior for which it was intended. In addition, these pairs are generated with some dispersion in their original configuration, so their discrimination is necessary for applications. Nevertheless, discrimination should be made after Ising distortion. Quantum control helps in both problems; making some projective measurements upon the pair to decide the original state to replace it, or just trying to reconstruct it using some procedures which do not altermore » their quantum nature. Results about the performance of these procedures are reported. First, we will work with pure systems studying restrictions and advantages. Then, we will extend these operations for mixed states generated with uncertainty in the time of distortion, correcting them by assuming the control prescriptions for the most probable one.« less

Quantum interpolation for high-resolution sensing

PubMed Central

Ajoy, Ashok; Liu, Yi-Xiang; Saha, Kasturi; Marseglia, Luca; Jaskula, Jean-Christophe; Bissbort, Ulf; Cappellaro, Paola

2017-01-01

Recent advances in engineering and control of nanoscale quantum sensors have opened new paradigms in precision metrology. Unfortunately, hardware restrictions often limit the sensor performance. In nanoscale magnetic resonance probes, for instance, finite sampling times greatly limit the achievable sensitivity and spectral resolution. Here we introduce a technique for coherent quantum interpolation that can overcome these problems. Using a quantum sensor associated with the nitrogen vacancy center in diamond, we experimentally demonstrate that quantum interpolation can achieve spectroscopy of classical magnetic fields and individual quantum spins with orders of magnitude finer frequency resolution than conventionally possible. Not only is quantum interpolation an enabling technique to extract structural and chemical information from single biomolecules, but it can be directly applied to other quantum systems for superresolution quantum spectroscopy. PMID:28196889

Quantum interpolation for high-resolution sensing.

PubMed

Ajoy, Ashok; Liu, Yi-Xiang; Saha, Kasturi; Marseglia, Luca; Jaskula, Jean-Christophe; Bissbort, Ulf; Cappellaro, Paola

2017-02-28

Recent advances in engineering and control of nanoscale quantum sensors have opened new paradigms in precision metrology. Unfortunately, hardware restrictions often limit the sensor performance. In nanoscale magnetic resonance probes, for instance, finite sampling times greatly limit the achievable sensitivity and spectral resolution. Here we introduce a technique for coherent quantum interpolation that can overcome these problems. Using a quantum sensor associated with the nitrogen vacancy center in diamond, we experimentally demonstrate that quantum interpolation can achieve spectroscopy of classical magnetic fields and individual quantum spins with orders of magnitude finer frequency resolution than conventionally possible. Not only is quantum interpolation an enabling technique to extract structural and chemical information from single biomolecules, but it can be directly applied to other quantum systems for superresolution quantum spectroscopy.

Quantum state sharing against the controller's cheating

NASA Astrophysics Data System (ADS)

Shi, Run-hua; Zhong, Hong; Huang, Liu-sheng

2013-08-01

Most existing QSTS schemes are equivalent to the controlled teleportation, in which a designated agent (i.e., the recoverer) can recover the teleported state with the help of the controllers. However, the controller may attempt to cheat the recoverer during the phase of recovering the secret state. How can we detect this cheating? In this paper, we considered the problem of detecting the controller's cheating in Quantum State Sharing, and further proposed an effective Quantum State Sharing scheme against the controller's cheating. We cleverly use Quantum Secret Sharing, Multiple Quantum States Sharing and decoy-particle techniques. In our scheme, via a previously shared entanglement state Alice can teleport multiple arbitrary multi-qubit states to Bob with the help of Charlie. Furthermore, by the classical information shared previously, Alice and Bob can check whether there is any cheating of Charlie. In addition, our scheme only needs to perform Bell-state and single-particle measurements, and to apply C-NOT gate and other single-particle unitary operations. With the present techniques, it is feasible to implement these necessary measurements and operations.

How quantum brain biology can rescue conscious free will

PubMed Central

Hameroff, Stuart

2012-01-01

Conscious “free will” is problematic because (1) brain mechanisms causing consciousness are unknown, (2) measurable brain activity correlating with conscious perception apparently occurs too late for real-time conscious response, consciousness thus being considered “epiphenomenal illusion,” and (3) determinism, i.e., our actions and the world around us seem algorithmic and inevitable. The Penrose–Hameroff theory of “orchestrated objective reduction (Orch OR)” identifies discrete conscious moments with quantum computations in microtubules inside brain neurons, e.g., 40/s in concert with gamma synchrony EEG. Microtubules organize neuronal interiors and regulate synapses. In Orch OR, microtubule quantum computations occur in integration phases in dendrites and cell bodies of integrate-and-fire brain neurons connected and synchronized by gap junctions, allowing entanglement of microtubules among many neurons. Quantum computations in entangled microtubules terminate by Penrose “objective reduction (OR),” a proposal for quantum state reduction and conscious moments linked to fundamental spacetime geometry. Each OR reduction selects microtubule states which can trigger axonal firings, and control behavior. The quantum computations are “orchestrated” by synaptic inputs and memory (thus “Orch OR”). If correct, Orch OR can account for conscious causal agency, resolving problem 1. Regarding problem 2, Orch OR can cause temporal non-locality, sending quantum information backward in classical time, enabling conscious control of behavior. Three lines of evidence for brain backward time effects are presented. Regarding problem 3, Penrose OR (and Orch OR) invokes non-computable influences from information embedded in spacetime geometry, potentially avoiding algorithmic determinism. In summary, Orch OR can account for real-time conscious causal agency, avoiding the need for consciousness to be seen as epiphenomenal illusion. Orch OR can rescue conscious free will. PMID:23091452

Nonadiabatic holonomic quantum computation in decoherence-free subspaces.

PubMed

Xu, G F; Zhang, J; Tong, D M; Sjöqvist, Erik; Kwek, L C

2012-10-26

Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, nonadiabatic holonomic quantum computation in decoherence-free subspaces, which avoids a long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize nonadiabatic holonomic quantum computation in decoherence-free subspaces. By using only three neighboring physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of quantum gates.

Quantum Adiabatic Brachistochrone

NASA Astrophysics Data System (ADS)

Rezakhani, A. T.; Kuo, W.-J.; Hamma, A.; Lidar, D. A.; Zanardi, P.

2009-08-01

We formulate a time-optimal approach to adiabatic quantum computation (AQC). A corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. This geometrization of AQC is demonstrated through two examples, where we show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance.

Quantum adiabatic brachistochrone.

PubMed

Rezakhani, A T; Kuo, W-J; Hamma, A; Lidar, D A; Zanardi, P

2009-08-21

We formulate a time-optimal approach to adiabatic quantum computation (AQC). A corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. This geometrization of AQC is demonstrated through two examples, where we show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance.

Optical Control of a Nuclear Spin in Diamond

NASA Astrophysics Data System (ADS)

Levonian, David; Goldman, Michael; Degreve, Kristiaan; Choi, Soonwon; Markham, Matthew; Twitchen, Daniel; Lukin, Mikhail

2017-04-01

The nitrogen-vacancy (NV) center in diamond has emerged as a promising candidate for quantum information and quantum communication applications. The NV center's potential as a quantum register is due to the long coherence time of its spin-triplet electronic ground state, the optical addressability of its electronic transitions, and the presence of nearby ancillary nuclear spins. The NV center's electronic spin and nearby nuclear spins are most commonly manipulated using applied microwave and RF fields, but this approach would be difficult to scale up for use with an array of NV-based quantum registers. In this context, all-optical manipulation would be more scalable, technically simpler, and potentially faster. Although all-optical control of the electronic spin has been demonstrated, it is an outstanding problem for the nuclear spins. Here, we use an optical Raman scheme to implement nuclear spin-specific control of the electronic spin and coherent control of the 14N nuclear spin.

Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning

NASA Astrophysics Data System (ADS)

Fujii, Keisuke; Nakajima, Kohei

2017-08-01

The quantum computer has an amazing potential of fast information processing. However, the realization of a digital quantum computer is still a challenging problem requiring highly accurate controls and key application strategies. Here we propose a platform, quantum reservoir computing, to solve these issues successfully by exploiting the natural quantum dynamics of ensemble systems, which are ubiquitous in laboratories nowadays, for machine learning. This framework enables ensemble quantum systems to universally emulate nonlinear dynamical systems including classical chaos. A number of numerical experiments show that quantum systems consisting of 5-7 qubits possess computational capabilities comparable to conventional recurrent neural networks of 100-500 nodes. This discovery opens up a paradigm for information processing with artificial intelligence powered by quantum physics.

Partial differential equations constrained combinatorial optimization on an adiabatic quantum computer

NASA Astrophysics Data System (ADS)

Chandra, Rishabh

Partial differential equation-constrained combinatorial optimization (PDECCO) problems are a mixture of continuous and discrete optimization problems. PDECCO problems have discrete controls, but since the partial differential equations (PDE) are continuous, the optimization space is continuous as well. Such problems have several applications, such as gas/water network optimization, traffic optimization, micro-chip cooling optimization, etc. Currently, no efficient classical algorithm which guarantees a global minimum for PDECCO problems exists. A new mapping has been developed that transforms PDECCO problem, which only have linear PDEs as constraints, into quadratic unconstrained binary optimization (QUBO) problems that can be solved using an adiabatic quantum optimizer (AQO). The mapping is efficient, it scales polynomially with the size of the PDECCO problem, requires only one PDE solve to form the QUBO problem, and if the QUBO problem is solved correctly and efficiently on an AQO, guarantees a global optimal solution for the original PDECCO problem.

Quantum Hamilton equations of motion for bound states of one-dimensional quantum systems

NASA Astrophysics Data System (ADS)

Köppe, J.; Patzold, M.; Grecksch, W.; Paul, W.

2018-06-01

On the basis of Nelson's stochastic mechanics derivation of the Schrödinger equation, a formal mathematical structure of non-relativistic quantum mechanics equivalent to the one in classical analytical mechanics has been established in the literature. We recently were able to augment this structure by deriving quantum Hamilton equations of motion by finding the Nash equilibrium of a stochastic optimal control problem, which is the generalization of Hamilton's principle of classical mechanics to quantum systems. We showed that these equations allow a description and numerical determination of the ground state of quantum problems without using the Schrödinger equation. We extend this approach here to deliver the complete discrete energy spectrum and related eigenfunctions for bound states of one-dimensional stationary quantum systems. We exemplify this analytically for the one-dimensional harmonic oscillator and numerically by analyzing a quartic double-well potential, a model of broad importance in many areas of physics. We furthermore point out a relation between the tunnel splitting of such models and mean first passage time concepts applied to Nelson's diffusion paths in the ground state.

Designing, programming, and optimizing a (small) quantum computer

NASA Astrophysics Data System (ADS)

Svore, Krysta

In 1982, Richard Feynman proposed to use a computer founded on the laws of quantum physics to simulate physical systems. In the more than thirty years since, quantum computers have shown promise to solve problems in number theory, chemistry, and materials science that would otherwise take longer than the lifetime of the universe to solve on an exascale classical machine. The practical realization of a quantum computer requires understanding and manipulating subtle quantum states while experimentally controlling quantum interference. It also requires an end-to-end software architecture for programming, optimizing, and implementing a quantum algorithm on the quantum device hardware. In this talk, we will introduce recent advances in connecting abstract theory to present-day real-world applications through software. We will highlight recent advancement of quantum algorithms and the challenges in ultimately performing a scalable solution on a quantum device.

Plug-and-play measurement-device-independent quantum key distribution

NASA Astrophysics Data System (ADS)

Choi, Yujun; Kwon, Osung; Woo, Minki; Oh, Kyunghwan; Han, Sang-Wook; Kim, Yong-Su; Moon, Sung

2016-03-01

Quantum key distribution (QKD) guarantees unconditional communication security based on the laws of quantum physics. However, practical QKD suffers from a number of quantum hackings due to the device imperfections. From the security standpoint, measurement-device-independent quantum key distribution (MDI-QKD) is in the limelight since it eliminates all the possible loopholes in detection. Due to active control units for mode matching between the photons from remote parties, however, the implementation of MDI-QKD is highly impractical. In this paper, we propose a method to resolve the mode matching problem while minimizing the use of active control units. By introducing the plug-and-play (P&P) concept into MDI-QKD, the indistinguishability in spectral and polarization modes between photons can naturally be guaranteed. We show the feasibility of P&P MDI-QKD with a proof-of-principle experiment.

Dynamic optimization and its relation to classical and quantum constrained systems

NASA Astrophysics Data System (ADS)

Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo

2017-08-01

We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac's bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closed-loop λ-strategy, the optimality condition for the action gives a consistency relation, which is associated to the Hamilton-Jacobi-Bellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Ψ(x , t) =e iS(x , t) in the quantum Schrödinger equation, a non-linear partial equation is obtained for the S function. For the right-hand side quantization, this is the Hamilton-Jacobi-Bellman equation, when S(x , t) is identified with the optimal value function. Thus, the Hamilton-Jacobi-Bellman equation in Bellman's maximum principle, can be interpreted as the quantum approach of the optimization problem.

Automating quantum experiment control

NASA Astrophysics Data System (ADS)

Stevens, Kelly E.; Amini, Jason M.; Doret, S. Charles; Mohler, Greg; Volin, Curtis; Harter, Alexa W.

2017-03-01

The field of quantum information processing is rapidly advancing. As the control of quantum systems approaches the level needed for useful computation, the physical hardware underlying the quantum systems is becoming increasingly complex. It is already becoming impractical to manually code control for the larger hardware implementations. In this chapter, we will employ an approach to the problem of system control that parallels compiler design for a classical computer. We will start with a candidate quantum computing technology, the surface electrode ion trap, and build a system instruction language which can be generated from a simple machine-independent programming language via compilation. We incorporate compile time generation of ion routing that separates the algorithm description from the physical geometry of the hardware. Extending this approach to automatic routing at run time allows for automated initialization of qubit number and placement and additionally allows for automated recovery after catastrophic events such as qubit loss. To show that these systems can handle real hardware, we present a simple demonstration system that routes two ions around a multi-zone ion trap and handles ion loss and ion placement. While we will mainly use examples from transport-based ion trap quantum computing, many of the issues and solutions are applicable to other architectures.

Generalized concurrence in boson sampling.

PubMed

Chin, Seungbeom; Huh, Joonsuk

2018-04-17

A fundamental question in linear optical quantum computing is to understand the origin of the quantum supremacy in the physical system. It is found that the multimode linear optical transition amplitudes are calculated through the permanents of transition operator matrices, which is a hard problem for classical simulations (boson sampling problem). We can understand this problem by considering a quantum measure that directly determines the runtime for computing the transition amplitudes. In this paper, we suggest a quantum measure named "Fock state concurrence sum" C S , which is the summation over all the members of "the generalized Fock state concurrence" (a measure analogous to the generalized concurrences of entanglement and coherence). By introducing generalized algorithms for computing the transition amplitudes of the Fock state boson sampling with an arbitrary number of photons per mode, we show that the minimal classical runtime for all the known algorithms directly depends on C S . Therefore, we can state that the Fock state concurrence sum C S behaves as a collective measure that controls the computational complexity of Fock state BS. We expect that our observation on the role of the Fock state concurrence in the generalized algorithm for permanents would provide a unified viewpoint to interpret the quantum computing power of linear optics.

Loop Quantum Gravity.

PubMed

Rovelli, Carlo

2008-01-01

The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime , is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii) A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler's "spacetime foam" intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the Bekenstein-Hawking black-hole entropy. (v) Low-energy calculations, yielding n -point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.

Quantum evolution: The case of weak localization for a 3D alloy-type Anderson model and application to Hamiltonian based quantum computation

NASA Astrophysics Data System (ADS)

Cao, Zhenwei

Over the years, people have found Quantum Mechanics to be extremely useful in explaining various physical phenomena from a microscopic point of view. Anderson localization, named after physicist P. W. Anderson, states that disorder in a crystal can cause non-spreading of wave packets, which is one possible mechanism (at single electron level) to explain metal-insulator transitions. The theory of quantum computation promises to bring greater computational power over classical computers by making use of some special features of Quantum Mechanics. The first part of this dissertation considers a 3D alloy-type model, where the Hamiltonian is the sum of the finite difference Laplacian corresponding to free motion of an electron and a random potential generated by a sign-indefinite single-site potential. The result shows that localization occurs in the weak disorder regime, i.e., when the coupling parameter lambda is very small, for energies E ≤ --Clambda 2. The second part of this dissertation considers adiabatic quantum computing (AQC) algorithms for the unstructured search problem to the case when the number of marked items is unknown. In an ideal situation, an explicit quantum algorithm together with a counting subroutine are given that achieve the optimal Grover speedup over classical algorithms, i.e., roughly speaking, reduce O(2n) to O(2n/2), where n is the size of the problem. However, if one considers more realistic settings, the result shows this quantum speedup is achievable only under a very rigid control precision requirement (e.g., exponentially small control error).

Optimal control of hybrid qubits: Implementing the quantum permutation algorithm

NASA Astrophysics Data System (ADS)

Rivera-Ruiz, C. M.; de Lima, E. F.; Fanchini, F. F.; Lopez-Richard, V.; Castelano, L. K.

2018-03-01

The optimal quantum control theory is employed to determine electric pulses capable of producing quantum gates with a fidelity higher than 0.9997, when noise is not taken into account. Particularly, these quantum gates were chosen to perform the permutation algorithm in hybrid qubits in double quantum dots (DQDs). The permutation algorithm is an oracle based quantum algorithm that solves the problem of the permutation parity faster than a classical algorithm without the necessity of entanglement between particles. The only requirement for achieving the speedup is the use of a one-particle quantum system with at least three levels. The high fidelity found in our results is closely related to the quantum speed limit, which is a measure of how fast a quantum state can be manipulated. Furthermore, we model charge noise by considering an average over the optimal field centered at different values of the reference detuning, which follows a Gaussian distribution. When the Gaussian spread is of the order of 5 μ eV (10% of the correct value), the fidelity is still higher than 0.95. Our scheme also can be used for the practical realization of different quantum algorithms in DQDs.

Controlling the influence of Auger recombination on the performance of quantum-dot light-emitting diodes

PubMed Central

Bae, Wan Ki; Park, Young-Shin; Lim, Jaehoon; Lee, Donggu; Padilha, Lazaro A.; McDaniel, Hunter; Robel, Istvan; Lee, Changhee; Pietryga, Jeffrey M.; Klimov, Victor I.

2013-01-01

Development of light-emitting diodes (LEDs) based on colloidal quantum dots is driven by attractive properties of these fluorophores such as spectrally narrow, tunable emission and facile processibility via solution-based methods. A current obstacle towards improved LED performance is an incomplete understanding of the roles of extrinsic factors, such as non-radiative recombination at surface defects, versus intrinsic processes, such as multicarrier Auger recombination or electron-hole separation due to applied electric field. Here we address this problem with studies that correlate the excited state dynamics of structurally engineered quantum dots with their emissive performance within LEDs. We find that because of significant charging of quantum dots with extra electrons, Auger recombination greatly impacts both LED efficiency and the onset of efficiency roll-off at high currents. Further, we demonstrate two specific approaches for mitigating this problem using heterostructured quantum dots, either by suppressing Auger decay through the introduction of an intermediate alloyed layer, or by using an additional shell that impedes electron transfer into the quantum dot to help balance electron and hole injection. PMID:24157692

Quantum Adiabatic Algorithms and Large Spin Tunnelling

NASA Technical Reports Server (NTRS)

Boulatov, A.; Smelyanskiy, V. N.

2003-01-01

We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in this paper. The algorithm is applied to a random binary optimization problem (a version of the 3-Satisfiability problem) where the n-bit cost function is symmetric with respect to the permutation of individual bits. The evolution paths are produced, using the generic control Hamiltonians H (r) that preserve the bit symmetry of the underlying optimization problem. In the case where the ground state of H(0) coincides with the totally-symmetric state of an n-qubit system the algorithm dynamics is completely described in terms of the motion of a spin-n/2. We show that different control Hamiltonians can be parameterized by a set of independent parameters that are expansion coefficients of H (r) in a certain universal set of operators. Only one of these operators can be responsible for avoiding the tunnelling in the spin-n/2 system during the quantum adiabatic algorithm. We show that it is possible to select a coefficient for this operator that guarantees a polynomial complexity of the algorithm for all problem instances. We show that a successful evolution path of the algorithm always corresponds to the trajectory of a classical spin-n/2 and provide a complete characterization of such paths.

Exponentially-Biased Ground-State Sampling of Quantum Annealing Machines with Transverse-Field Driving Hamiltonians

NASA Technical Reports Server (NTRS)

Mandra, Salvatore

2017-01-01

We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated to a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.

Time-optimal thermalization of single-mode Gaussian states

NASA Astrophysics Data System (ADS)

Carlini, Alberto; Mari, Andrea; Giovannetti, Vittorio

2014-11-01

We consider the problem of time-optimal control of a continuous bosonic quantum system subject to the action of a Markovian dissipation. In particular, we consider the case of a one-mode Gaussian quantum system prepared in an arbitrary initial state and which relaxes to the steady state due to the action of the dissipative channel. We assume that the unitary part of the dynamics is represented by Gaussian operations which preserve the Gaussian nature of the quantum state, i.e., arbitrary phase rotations, bounded squeezing, and unlimited displacements. In the ideal ansatz of unconstrained quantum control (i.e., when the unitary phase rotations, squeezing, and displacement of the mode can be performed instantaneously), we study how control can be optimized for speeding up the relaxation towards the fixed point of the dynamics and we analytically derive the optimal relaxation time. Our model has potential and interesting applications to the control of modes of electromagnetic radiation and of trapped levitated nanospheres.

On the Effect of Dipole-Dipole Interactions on the Quantum Statistics of Surface Plasmons in Multiparticle Spaser Systems

NASA Astrophysics Data System (ADS)

Shesterikov, A. V.; Gubin, M. Yu.; Karpov, S. N.; Prokhorov, A. V.

2018-04-01

The problem of controlling the quantum dynamics of localized plasmons has been considered in the model of a four-particle spaser composed of metallic nanoparticles and semiconductor quantum dots. Conditions for the observation of stable steady-state regimes of the formation of surface plasmons in this model have been determined in the mean-field approximation. It has been shown that the presence of strong dipole-dipole interactions between metallic nanoparticles of the spaser system leads to a considerable change in the quantum statistics of plasmons generated on the nanoparticles.

Parameter Estimation of Fractional-Order Chaotic Systems by Using Quantum Parallel Particle Swarm Optimization Algorithm

PubMed Central

Huang, Yu; Guo, Feng; Li, Yongling; Liu, Yufeng

2015-01-01

Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO) is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm. PMID:25603158

Efficient quantum transmission in multiple-source networks.

PubMed

Luo, Ming-Xing; Xu, Gang; Chen, Xiu-Bo; Yang, Yi-Xian; Wang, Xiaojun

2014-04-02

A difficult problem in quantum network communications is how to efficiently transmit quantum information over large-scale networks with common channels. We propose a solution by developing a quantum encoding approach. Different quantum states are encoded into a coherent superposition state using quantum linear optics. The transmission congestion in the common channel may be avoided by transmitting the superposition state. For further decoding and continued transmission, special phase transformations are applied to incoming quantum states using phase shifters such that decoders can distinguish outgoing quantum states. These phase shifters may be precisely controlled using classical chaos synchronization via additional classical channels. Based on this design and the reduction of multiple-source network under the assumption of restricted maximum-flow, the optimal scheme is proposed for specially quantized multiple-source network. In comparison with previous schemes, our scheme can greatly increase the transmission efficiency.

EDITORIAL: Quantum control theory for coherence and information dynamics Quantum control theory for coherence and information dynamics

NASA Astrophysics Data System (ADS)

Viola, Lorenza; Tannor, David

2011-08-01

Precisely characterizing and controlling the dynamics of realistic open quantum systems has emerged in recent years as a key challenge across contemporary quantum sciences and technologies, with implications ranging from physics, chemistry and applied mathematics to quantum information processing (QIP) and quantum engineering. Quantum control theory aims to provide both a general dynamical-system framework and a constructive toolbox to meet this challenge. The purpose of this special issue of Journal of Physics B: Atomic, Molecular and Optical Physics is to present a state-of-the-art account of recent advances and current trends in the field, as reflected in two international meetings that were held on the subject over the last summer and which motivated in part the compilation of this volume—the Topical Group: Frontiers in Open Quantum Systems and Quantum Control Theory, held at the Institute for Theoretical Atomic, Molecular and Optical Physics (ITAMP) in Cambridge, Massachusetts (USA), from 1-14 August 2010, and the Safed Workshop on Quantum Decoherence and Thermodynamics Control, held in Safed (Israel), from 22-27 August 2010. Initial developments in quantum control theory date back to (at least) the early 1980s, and have been largely inspired by the well-established mathematical framework for classical dynamical systems. As the above-mentioned meetings made clear, and as the burgeoning body of literature on the subject testifies, quantum control has grown since then well beyond its original boundaries, and has by now evolved into a highly cross-disciplinary field which, while still fast-moving, is also entering a new phase of maturity, sophistication, and integration. Two trends deserve special attention: on the one hand, a growing emphasis on control tasks and methodologies that are specifically motivated by QIP, in addition and in parallel to applications in more traditional areas where quantum coherence is nevertheless vital (such as, for instance, quantum control of chemical reactions or high-resolution magnetic resonance spectroscopy); on the other hand, an unprecedented demand for close coupling between theory and experiment, with theoretical developments becoming more and more attuned to and driven by experimental advances as different quantum technologies continue to evolve at an impressive pace in the laboratory. Altogether, these two trends account for several of the recurrent themes in this volume, as well as in the current quantum control literature as a whole: namely, the quest for control strategies that can attain the highest degree of precision and robustness possible, while striving for efficiency and, ultimately, optimality in achieving the intended control task under realistic operational constraints. From a theory standpoint, this makes it imperative to take into account increasingly more realistic control settings; to assess the quantitative impact of limited control resources and/or system knowledge; and to provide a rigorous and general foundation for existing experimental approaches in order to further enhance applicability and performance. From an experimental standpoint, renewed emphasis is in turn placed on validating theoretical predictions and benchmarking performance, so that the limiting constraints can be singled out for additional theoretical analysis and guidance. This ongoing cross-talk is clearly reflected in this collection, which brings together theoreticians and experimentalists, with a significant fraction of the papers reporting on combined quantum control theory-experiment efforts. While a precise categorization would neither be possible nor desirable, contributions to this volume have been loosely grouped into five broad sections. This grouping has been made in the hope that connections between different problems and/or technical approaches will become more transparent, facilitating the transfer of concepts and methods. The special issue opens with a section devoted to open-loop control methods, with special emphasis on dynamical decoupling (DD), which is becoming an increasingly important tool for decoherence control at the physical 'quantum firmware' level. In addition to including original research results, the first two articles, by Brion et al and Biercuk et al, also serve to pedagogically review some background in their respective subjects. In particular, Brion et al revisit one of the conceptually simplest approaches to open-loop manipulation of both closed and open quantum systems, nonholonomic control, motivated by its broad applicability to QIP settings. A special instance of open-loop control based on sequences of (nearly) instantaneous `bang-bang' pulses is addressed by Biercuk et al, who reformulate the simplest DD scenario, suppression of phase decoherence in a single qubit, as a filter-design problem. Peng et al report on the implementation of 'concatenated' DD for arbitrary single-qubit decoherence in the context of nuclear magnetic resonance QIP. A dedicated analysis of the performance of different DD schemes in the presence of realistic pulse errors is given by Wang and Dobrovitski. DD is also one of the strategies used by Lucamarini et al to reduce polarization decoherence in a photon qubit. These authors additionally report on the use of active feedback to counter transmission noise, effectively setting the stage for the second section, which is centered on closed-loop control. Unlike in open-loop control, measurement is an essential ingredient in closed-loop schemes aimed at both reliably identifying features of the target quantum system and further modifying its dynamics. The importance of directly measuring the spectrum of the underlying system-environment coupling is stressed by Almog et al, who show how this knowledge is crucial, in particular, for predicting the performance of DD sequences in experiments and for optimizing performance. Riofrio et al address a weak-measurement protocol for implementing quantum state tomography, which is a necessary 'primitive' for inferring the target quantum state and thereby diagnosing the control performance. Next, the impact of realistic control and system imperfections in continuous-time Markovian feedback strategies for rapid state preparation is analyzed by Combes and Wiseman. A prominent role is played in the special issue by optimal control (OC) approaches, reflecting their central importance for quantum control and QIP. The OC contributions have been divided into two separate sections, depending on whether the target dynamics is modeled as Hamiltonian (section 3) or dissipative (section 4), respectively. The contribution by Beltrani et al deals with `control landscapes', which provide a foundation for analyzing the performance of numerical OC algorithms and their robustness against control errors. Specifically, this paper characterizes geometric properties of the control landscape, relevant to the optimal control of state-to-state transitions. Application of OC theory to the problem of population transfer and coherence enhancement in Λ-systems is studied by Kumar et al, whereas Goerz et al report on the OC-design of a high-fidelity controlled phase-gate in atomic qubits. The robustness of an OC solution is specifically addressed by Negretti et al, along with an approach for identifying easily implementable while still 'close-to-optimal' control pulses. Powerful relaxation-optimized OC schemes (based on so-called opengrape algorithms) for generating unitary target gates in the presence of known dissipation parameters are discussed by Schulte-Herbrüggen et al. Next, Lapert et al report on the problem of time-optimal control of spin-1/2 systems undergoing Bloch relaxation dynamics, highlighting the crucial role played by singular extremals in the control synthesis. Alternative approaches for optimized control of qubits exposed to various decoherence processes are developed by Esher et al and Xue et al, based on a perturbative 'bath-optimized' formalism and on numerical optimization via a genetic algorithm, respectively. Testifying to the richness of the field, the volume concludes with four contributions that address a diverse range of problems. The exploitation of properties of adiabatic quantum evolutions is common to the first two papers. In particular, Legthtas et al offer a rigorous explanation for the robustness of a control protocol, chirped pulsing, that is widely employed in 'adiabatic rapid passage' experiments, while Han et al present a theoretical framework for adiabatic Raman photo-association schemes relevant to ultracold atomic systems. In the context of cavity quantum electrodynamics, Montenegro and Orszag describe how to engineer a system of two atoms coupled to distant lossy cavities so that stable atomic entanglement is generated. Finally, still very little is known about the physical mechanisms that are responsible for and control the experimentally observed 'coherent' features of transport phenomena in biological systems. The last contribution by Alicki and Giraldi analyzes energy transport in dynamical systems that can be modeled as 'quantum networks', and points to this fascinating emerging frontier. It is our hope that the above papers may help readers to gain an overview of some of the main trends in current quantum control efforts, both theoretical and experimental. In closing, we take the opportunity to thank the organizations which sponsored the above-mentioned ITAMP Topical Group (the United States National Science Foundation and Harvard University) and the Safed Workshop (the Israeli Science Foundation, the Safed Scientific Workshop program, CECAM and ACAM). Last but not least our sincere gratitude goes to all of the contributors to the volume and the reviewers as well as the J. Phys. B staff, for their respective efforts in preparing the papers and ensuring the overall quality of this special issue.

Practical experimental certification of computational quantum gates using a twirling procedure.

PubMed

Moussa, Osama; da Silva, Marcus P; Ryan, Colm A; Laflamme, Raymond

2012-08-17

Because of the technical difficulty of building large quantum computers, it is important to be able to estimate how faithful a given implementation is to an ideal quantum computer. The common approach of completely characterizing the computation process via quantum process tomography requires an exponential amount of resources, and thus is not practical even for relatively small devices. We solve this problem by demonstrating that twirling experiments previously used to characterize the average fidelity of quantum memories efficiently can be easily adapted to estimate the average fidelity of the experimental implementation of important quantum computation processes, such as unitaries in the Clifford group, in a practical and efficient manner with applicability in current quantum devices. Using this procedure, we demonstrate state-of-the-art coherent control of an ensemble of magnetic moments of nuclear spins in a single crystal solid by implementing the encoding operation for a 3-qubit code with only a 1% degradation in average fidelity discounting preparation and measurement errors. We also highlight one of the advances that was instrumental in achieving such high fidelity control.

Quadratic constrained mixed discrete optimization with an adiabatic quantum optimizer

NASA Astrophysics Data System (ADS)

Chandra, Rishabh; Jacobson, N. Tobias; Moussa, Jonathan E.; Frankel, Steven H.; Kais, Sabre

2014-07-01

We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic constrained mixed discrete optimization (QCMDO) problem. QCMDO problems are NP-hard, and no efficient classical algorithm for their solution is known. Included in the class of QCMDO problems are combinatorial optimization problems constrained by a linear partial differential equation (PDE) or system of linear PDEs. An essential complication commonly encountered in solving this type of problem is that the linear constraint may introduce many intermediate continuous variables into the optimization while the computational cost grows exponentially with problem size. We resolve this difficulty by developing a constructive mapping from QCMDO to quadratic unconstrained binary optimization (QUBO) such that the size of the QUBO problem depends only on the number of discrete control variables. With a suitable embedding, taking into account the physical constraints of the realizable coupling graph, the resulting QUBO problem can be implemented on an existing AQO. The mapping itself is efficient, scaling cubically with the number of continuous variables in the general case and linearly in the PDE case if an efficient preconditioner is available.

Reaching Agreement in Quantum Hybrid Networks.

PubMed

Shi, Guodong; Li, Bo; Miao, Zibo; Dower, Peter M; James, Matthew R

2017-07-20

We consider a basic quantum hybrid network model consisting of a number of nodes each holding a qubit, for which the aim is to drive the network to a consensus in the sense that all qubits reach a common state. Projective measurements are applied serving as control means, and the measurement results are exchanged among the nodes via classical communication channels. In this way the quantum-opeartion/classical-communication nature of hybrid quantum networks is captured, although coherent states and joint operations are not taken into consideration in order to facilitate a clear and explicit analysis. We show how to carry out centralized optimal path planning for this network with all-to-all classical communications, in which case the problem becomes a stochastic optimal control problem with a continuous action space. To overcome the computation and communication obstacles facing the centralized solutions, we also develop a distributed Pairwise Qubit Projection (PQP) algorithm, where pairs of nodes meet at a given time and respectively perform measurements at their geometric average. We show that the qubit states are driven to a consensus almost surely along the proposed PQP algorithm, and that the expected qubit density operators converge to the average of the network's initial values.

Qubit Architecture with High Coherence and Fast Tunable Coupling.

PubMed

Chen, Yu; Neill, C; Roushan, P; Leung, N; Fang, M; Barends, R; Kelly, J; Campbell, B; Chen, Z; Chiaro, B; Dunsworth, A; Jeffrey, E; Megrant, A; Mutus, J Y; O'Malley, P J J; Quintana, C M; Sank, D; Vainsencher, A; Wenner, J; White, T C; Geller, Michael R; Cleland, A N; Martinis, John M

2014-11-28

We introduce a superconducting qubit architecture that combines high-coherence qubits and tunable qubit-qubit coupling. With the ability to set the coupling to zero, we demonstrate that this architecture is protected from the frequency crowding problems that arise from fixed coupling. More importantly, the coupling can be tuned dynamically with nanosecond resolution, making this architecture a versatile platform with applications ranging from quantum logic gates to quantum simulation. We illustrate the advantages of dynamical coupling by implementing a novel adiabatic controlled-z gate, with a speed approaching that of single-qubit gates. Integrating coherence and scalable control, the introduced qubit architecture provides a promising path towards large-scale quantum computation and simulation.

Quantum Computing: Solving Complex Problems

ScienceCinema

DiVincenzo, David

2018-05-22

One of the motivating ideas of quantum computation was that there could be a new kind of machine that would solve hard problems in quantum mechanics. There has been significant progress towards the experimental realization of these machines (which I will review), but there are still many questions about how such a machine could solve computational problems of interest in quantum physics. New categorizations of the complexity of computational problems have now been invented to describe quantum simulation. The bad news is that some of these problems are believed to be intractable even on a quantum computer, falling into a quantum analog of the NP class. The good news is that there are many other new classifications of tractability that may apply to several situations of physical interest.

An Integrated Development Environment for Adiabatic Quantum Programming

DOE Office of Scientific and Technical Information (OSTI.GOV)

Humble, Travis S; McCaskey, Alex; Bennink, Ryan S

2014-01-01

Adiabatic quantum computing is a promising route to the computational power afforded by quantum information processing. The recent availability of adiabatic hardware raises the question of how well quantum programs perform. Benchmarking behavior is challenging since the multiple steps to synthesize an adiabatic quantum program are highly tunable. We present an adiabatic quantum programming environment called JADE that provides control over all the steps taken during program development. JADE captures the workflow needed to rigorously benchmark performance while also allowing a variety of problem types, programming techniques, and processor configurations. We have also integrated JADE with a quantum simulation enginemore » that enables program profiling using numerical calculation. The computational engine supports plug-ins for simulation methodologies tailored to various metrics and computing resources. We present the design, integration, and deployment of JADE and discuss its use for benchmarking adiabatic quantum programs.« less

Efficient Quantum Transmission in Multiple-Source Networks

PubMed Central

Luo, Ming-Xing; Xu, Gang; Chen, Xiu-Bo; Yang, Yi-Xian; Wang, Xiaojun

2014-01-01

A difficult problem in quantum network communications is how to efficiently transmit quantum information over large-scale networks with common channels. We propose a solution by developing a quantum encoding approach. Different quantum states are encoded into a coherent superposition state using quantum linear optics. The transmission congestion in the common channel may be avoided by transmitting the superposition state. For further decoding and continued transmission, special phase transformations are applied to incoming quantum states using phase shifters such that decoders can distinguish outgoing quantum states. These phase shifters may be precisely controlled using classical chaos synchronization via additional classical channels. Based on this design and the reduction of multiple-source network under the assumption of restricted maximum-flow, the optimal scheme is proposed for specially quantized multiple-source network. In comparison with previous schemes, our scheme can greatly increase the transmission efficiency. PMID:24691590

A cross-disciplinary introduction to quantum annealing-based algorithms

NASA Astrophysics Data System (ADS)

Venegas-Andraca, Salvador E.; Cruz-Santos, William; McGeoch, Catherine; Lanzagorta, Marco

2018-04-01

A central goal in quantum computing is the development of quantum hardware and quantum algorithms in order to analyse challenging scientific and engineering problems. Research in quantum computation involves contributions from both physics and computer science; hence this article presents a concise introduction to basic concepts from both fields that are used in annealing-based quantum computation, an alternative to the more familiar quantum gate model. We introduce some concepts from computer science required to define difficult computational problems and to realise the potential relevance of quantum algorithms to find novel solutions to those problems. We introduce the structure of quantum annealing-based algorithms as well as two examples of this kind of algorithms for solving instances of the max-SAT and Minimum Multicut problems. An overview of the quantum annealing systems manufactured by D-Wave Systems is also presented.

Controlled Quantum Packets

NASA Technical Reports Server (NTRS)

DeMartino, Salvatore; DeSiena, Silvio

1996-01-01

We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.

Quantum Optimization of Fully Connected Spin Glasses

NASA Astrophysics Data System (ADS)

Venturelli, Davide; Mandrà, Salvatore; Knysh, Sergey; O'Gorman, Bryan; Biswas, Rupak; Smelyanskiy, Vadim

2015-07-01

Many NP-hard problems can be seen as the task of finding a ground state of a disordered highly connected Ising spin glass. If solutions are sought by means of quantum annealing, it is often necessary to represent those graphs in the annealer's hardware by means of the graph-minor embedding technique, generating a final Hamiltonian consisting of coupled chains of ferromagnetically bound spins, whose binding energy is a free parameter. In order to investigate the effect of embedding on problems of interest, the fully connected Sherrington-Kirkpatrick model with random ±1 couplings is programmed on the D-Wave TwoTM annealer using up to 270 qubits interacting on a Chimera-type graph. We present the best embedding prescriptions for encoding the Sherrington-Kirkpatrick problem in the Chimera graph. The results indicate that the optimal choice of embedding parameters could be associated with the emergence of the spin-glass phase of the embedded problem, whose presence was previously uncertain. This optimal parameter setting allows the performance of the quantum annealer to compete with (and potentially outperform, in the absence of analog control errors) optimized simulated annealing algorithms.

Unidirectional Quantum Remote Control: Teleportation of Control-State

NASA Astrophysics Data System (ADS)

Zheng, Yi-Zhuang; Gu, Yong-Jian; Wu, Gui-Chu; Guo, Guang-Can

2003-08-01

We investigate the problem of teleportation of unitary operations by unidirectional control-state teleportation and propose a scheme called unidirectional quantum remote control. The scheme is based on the isomorphism between operation and state. It allows us to store a unitary operation in a control state, thereby teleportation of the unitary operation can be implemented by unidirectional teleportation of the control-state. We find that the probability of success for implementing an arbitrary unitary operation on arbitrary M-qubit state by unidirectional control-state teleportation is 4-M, and 2M ebits and 4M cbits are consumed in each teleportation. The project supported by the National Fundamental Research Programme (2001CB309300) and the Zhejiang Provincial Natural Science Foundation of China under Grant No. 102068

Exploiting Quantum Resonance to Solve Combinatorial Problems

NASA Technical Reports Server (NTRS)

Zak, Michail; Fijany, Amir

2006-01-01

Quantum resonance would be exploited in a proposed quantum-computing approach to the solution of combinatorial optimization problems. In quantum computing in general, one takes advantage of the fact that an algorithm cannot be decoupled from the physical effects available to implement it. Prior approaches to quantum computing have involved exploitation of only a subset of known quantum physical effects, notably including parallelism and entanglement, but not including resonance. In the proposed approach, one would utilize the combinatorial properties of tensor-product decomposability of unitary evolution of many-particle quantum systems for physically simulating solutions to NP-complete problems (a class of problems that are intractable with respect to classical methods of computation). In this approach, reinforcement and selection of a desired solution would be executed by means of quantum resonance. Classes of NP-complete problems that are important in practice and could be solved by the proposed approach include planning, scheduling, search, and optimal design.

Efficient classical simulation of the Deutsch-Jozsa and Simon's algorithms

NASA Astrophysics Data System (ADS)

Johansson, Niklas; Larsson, Jan-Åke

2017-09-01

A long-standing aim of quantum information research is to understand what gives quantum computers their advantage. This requires separating problems that need genuinely quantum resources from those for which classical resources are enough. Two examples of quantum speed-up are the Deutsch-Jozsa and Simon's problem, both efficiently solvable on a quantum Turing machine, and both believed to lack efficient classical solutions. Here we present a framework that can simulate both quantum algorithms efficiently, solving the Deutsch-Jozsa problem with probability 1 using only one oracle query, and Simon's problem using linearly many oracle queries, just as expected of an ideal quantum computer. The presented simulation framework is in turn efficiently simulatable in a classical probabilistic Turing machine. This shows that the Deutsch-Jozsa and Simon's problem do not require any genuinely quantum resources, and that the quantum algorithms show no speed-up when compared with their corresponding classical simulation. Finally, this gives insight into what properties are needed in the two algorithms and calls for further study of oracle separation between quantum and classical computation.

From transistor to trapped-ion computers for quantum chemistry.

PubMed

Yung, M-H; Casanova, J; Mezzacapo, A; McClean, J; Lamata, L; Aspuru-Guzik, A; Solano, E

2014-01-07

Over the last few decades, quantum chemistry has progressed through the development of computational methods based on modern digital computers. However, these methods can hardly fulfill the exponentially-growing resource requirements when applied to large quantum systems. As pointed out by Feynman, this restriction is intrinsic to all computational models based on classical physics. Recently, the rapid advancement of trapped-ion technologies has opened new possibilities for quantum control and quantum simulations. Here, we present an efficient toolkit that exploits both the internal and motional degrees of freedom of trapped ions for solving problems in quantum chemistry, including molecular electronic structure, molecular dynamics, and vibronic coupling. We focus on applications that go beyond the capacity of classical computers, but may be realizable on state-of-the-art trapped-ion systems. These results allow us to envision a new paradigm of quantum chemistry that shifts from the current transistor to a near-future trapped-ion-based technology.

From transistor to trapped-ion computers for quantum chemistry

PubMed Central

Yung, M.-H.; Casanova, J.; Mezzacapo, A.; McClean, J.; Lamata, L.; Aspuru-Guzik, A.; Solano, E.

2014-01-01

Over the last few decades, quantum chemistry has progressed through the development of computational methods based on modern digital computers. However, these methods can hardly fulfill the exponentially-growing resource requirements when applied to large quantum systems. As pointed out by Feynman, this restriction is intrinsic to all computational models based on classical physics. Recently, the rapid advancement of trapped-ion technologies has opened new possibilities for quantum control and quantum simulations. Here, we present an efficient toolkit that exploits both the internal and motional degrees of freedom of trapped ions for solving problems in quantum chemistry, including molecular electronic structure, molecular dynamics, and vibronic coupling. We focus on applications that go beyond the capacity of classical computers, but may be realizable on state-of-the-art trapped-ion systems. These results allow us to envision a new paradigm of quantum chemistry that shifts from the current transistor to a near-future trapped-ion-based technology. PMID:24395054

Engineering two-photon high-dimensional states through quantum interference

PubMed Central

Zhang, Yingwen; Roux, Filippus S.; Konrad, Thomas; Agnew, Megan; Leach, Jonathan; Forbes, Andrew

2016-01-01

Many protocols in quantum science, for example, linear optical quantum computing, require access to large-scale entangled quantum states. Such systems can be realized through many-particle qubits, but this approach often suffers from scalability problems. An alternative strategy is to consider a lesser number of particles that exist in high-dimensional states. The spatial modes of light are one such candidate that provides access to high-dimensional quantum states, and thus they increase the storage and processing potential of quantum information systems. We demonstrate the controlled engineering of two-photon high-dimensional states entangled in their orbital angular momentum through Hong-Ou-Mandel interference. We prepare a large range of high-dimensional entangled states and implement precise quantum state filtering. We characterize the full quantum state before and after the filter, and are thus able to determine that only the antisymmetric component of the initial state remains. This work paves the way for high-dimensional processing and communication of multiphoton quantum states, for example, in teleportation beyond qubits. PMID:26933685

Quantum theory of multiple-input-multiple-output Markovian feedback with diffusive measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chia, A.; Wiseman, H. M.

2011-07-15

Feedback control engineers have been interested in multiple-input-multiple-output (MIMO) extensions of single-input-single-output (SISO) results of various kinds due to its rich mathematical structure and practical applications. An outstanding problem in quantum feedback control is the extension of the SISO theory of Markovian feedback by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)] to multiple inputs and multiple outputs. Here we generalize the SISO homodyne-mediated feedback theory to allow for multiple inputs, multiple outputs, and arbitrary diffusive quantum measurements. We thus obtain a MIMO framework which resembles the SISO theory and whose additional mathematical structure is highlighted by the extensivemore » use of vector-operator algebra.« less

A case study in programming a quantum annealer for hard operational planning problems

NASA Astrophysics Data System (ADS)

Rieffel, Eleanor G.; Venturelli, Davide; O'Gorman, Bryan; Do, Minh B.; Prystay, Elicia M.; Smelyanskiy, Vadim N.

2015-01-01

We report on a case study in programming an early quantum annealer to attack optimization problems related to operational planning. While a number of studies have looked at the performance of quantum annealers on problems native to their architecture, and others have examined performance of select problems stemming from an application area, ours is one of the first studies of a quantum annealer's performance on parametrized families of hard problems from a practical domain. We explore two different general mappings of planning problems to quadratic unconstrained binary optimization (QUBO) problems, and apply them to two parametrized families of planning problems, navigation-type and scheduling-type. We also examine two more compact, but problem-type specific, mappings to QUBO, one for the navigation-type planning problems and one for the scheduling-type planning problems. We study embedding properties and parameter setting and examine their effect on the efficiency with which the quantum annealer solves these problems. From these results, we derive insights useful for the programming and design of future quantum annealers: problem choice, the mapping used, the properties of the embedding, and the annealing profile all matter, each significantly affecting the performance.

Quantum Heterogeneous Computing for Satellite Positioning Optimization

NASA Astrophysics Data System (ADS)

Bass, G.; Kumar, V.; Dulny, J., III

2016-12-01

Hard optimization problems occur in many fields of academic study and practical situations. We present results in which quantum heterogeneous computing is used to solve a real-world optimization problem: satellite positioning. Optimization problems like this can scale very rapidly with problem size, and become unsolvable with traditional brute-force methods. Typically, such problems have been approximately solved with heuristic approaches; however, these methods can take a long time to calculate and are not guaranteed to find optimal solutions. Quantum computing offers the possibility of producing significant speed-up and improved solution quality. There are now commercially available quantum annealing (QA) devices that are designed to solve difficult optimization problems. These devices have 1000+ quantum bits, but they have significant hardware size and connectivity limitations. We present a novel heterogeneous computing stack that combines QA and classical machine learning and allows the use of QA on problems larger than the quantum hardware could solve in isolation. We begin by analyzing the satellite positioning problem with a heuristic solver, the genetic algorithm. The classical computer's comparatively large available memory can explore the full problem space and converge to a solution relatively close to the true optimum. The QA device can then evolve directly to the optimal solution within this more limited space. Preliminary experiments, using the Quantum Monte Carlo (QMC) algorithm to simulate QA hardware, have produced promising results. Working with problem instances with known global minima, we find a solution within 8% in a matter of seconds, and within 5% in a few minutes. Future studies include replacing QMC with commercially available quantum hardware and exploring more problem sets and model parameters. Our results have important implications for how heterogeneous quantum computing can be used to solve difficult optimization problems in any field.

Advanced Concepts in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Esposito, Giampiero; Marmo, Giuseppe; Miele, Gennaro; Sudarshan, George

2014-11-01

Preface; 1. Introduction: the need for a quantum theory; 2. Experimental foundations of quantum theory; 3. Waves and particles; 4. Schrödinger picture, Heisenberg picture and probabilistic aspects; 5. Integrating the equations of motion; 6. Elementary applications: 1-dimensional problems; 7. Elementary applications: multidimensional problems; 8. Coherent states and related formalism; 9. Introduction to spin; 10. Symmetries in quantum mechanics; 11. Approximation methods; 12. Modern pictures of quantum mechanics; 13. Formulations of quantum mechanics and their physical implications; 14. Exam problems; Glossary of geometric concepts; References; Index.

From quantum foundations to applications and back.

PubMed

Gisin, Nicolas; Fröwis, Florian

2018-07-13

Quantum non-locality has been an extremely fruitful subject of research, leading the scientific revolution towards quantum information science, in particular, to device-independent quantum information processing. We argue that the time is ripe to work on another basic problem in the foundations of quantum physics, the quantum measurement problem, which should produce good physics in theoretical, mathematical, experimental and applied physics. We briefly review how quantum non-locality contributed to physics (including some outstanding open problems) and suggest ways in which questions around macroscopic quantumness could equally contribute to all aspects of physics.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Computational Studies of Strongly Correlated Quantum Matter

NASA Astrophysics Data System (ADS)

Shi, Hao

The study of strongly correlated quantum many-body systems is an outstanding challenge. Highly accurate results are needed for the understanding of practical and fundamental problems in condensed-matter physics, high energy physics, material science, quantum chemistry and so on. Our familiar mean-field or perturbative methods tend to be ineffective. Numerical simulations provide a promising approach for studying such systems. The fundamental difficulty of numerical simulation is that the dimension of the Hilbert space needed to describe interacting systems increases exponentially with the system size. Quantum Monte Carlo (QMC) methods are one of the best approaches to tackle the problem of enormous Hilbert space. They have been highly successful for boson systems and unfrustrated spin models. For systems with fermions, the exchange symmetry in general causes the infamous sign problem, making the statistical noise in the computed results grow exponentially with the system size. This hinders our understanding of interesting physics such as high-temperature superconductivity, metal-insulator phase transition. In this thesis, we present a variety of new developments in the auxiliary-field quantum Monte Carlo (AFQMC) methods, including the incorporation of symmetry in both the trial wave function and the projector, developing the constraint release method, using the force-bias to drastically improve the efficiency in Metropolis framework, identifying and solving the infinite variance problem, and sampling Hartree-Fock-Bogoliubov wave function. With these developments, some of the most challenging many-electron problems are now under control. We obtain an exact numerical solution of two-dimensional strongly interacting Fermi atomic gas, determine the ground state properties of the 2D Fermi gas with Rashba spin-orbit coupling, provide benchmark results for the ground state of the two-dimensional Hubbard model, and establish that the Hubbard model has a stripe order in the underdoped region.

A quantum annealing approach for fault detection and diagnosis of graph-based systems

NASA Astrophysics Data System (ADS)

Perdomo-Ortiz, A.; Fluegemann, J.; Narasimhan, S.; Biswas, R.; Smelyanskiy, V. N.

2015-02-01

Diagnosing the minimal set of faults capable of explaining a set of given observations, e.g., from sensor readouts, is a hard combinatorial optimization problem usually tackled with artificial intelligence techniques. We present the mapping of this combinatorial problem to quadratic unconstrained binary optimization (QUBO), and the experimental results of instances embedded onto a quantum annealing device with 509 quantum bits. Besides being the first time a quantum approach has been proposed for problems in the advanced diagnostics community, to the best of our knowledge this work is also the first research utilizing the route Problem → QUBO → Direct embedding into quantum hardware, where we are able to implement and tackle problem instances with sizes that go beyond previously reported toy-model proof-of-principle quantum annealing implementations; this is a significant leap in the solution of problems via direct-embedding adiabatic quantum optimization. We discuss some of the programmability challenges in the current generation of the quantum device as well as a few possible ways to extend this work to more complex arbitrary network graphs.

Quantum routing of single optical photons with a superconducting flux qubit

NASA Astrophysics Data System (ADS)

Xia, Keyu; Jelezko, Fedor; Twamley, Jason

2018-05-01

Interconnecting optical photons with superconducting circuits is a challenging problem but essential for building long-range superconducting quantum networks. We propose a hybrid quantum interface between the microwave and optical domains where the propagation of a single-photon pulse along a nanowaveguide is controlled in a coherent way by tuning the electromagnetically induced transparency window with the quantum state of a flux qubit mediated by the spin in a nanodiamond. The qubit can route a single-photon pulse using the nanodiamond into a quantum superposition of paths without the aid of an optical cavity—simplifying the setup. By preparing the flux qubit in a superposition state our cavityless scheme creates a hybrid state-path entanglement between a flying single optical photon and a static superconducting qubit.

Categorization of Quantum Mechanics Problems by Professors and Students

ERIC Educational Resources Information Center

Lin, Shih-Yin; Singh, Chandralekha

2010-01-01

We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honours-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty…

Digitized adiabatic quantum computing with a superconducting circuit.

PubMed

Barends, R; Shabani, A; Lamata, L; Kelly, J; Mezzacapo, A; Las Heras, U; Babbush, R; Fowler, A G; Campbell, B; Chen, Yu; Chen, Z; Chiaro, B; Dunsworth, A; Jeffrey, E; Lucero, E; Megrant, A; Mutus, J Y; Neeley, M; Neill, C; O'Malley, P J J; Quintana, C; Roushan, P; Sank, D; Vainsencher, A; Wenner, J; White, T C; Solano, E; Neven, H; Martinis, John M

2016-06-09

Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.

Heterogeneous quantum computing for satellite constellation optimization: solving the weighted k-clique problem

NASA Astrophysics Data System (ADS)

Bass, Gideon; Tomlin, Casey; Kumar, Vaibhaw; Rihaczek, Pete; Dulny, Joseph, III

2018-04-01

NP-hard optimization problems scale very rapidly with problem size, becoming unsolvable with brute force methods, even with supercomputing resources. Typically, such problems have been approximated with heuristics. However, these methods still take a long time and are not guaranteed to find an optimal solution. Quantum computing offers the possibility of producing significant speed-up and improved solution quality. Current quantum annealing (QA) devices are designed to solve difficult optimization problems, but they are limited by hardware size and qubit connectivity restrictions. We present a novel heterogeneous computing stack that combines QA and classical machine learning, allowing the use of QA on problems larger than the hardware limits of the quantum device. These results represent experiments on a real-world problem represented by the weighted k-clique problem. Through this experiment, we provide insight into the state of quantum machine learning.

A review on economic emission dispatch problems using quantum computational intelligence

NASA Astrophysics Data System (ADS)

Mahdi, Fahad Parvez; Vasant, Pandian; Kallimani, Vish; Abdullah-Al-Wadud, M.

2016-11-01

Economic emission dispatch (EED) problems are one of the most crucial problems in power systems. Growing energy demand, limitation of natural resources and global warming make this topic into the center of discussion and research. This paper reviews the use of Quantum Computational Intelligence (QCI) in solving Economic Emission Dispatch problems. QCI techniques like Quantum Genetic Algorithm (QGA) and Quantum Particle Swarm Optimization (QPSO) algorithm are discussed here. This paper will encourage the researcher to use more QCI based algorithm to get better optimal result for solving EED problems.

A parallel adaptive quantum genetic algorithm for the controllability of arbitrary networks.

PubMed

Li, Yuhong; Gong, Guanghong; Li, Ni

2018-01-01

In this paper, we propose a novel algorithm-parallel adaptive quantum genetic algorithm-which can rapidly determine the minimum control nodes of arbitrary networks with both control nodes and state nodes. The corresponding network can be fully controlled with the obtained control scheme. We transformed the network controllability issue into a combinational optimization problem based on the Popov-Belevitch-Hautus rank condition. A set of canonical networks and a list of real-world networks were experimented. Comparison results demonstrated that the algorithm was more ideal to optimize the controllability of networks, especially those larger-size networks. We demonstrated subsequently that there were links between the optimal control nodes and some network statistical characteristics. The proposed algorithm provides an effective approach to improve the controllability optimization of large networks or even extra-large networks with hundreds of thousands nodes.

An approach to optimal semi-active control of vibration energy harvesting based on MEMS

NASA Astrophysics Data System (ADS)

Rojas, Rafael A.; Carcaterra, Antonio

2018-07-01

In this paper the energy harvesting problem involving typical MEMS technology is reduced to an optimal control problem, where the objective function is the absorption of the maximum amount of energy in a given time interval from a vibrating environment. The interest here is to identify a physical upper bound for this energy storage. The mathematical tool is a new optimal control called Krotov's method, that has not yet been applied to engineering problems, except in quantum dynamics. This approach leads to identify new maximum bounds to the energy harvesting performance. Novel MEMS-based device control configurations for vibration energy harvesting are proposed with particular emphasis to piezoelectric, electromagnetic and capacitive circuits.

Non-Markovian quantum feedback networks II: Controlled flows

NASA Astrophysics Data System (ADS)

Gough, John E.

2017-06-01

The concept of a controlled flow of a dynamical system, especially when the controlling process feeds information back about the system, is of central importance in control engineering. In this paper, we build on the ideas presented by Bouten and van Handel [Quantum Stochastics and Information: Statistics, Filtering and Control (World Scientific, 2008)] and develop a general theory of quantum feedback. We elucidate the relationship between the controlling processes, Z, and the measured processes, Y, and to this end we make a distinction between what we call the input picture and the output picture. We should note that the input-output relations for the noise fields have additional terms not present in the standard theory but that the relationship between the control processes and measured processes themselves is internally consistent—we do this for the two main cases of quadrature measurement and photon-counting measurement. The theory is general enough to include a modulating filter which post-processes the measurement readout Y before returning to the system. This opens up the prospect of applying very general engineering feedback control techniques to open quantum systems in a systematic manner, and we consider a number of specific modulating filter problems. Finally, we give a brief argument as to why most of the rules for making instantaneous feedback connections [J. Gough and M. R. James, Commun. Math. Phys. 287, 1109 (2009)] ought to apply for controlled dynamical networks as well.

Completing the physical representation of quantum algorithms provides a retrocausal explanation of the speedup

NASA Astrophysics Data System (ADS)

Castagnoli, Giuseppe

2017-05-01

The usual representation of quantum algorithms, limited to the process of solving the problem, is physically incomplete as it lacks the initial measurement. We extend it to the process of setting the problem. An initial measurement selects a problem setting at random, and a unitary transformation sends it into the desired setting. The extended representation must be with respect to Bob, the problem setter, and any external observer. It cannot be with respect to Alice, the problem solver. It would tell her the problem setting and thus the solution of the problem implicit in it. In the representation to Alice, the projection of the quantum state due to the initial measurement should be postponed until the end of the quantum algorithm. In either representation, there is a unitary transformation between the initial and final measurement outcomes. As a consequence, the final measurement of any ℛ-th part of the solution could select back in time a corresponding part of the random outcome of the initial measurement; the associated projection of the quantum state should be advanced by the inverse of that unitary transformation. This, in the representation to Alice, would tell her, before she begins her problem solving action, that part of the solution. The quantum algorithm should be seen as a sum over classical histories in each of which Alice knows in advance one of the possible ℛ-th parts of the solution and performs the oracle queries still needed to find it - this for the value of ℛ that explains the algorithm's speedup. We have a relation between retrocausality ℛ and the number of oracle queries needed to solve an oracle problem quantumly. All the oracle problems examined can be solved with any value of ℛ up to an upper bound attained by the optimal quantum algorithm. This bound is always in the vicinity of 1/2 . Moreover, ℛ =1/2 always provides the order of magnitude of the number of queries needed to solve the problem in an optimal quantum way. If this were true for any oracle problem, as plausible, it would solve the quantum query complexity problem.

Experimental quantum compressed sensing for a seven-qubit system

PubMed Central

Riofrío, C. A.; Gross, D.; Flammia, S. T.; Monz, T.; Nigg, D.; Blatt, R.; Eisert, J.

2017-01-01

Well-controlled quantum devices with their increasing system size face a new roadblock hindering further development of quantum technologies. The effort of quantum tomography—the reconstruction of states and processes of a quantum device—scales unfavourably: state-of-the-art systems can no longer be characterized. Quantum compressed sensing mitigates this problem by reconstructing states from incomplete data. Here we present an experimental implementation of compressed tomography of a seven-qubit system—a topological colour code prepared in a trapped ion architecture. We are in the highly incomplete—127 Pauli basis measurement settings—and highly noisy—100 repetitions each—regime. Originally, compressed sensing was advocated for states with few non-zero eigenvalues. We argue that low-rank estimates are appropriate in general since statistical noise enables reliable reconstruction of only the leading eigenvectors. The remaining eigenvectors behave consistently with a random-matrix model that carries no information about the true state. PMID:28513587

Two new Controlled not Gate Based Quantum Secret Sharing Protocols without Entanglement Attenuation

NASA Astrophysics Data System (ADS)

Zhu, Zhen-Chao; Hu, Ai-Qun; Fu, An-Min

2016-05-01

In this paper, we propose two new controlled not gate based quantum secret sharing protocols. In these two protocols, each photon only travels once, which guarantees the agents located in long distance can be able to derive the dealer's secret without suffering entanglement attenuation problem. The protocols are secure against trojan horse attack, intercept-resend attack, entangle-measure attack and entanglement-swapping attack. The theoretical efficiency for qubits of these two protocols can approach 100 %, except those used for eavesdropping checking, all entangled states can be used for final secret sharing.

Matrix Results and Techniques in Quantum Information Science and Related Topics

NASA Astrophysics Data System (ADS)

Pelejo, Diane Christine

In this dissertation, we present several matrix-related problems and results motivated by quantum information theory. Some background material of quantum information science will be discussed in chapter 1, while chapter 7 gives a summary of results and concluding remarks. In chapter 2, we look at 2n x 2 n unitary matrices, which describe operations on a closed n-qubit system. We define a set of simple quantum gates, called controlled single qubit gates, and their associated operational cost. We then present a recurrence scheme to decompose a general 2n x 2n unitary matrix to the product of no more than 2n-12n-1 single qubit gates with small number of controls. In chapter 3, we address the problem of finding a specific element phi among a given set of quantum channels S that will produce the optimal value of a scalar function D(rho 1,phi(rho2)), on two fixed quantum states rho 1 and rho2. Some of the functions we considered for D(·,·) are the trace distance, quantum fidelity and quantum relative entropy. We discuss the optimal solution when S is the set of unitary quantum channels, the set of mixed unitary channels, the set of unital quantum channels, and the set of all quantum channels. In chapter 4, we focus on the spectral properties of qubit-qudit bipartite states with a maximally mixed qudit subsystem. More specifically, given positive numbers a1 ≥ ... ≥ a 2n ≥ 0, we want to determine if there exist a 2n x 2n density matrix rho having eigenvalues a1,..., a2n and satisfying tr 1(rho)=1/n In. This problem is a special case of the more general quantum marginal problem. We give the minimal necessary and sufficient conditions on a1,..., a2n for n ≤ 6 and state some observations on general values of n.. In chapter 5, we discuss the numerical method of alternating projections and illustrate its usefulness in: (a) constructing a quantum channel, if it exists, such that phi(rho(1))=sigma(1),...,phi(rho (k))=sigma(k) for given rho (1),...,rho(k) ∈ Dn and sigma(1),...,sigma (k) ∈ Dm, (b) constructing a multipartite state rho having a prescribed set of reduced states rho1,..., rhor on r of its subsystems, (c) constructing a multipartite staterho having prescribed reduced states and additional properties such as having prescribed eigenvalues, prescribed rank or low von Neuman entropy; and (d) determining if a square matrix A can be written as a product of two positive semidefinite contractions. In chapter 6, we examine the shape of the Minkowski product of convex subsets K1 and K2 of C given by K1K 2 = {ab: a ∈ K1, b ∈ K2}, which has applications in the study of the product numerical range and quantum error-correction. In Karol, it was conjectured that K1K 2 is star-shaped when K1 and K2 are convex. We give counterexamples to show that this conjecture does not hold in general but we show that the set K 1K2 is star-shaped if K 1 is a line segment or a circular disk.

Architectures for Quantum Simulation Showing a Quantum Speedup

NASA Astrophysics Data System (ADS)

Bermejo-Vega, Juan; Hangleiter, Dominik; Schwarz, Martin; Raussendorf, Robert; Eisert, Jens

2018-04-01

One of the main aims in the field of quantum simulation is to achieve a quantum speedup, often referred to as "quantum computational supremacy," referring to the experimental realization of a quantum device that computationally outperforms classical computers. In this work, we show that one can devise versatile and feasible schemes of two-dimensional, dynamical, quantum simulators showing such a quantum speedup, building on intermediate problems involving nonadaptive, measurement-based, quantum computation. In each of the schemes, an initial product state is prepared, potentially involving an element of randomness as in disordered models, followed by a short-time evolution under a basic translationally invariant Hamiltonian with simple nearest-neighbor interactions and a mere sampling measurement in a fixed basis. The correctness of the final-state preparation in each scheme is fully efficiently certifiable. We discuss experimental necessities and possible physical architectures, inspired by platforms of cold atoms in optical lattices and a number of others, as well as specific assumptions that enter the complexity-theoretic arguments. This work shows that benchmark settings exhibiting a quantum speedup may require little control, in contrast to universal quantum computing. Thus, our proposal puts a convincing experimental demonstration of a quantum speedup within reach in the near term.

A Blueprint for Demonstrating Quantum Supremacy with Superconducting Qubits

NASA Technical Reports Server (NTRS)

Kechedzhi, Kostyantyn

2018-01-01

Long coherence times and high fidelity control recently achieved in scalable superconducting circuits paved the way for the growing number of experimental studies of many-qubit quantum coherent phenomena in these devices. Albeit full implementation of quantum error correction and fault tolerant quantum computation remains a challenge the near term pre-error correction devices could allow new fundamental experiments despite inevitable accumulation of errors. One such open question foundational for quantum computing is achieving the so called quantum supremacy, an experimental demonstration of a computational task that takes polynomial time on the quantum computer whereas the best classical algorithm would require exponential time and/or resources. It is possible to formulate such a task for a quantum computer consisting of less than a 100 qubits. The computational task we consider is to provide approximate samples from a non-trivial quantum distribution. This is a generalization for the case of superconducting circuits of ideas behind boson sampling protocol for quantum optics introduced by Arkhipov and Aaronson. In this presentation we discuss a proof-of-principle demonstration of such a sampling task on a 9-qubit chain of superconducting gmon qubits developed by Google. We discuss theoretical analysis of the driven evolution of the device resulting in output approximating samples from a uniform distribution in the Hilbert space, a quantum chaotic state. We analyze quantum chaotic characteristics of the output of the circuit and the time required to generate a sufficiently complex quantum distribution. We demonstrate that the classical simulation of the sampling output requires exponential resources by connecting the task of calculating the output amplitudes to the sign problem of the Quantum Monte Carlo method. We also discuss the detailed theoretical modeling required to achieve high fidelity control and calibration of the multi-qubit unitary evolution in the device. We use a novel cross-entropy statistical metric as a figure of merit to verify the output and calibrate the device controls. Finally, we demonstrate the statistics of the wave function amplitudes generated on the 9-gmon chain and verify the quantum chaotic nature of the generated quantum distribution. This verifies the implementation of the quantum supremacy protocol.

A strategy for quantum algorithm design assisted by machine learning

NASA Astrophysics Data System (ADS)

Bang, Jeongho; Ryu, Junghee; Yoo, Seokwon; Pawłowski, Marcin; Lee, Jinhyoung

2014-07-01

We propose a method for quantum algorithm design assisted by machine learning. The method uses a quantum-classical hybrid simulator, where a ‘quantum student’ is being taught by a ‘classical teacher’. In other words, in our method, the learning system is supposed to evolve into a quantum algorithm for a given problem, assisted by a classical main-feedback system. Our method is applicable for designing quantum oracle-based algorithms. We chose, as a case study, an oracle decision problem, called a Deutsch-Jozsa problem. We showed by using Monte Carlo simulations that our simulator can faithfully learn a quantum algorithm for solving the problem for a given oracle. Remarkably, the learning time is proportional to the square root of the total number of parameters, rather than showing the exponential dependence found in the classical machine learning-based method.

The quantum pinch effect in semiconducting quantum wires: A bird’s-eye view

NASA Astrophysics Data System (ADS)

Kushwaha, Manvir S.

2016-01-01

Those who measure success with culmination do not seem to be aware that life is a journey not a destination. This spirit is best reflected in the unceasing failures in efforts for solving the problem of controlled thermonuclear fusion for even the simplest pinches for over decades; and the nature keeps us challenging with examples. However, these efforts have permitted researchers the obtention of a dense plasma with a lifetime that, albeit short, is sufficient to study the physics of the pinch effect, to create methods of plasma diagnostics, and to develop a modern theory of plasma processes. Most importantly, they have impregnated the solid state plasmas, particularly the electron-hole plasmas in semiconductors, which do not suffer from the issues related with the confinement and which have demonstrated their potential not only for the fundamental physics but also for the device physics. Here, we report on a two-component, cylindrical, quasi-one-dimensional quantum plasma subjected to a radial confining harmonic potential and an applied magnetic field in the symmetric gauge. It is demonstrated that such a system, as can be realized in semiconducting quantum wires, offers an excellent medium for observing the quantum pinch effect at low temperatures. An exact analytical solution of the problem allows us to make significant observations: Surprisingly, in contrast to the classical pinch effect, the particle density as well as the current density display a determinable maximum before attaining a minimum at the surface of the quantum wire. The effect will persist as long as the equilibrium pair density is sustained. Therefore, the technological promise that emerges is the route to the precise electronic devices that will control the particle beams at the nanoscale.

Cross-Talk in Superconducting Transmon Quantum Computing Architecture

NASA Astrophysics Data System (ADS)

Abraham, David; Chow, Jerry; Corcoles, Antonio; Rothwell, Mary; Keefe, George; Gambetta, Jay; Steffen, Matthias; IBM Quantum Computing Team

2013-03-01

Superconducting transmon quantum computing test structures often exhibit significant undesired cross-talk. For experiments with only a handful of qubits this cross-talk can be quantified and understood, and therefore corrected. As quantum computing circuits become more complex, and thereby contain increasing numbers of qubits and resonators, it becomes more vital that the inadvertent coupling between these elements is minimized. The task of accurately controlling each single qubit to the level of precision required throughout the realization of a quantum algorithm is difficult by itself, but coupled with the need of nulling out leakage signals from neighboring qubits or resonators would quickly become impossible. We discuss an approach to solve this critical problem. We acknowledge support from IARPA under contract W911NF-10-1-0324.

Provable classically intractable sampling with measurement-based computation in constant time

NASA Astrophysics Data System (ADS)

Sanders, Stephen; Miller, Jacob; Miyake, Akimasa

We present a constant-time measurement-based quantum computation (MQC) protocol to perform a classically intractable sampling problem. We sample from the output probability distribution of a subclass of the instantaneous quantum polynomial time circuits introduced by Bremner, Montanaro and Shepherd. In contrast with the usual circuit model, our MQC implementation includes additional randomness due to byproduct operators associated with the computation. Despite this additional randomness we show that our sampling task cannot be efficiently simulated by a classical computer. We extend previous results to verify the quantum supremacy of our sampling protocol efficiently using only single-qubit Pauli measurements. Center for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131, USA.

A subgradient approach for constrained binary optimization via quantum adiabatic evolution

NASA Astrophysics Data System (ADS)

Karimi, Sahar; Ronagh, Pooya

2017-08-01

Outer approximation method has been proposed for solving the Lagrangian dual of a constrained binary quadratic programming problem via quantum adiabatic evolution in the literature. This should be an efficient prescription for solving the Lagrangian dual problem in the presence of an ideally noise-free quantum adiabatic system. However, current implementations of quantum annealing systems demand methods that are efficient at handling possible sources of noise. In this paper, we consider a subgradient method for finding an optimal primal-dual pair for the Lagrangian dual of a constrained binary polynomial programming problem. We then study the quadratic stable set (QSS) problem as a case study. We see that this method applied to the QSS problem can be viewed as an instance-dependent penalty-term approach that avoids large penalty coefficients. Finally, we report our experimental results of using the D-Wave 2X quantum annealer and conclude that our approach helps this quantum processor to succeed more often in solving these problems compared to the usual penalty-term approaches.

Performance of Quantum Annealers on Hard Scheduling Problems

NASA Astrophysics Data System (ADS)

Pokharel, Bibek; Venturelli, Davide; Rieffel, Eleanor

Quantum annealers have been employed to attack a variety of optimization problems. We compared the performance of the current D-Wave 2X quantum annealer to that of the previous generation D-Wave Two quantum annealer on scheduling-type planning problems. Further, we compared the effect of different anneal times, embeddings of the logical problem, and different settings of the ferromagnetic coupling JF across the logical vertex-model on the performance of the D-Wave 2X quantum annealer. Our results show that at the best settings, the scaling of expected anneal time to solution for D-WAVE 2X is better than that of the DWave Two, but still inferior to that of state of the art classical solvers on these problems. We discuss the implication of our results for the design and programming of future quantum annealers. Supported by NASA Ames Research Center.

Witnessing eigenstates for quantum simulation of Hamiltonian spectra

PubMed Central

Santagati, Raffaele; Wang, Jianwei; Gentile, Antonio A.; Paesani, Stefano; Wiebe, Nathan; McClean, Jarrod R.; Morley-Short, Sam; Shadbolt, Peter J.; Bonneau, Damien; Silverstone, Joshua W.; Tew, David P.; Zhou, Xiaoqi; O’Brien, Jeremy L.; Thompson, Mark G.

2018-01-01

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. We introduce the concept of an “eigenstate witness” and, through it, provide a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32 bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress toward quantum chemistry on quantum computers. PMID:29387796

Quantum simulator review

NASA Astrophysics Data System (ADS)

Bednar, Earl; Drager, Steven L.

2007-04-01

Quantum information processing's objective is to utilize revolutionary computing capability based on harnessing the paradigm shift offered by quantum computing to solve classically hard and computationally challenging problems. Some of our computationally challenging problems of interest include: the capability for rapid image processing, rapid optimization of logistics, protecting information, secure distributed simulation, and massively parallel computation. Currently, one important problem with quantum information processing is that the implementation of quantum computers is difficult to realize due to poor scalability and great presence of errors. Therefore, we have supported the development of Quantum eXpress and QuIDD Pro, two quantum computer simulators running on classical computers for the development and testing of new quantum algorithms and processes. This paper examines the different methods used by these two quantum computing simulators. It reviews both simulators, highlighting each simulators background, interface, and special features. It also demonstrates the implementation of current quantum algorithms on each simulator. It concludes with summary comments on both simulators.

Demonstration of essentiality of entanglement in a Deutsch-like quantum algorithm

NASA Astrophysics Data System (ADS)

Huang, He-Liang; Goswami, Ashutosh K.; Bao, Wan-Su; Panigrahi, Prasanta K.

2018-06-01

Quantum algorithms can be used to efficiently solve certain classically intractable problems by exploiting quantum parallelism. However, the effectiveness of quantum entanglement in quantum computing remains a question of debate. This study presents a new quantum algorithm that shows entanglement could provide advantages over both classical algorithms and quantum algo- rithms without entanglement. Experiments are implemented to demonstrate the proposed algorithm using superconducting qubits. Results show the viability of the algorithm and suggest that entanglement is essential in obtaining quantum speedup for certain problems in quantum computing. The study provides reliable and clear guidance for developing useful quantum algorithms.

Digital quantum simulators in a scalable architecture of hybrid spin-photon qubits

PubMed Central

Chiesa, Alessandro; Santini, Paolo; Gerace, Dario; Raftery, James; Houck, Andrew A.; Carretta, Stefano

2015-01-01

Resolving quantum many-body problems represents one of the greatest challenges in physics and physical chemistry, due to the prohibitively large computational resources that would be required by using classical computers. A solution has been foreseen by directly simulating the time evolution through sequences of quantum gates applied to arrays of qubits, i.e. by implementing a digital quantum simulator. Superconducting circuits and resonators are emerging as an extremely promising platform for quantum computation architectures, but a digital quantum simulator proposal that is straightforwardly scalable, universal, and realizable with state-of-the-art technology is presently lacking. Here we propose a viable scheme to implement a universal quantum simulator with hybrid spin-photon qubits in an array of superconducting resonators, which is intrinsically scalable and allows for local control. As representative examples we consider the transverse-field Ising model, a spin-1 Hamiltonian, and the two-dimensional Hubbard model and we numerically simulate the scheme by including the main sources of decoherence. PMID:26563516

Complexity of the Quantum Adiabatic Algorithm

NASA Astrophysics Data System (ADS)

Hen, Itay

2013-03-01

The Quantum Adiabatic Algorithm (QAA) has been proposed as a mechanism for efficiently solving optimization problems on a quantum computer. Since adiabatic computation is analog in nature and does not require the design and use of quantum gates, it can be thought of as a simpler and perhaps more profound method for performing quantum computations that might also be easier to implement experimentally. While these features have generated substantial research in QAA, to date there is still a lack of solid evidence that the algorithm can outperform classical optimization algorihms. Here, we discuss several aspects of the quantum adiabatic algorithm: We analyze the efficiency of the algorithm on several ``hard'' (NP) computational problems. Studying the size dependence of the typical minimum energy gap of the Hamiltonians of these problems using quantum Monte Carlo methods, we find that while for most problems the minimum gap decreases exponentially with the size of the problem, indicating that the QAA is not more efficient than existing classical search algorithms, for other problems there is evidence to suggest that the gap may be polynomial near the phase transition. We also discuss applications of the QAA to ``real life'' problems and how they can be implemented on currently available (albeit prototypical) quantum hardware such as ``D-Wave One'', that impose serious restrictions as to which type of problems may be tested. Finally, we discuss different approaches to find improved implementations of the algorithm such as local adiabatic evolution, adaptive methods, local search in Hamiltonian space and others.

Quantum chi-squared and goodness of fit testing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Temme, Kristan; Verstraete, Frank

2015-01-15

A quantum mechanical hypothesis test is presented for the hypothesis that a certain setup produces a given quantum state. Although the classical and the quantum problems are very much related to each other, the quantum problem is much richer due to the additional optimization over the measurement basis. A goodness of fit test for i.i.d quantum states is developed and a max-min characterization for the optimal measurement is introduced. We find the quantum measurement which leads both to the maximal Pitman and Bahadur efficiencies, and determine the associated divergence rates. We discuss the relationship of the quantum goodness of fitmore » test to the problem of estimating multiple parameters from a density matrix. These problems are found to be closely related and we show that the largest error of an optimal strategy, determined by the smallest eigenvalue of the Fisher information matrix, is given by the divergence rate of the goodness of fit test.« less

Adiabatic quantum computation with neutral atoms via the Rydberg blockade

NASA Astrophysics Data System (ADS)

Goyal, Krittika; Deutsch, Ivan

2011-05-01

We study a trapped-neutral-atom implementation of the adiabatic model of quantum computation whereby the Hamiltonian of a set of interacting qubits is changed adiabatically so that its ground state evolves to the desired output of the algorithm. We employ the ``Rydberg blockade interaction,'' which previously has been used to implement two-qubit entangling gates in the quantum circuit model. Here it is employed via off-resonant virtual dressing of the excited levels, so that atoms always remain in the ground state. The resulting dressed-Rydberg interaction is insensitive to the distance between the atoms within a certain blockade radius, making this process robust to temperature and vibrational fluctuations. Single qubit interactions are implemented with global microwaves and atoms are locally addressed with light shifts. With these ingredients, we study a protocol to implement the two-qubit Quadratic Unconstrained Binary Optimization (QUBO) problem. We model atom trapping, addressing, coherent evolution, and decoherence. We also explore collective control of the many-atom system and generalize the QUBO problem to multiple qubits. We study a trapped-neutral-atom implementation of the adiabatic model of quantum computation whereby the Hamiltonian of a set of interacting qubits is changed adiabatically so that its ground state evolves to the desired output of the algorithm. We employ the ``Rydberg blockade interaction,'' which previously has been used to implement two-qubit entangling gates in the quantum circuit model. Here it is employed via off-resonant virtual dressing of the excited levels, so that atoms always remain in the ground state. The resulting dressed-Rydberg interaction is insensitive to the distance between the atoms within a certain blockade radius, making this process robust to temperature and vibrational fluctuations. Single qubit interactions are implemented with global microwaves and atoms are locally addressed with light shifts. With these ingredients, we study a protocol to implement the two-qubit Quadratic Unconstrained Binary Optimization (QUBO) problem. We model atom trapping, addressing, coherent evolution, and decoherence. We also explore collective control of the many-atom system and generalize the QUBO problem to multiple qubits. We acknowledge funding from the AQUARIUS project, Sandia National Laboratories

Quantum computation with coherent spin states and the close Hadamard problem

NASA Astrophysics Data System (ADS)

Adcock, Mark R. A.; Høyer, Peter; Sanders, Barry C.

2016-04-01

We study a model of quantum computation based on the continuously parameterized yet finite-dimensional Hilbert space of a spin system. We explore the computational powers of this model by analyzing a pilot problem we refer to as the close Hadamard problem. We prove that the close Hadamard problem can be solved in the spin system model with arbitrarily small error probability in a constant number of oracle queries. We conclude that this model of quantum computation is suitable for solving certain types of problems. The model is effective for problems where symmetries between the structure of the information associated with the problem and the structure of the unitary operators employed in the quantum algorithm can be exploited.

Adiabatic Quantum Computation with Neutral Atoms

NASA Astrophysics Data System (ADS)

Biedermann, Grant

2013-03-01

We are implementing a new platform for adiabatic quantum computation (AQC)[2] based on trapped neutral atoms whose coupling is mediated by the dipole-dipole interactions of Rydberg states. Ground state cesium atoms are dressed by laser fields in a manner conditional on the Rydberg blockade mechanism,[3,4] thereby providing the requisite entangling interactions. As a benchmark we study a Quadratic Unconstrained Binary Optimization (QUBO) problem whose solution is found in the ground state spin configuration of an Ising-like model. In collaboration with Lambert Parazzoli, Sandia National Laboratories; Aaron Hankin, Center for Quantum Information and Control (CQuIC), University of New Mexico; James Chin-Wen Chou, Yuan-Yu Jau, Peter Schwindt, Cort Johnson, and George Burns, Sandia National Laboratories; Tyler Keating, Krittika Goyal, and Ivan Deutsch, Center for Quantum Information and Control (CQuIC), University of New Mexico; and Andrew Landahl, Sandia National Laboratories. This work was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories

Effect of local minima on adiabatic quantum optimization.

PubMed

Amin, M H S

2008-04-04

We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian. We show that, for problems that have an exponentially large number of local minima close to the global minimum, the gap becomes exponentially small making the computation time exponentially long. The quantum advantage of adiabatic quantum computation may then be accessed only via the local adiabatic evolution, which requires phase coherence throughout the evolution and knowledge of the spectrum. Such problems, therefore, are not suitable for adiabatic quantum computation.

A device-oriented optimizer for solving ground state problems on an approximate quantum computer, Part II: Experiments for interacting spin and molecular systems

NASA Astrophysics Data System (ADS)

Kandala, Abhinav; Mezzacapo, Antonio; Temme, Kristan; Bravyi, Sergey; Takita, Maika; Chavez-Garcia, Jose; Córcoles, Antonio; Smolin, John; Chow, Jerry; Gambetta, Jay

Hybrid quantum-classical algorithms can be used to find variational solutions to generic quantum problems. Here, we present an experimental implementation of a device-oriented optimizer that uses superconducting quantum hardware. The experiment relies on feedback between the quantum device and classical optimization software which is robust to measurement noise. Our device-oriented approach uses naturally available interactions for the preparation of trial states. We demonstrate the application of this technique for solving interacting spin and molecular structure problems.

Students' Epistemological Framing in Quantum Mechanics Problem Solving

ERIC Educational Resources Information Center

Modir, Bahar; Thompson, John D.; Sayre, Eleanor C.

2017-01-01

Students' difficulties in quantum mechanics may be the result of unproductive framing and not a fundamental inability to solve the problems or misconceptions about physics content. We observed groups of students solving quantum mechanics problems in an upper-division physics course. Using the lens of epistemological framing, we investigated four…

Flux qubit interaction with rapid single-flux quantum logic circuits: Control and readout

NASA Astrophysics Data System (ADS)

Klenov, N. V.; Kuznetsov, A. V.; Soloviev, I. I.; Bakurskiy, S. V.; Denisenko, M. V.; Satanin, A. M.

2017-07-01

We present the results of an analytical study and numerical simulation of the dynamics of a superconducting three-Josephson-junction (3JJ) flux qubit magnetically coupled with rapid single-flux quantum (RSFQ) logic circuit, which demonstrate the fundamental possibility of implementing the simplest logic operations at picosecond times, as well as rapid non-destructive readout. It is shown that when solving optimization problems, the qubit dynamics can be conveniently interpreted as a precession of the magnetic moment vector around the direction of the magnetic field. In this case, the role of magnetic field components is played by combinations of the Hamiltonian matrix elements, and the role of the magnetic moment is played by the Bloch vector. Features of the 3JJ qubit model are discussed during the analysis of how the qubit is affected by exposure to a short control pulse, as are the similarities between the Bloch and Landau-Lifshitz-Gilbert equations. An analysis of solutions to the Bloch equations made it possible to develop recommendations for the use of readout RSFQ circuits in implementing an optimal interface between the classical and quantum parts of the computer system, as well as to justify the use of single-quantum logic in order to control superconducting quantum circuits on a chip.

Unraveling Quantum Annealers using Classical Hardness

PubMed Central

Martin-Mayor, Victor; Hen, Itay

2015-01-01

Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, commonly referred to as ‘D-Wave’ chips, promise to solve practical optimization problems potentially faster than conventional ‘classical’ computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of experimental quantum annealers from their classical thermal counterparts. Inspired by recent results in spin-glass theory that recognize ‘temperature chaos’ as the underlying mechanism responsible for the computational intractability of hard optimization problems, we devise a general method to quantify the performance of quantum annealers on optimization problems suffering from varying degrees of temperature chaos: A superior performance of quantum annealers over classical algorithms on these may allude to the role that quantum effects play in providing speedup. We utilize our method to experimentally study the D-Wave Two chip on different temperature-chaotic problems and find, surprisingly, that its performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss several purely classical effects that possibly mask the quantum behavior of the chip. PMID:26483257

Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet

NASA Astrophysics Data System (ADS)

Gärttner, Martin; Bohnet, Justin G.; Safavi-Naini, Arghavan; Wall, Michael L.; Bollinger, John J.; Rey, Ana Maria

2017-08-01

Controllable arrays of ions and ultracold atoms can simulate complex many-body phenomena and may provide insights into unsolved problems in modern science. To this end, experimentally feasible protocols for quantifying the buildup of quantum correlations and coherence are needed, as performing full state tomography does not scale favourably with the number of particles. Here we develop and experimentally demonstrate such a protocol, which uses time reversal of the many-body dynamics to measure out-of-time-order correlation functions (OTOCs) in a long-range Ising spin quantum simulator with more than 100 ions in a Penning trap. By measuring a family of OTOCs as a function of a tunable parameter we obtain fine-grained information about the state of the system encoded in the multiple quantum coherence spectrum, extract the quantum state purity, and demonstrate the buildup of up to 8-body correlations. Future applications of this protocol could enable studies of many-body localization, quantum phase transitions, and tests of the holographic duality between quantum and gravitational systems.

Step-by-step magic state encoding for efficient fault-tolerant quantum computation

PubMed Central

Goto, Hayato

2014-01-01

Quantum error correction allows one to make quantum computers fault-tolerant against unavoidable errors due to decoherence and imperfect physical gate operations. However, the fault-tolerant quantum computation requires impractically large computational resources for useful applications. This is a current major obstacle to the realization of a quantum computer. In particular, magic state distillation, which is a standard approach to universality, consumes the most resources in fault-tolerant quantum computation. For the resource problem, here we propose step-by-step magic state encoding for concatenated quantum codes, where magic states are encoded step by step from the physical level to the logical one. To manage errors during the encoding, we carefully use error detection. Since the sizes of intermediate codes are small, it is expected that the resource overheads will become lower than previous approaches based on the distillation at the logical level. Our simulation results suggest that the resource requirements for a logical magic state will become comparable to those for a single logical controlled-NOT gate. Thus, the present method opens a new possibility for efficient fault-tolerant quantum computation. PMID:25511387

Step-by-step magic state encoding for efficient fault-tolerant quantum computation.

PubMed

Goto, Hayato

2014-12-16

Quantum error correction allows one to make quantum computers fault-tolerant against unavoidable errors due to decoherence and imperfect physical gate operations. However, the fault-tolerant quantum computation requires impractically large computational resources for useful applications. This is a current major obstacle to the realization of a quantum computer. In particular, magic state distillation, which is a standard approach to universality, consumes the most resources in fault-tolerant quantum computation. For the resource problem, here we propose step-by-step magic state encoding for concatenated quantum codes, where magic states are encoded step by step from the physical level to the logical one. To manage errors during the encoding, we carefully use error detection. Since the sizes of intermediate codes are small, it is expected that the resource overheads will become lower than previous approaches based on the distillation at the logical level. Our simulation results suggest that the resource requirements for a logical magic state will become comparable to those for a single logical controlled-NOT gate. Thus, the present method opens a new possibility for efficient fault-tolerant quantum computation.

Interpretations of Quantum Theory in the Light of Modern Cosmology

NASA Astrophysics Data System (ADS)

Castagnino, Mario; Fortin, Sebastian; Laura, Roberto; Sudarsky, Daniel

2017-11-01

The difficult issues related to the interpretation of quantum mechanics and, in particular, the "measurement problem" are revisited using as motivation the process of generation of structure from quantum fluctuations in inflationary cosmology. The unessential mathematical complexity of the particular problem is bypassed, facilitating the discussion of the conceptual issues, by considering, within the paradigm set up by the cosmological problem, another problem where symmetry serves as a focal point: a simplified version of Mott's problem.

Fundamental Study on Quantum Nanojets

DTIC Science & Technology

2004-08-01

Pergamon Press. Bell , J. S . 1966 On the problem of hidden variables in quantum mechanics. Rev. of Modern Phys., 38, 447. Berndl, K., Daumer, M...fluid dynamics based on two quantum mechanical perspectives; Schrödinger’s wave mechanics and quantum fluid dynamics based on Hamilton-Jacoby...References 8 2). Direct Problems a). Quantum fluid dynamics formalism based on Hamilton-Jacoby equation are adapted for the numerical

Algorithms Bridging Quantum Computation and Chemistry

NASA Astrophysics Data System (ADS)

McClean, Jarrod Ryan

The design of new materials and chemicals derived entirely from computation has long been a goal of computational chemistry, and the governing equation whose solution would permit this dream is known. Unfortunately, the exact solution to this equation has been far too expensive and clever approximations fail in critical situations. Quantum computers offer a novel solution to this problem. In this work, we develop not only new algorithms to use quantum computers to study hard problems in chemistry, but also explore how such algorithms can help us to better understand and improve our traditional approaches. In particular, we first introduce a new method, the variational quantum eigensolver, which is designed to maximally utilize the quantum resources available in a device to solve chemical problems. We apply this method in a real quantum photonic device in the lab to study the dissociation of the helium hydride (HeH+) molecule. We also enhance this methodology with architecture specific optimizations on ion trap computers and show how linear-scaling techniques from traditional quantum chemistry can be used to improve the outlook of similar algorithms on quantum computers. We then show how studying quantum algorithms such as these can be used to understand and enhance the development of classical algorithms. In particular we use a tool from adiabatic quantum computation, Feynman's Clock, to develop a new discrete time variational principle and further establish a connection between real-time quantum dynamics and ground state eigenvalue problems. We use these tools to develop two novel parallel-in-time quantum algorithms that outperform competitive algorithms as well as offer new insights into the connection between the fermion sign problem of ground states and the dynamical sign problem of quantum dynamics. Finally we use insights gained in the study of quantum circuits to explore a general notion of sparsity in many-body quantum systems. In particular we use developments from the field of compressed sensing to find compact representations of ground states. As an application we study electronic systems and find solutions dramatically more compact than traditional configuration interaction expansions, offering hope to extend this methodology to challenging systems in chemical and material design.

Investigations of quantum heuristics for optimization

NASA Astrophysics Data System (ADS)

Rieffel, Eleanor; Hadfield, Stuart; Jiang, Zhang; Mandra, Salvatore; Venturelli, Davide; Wang, Zhihui

We explore the design of quantum heuristics for optimization, focusing on the quantum approximate optimization algorithm, a metaheuristic developed by Farhi, Goldstone, and Gutmann. We develop specific instantiations of the of quantum approximate optimization algorithm for a variety of challenging combinatorial optimization problems. Through theoretical analyses and numeric investigations of select problems, we provide insight into parameter setting and Hamiltonian design for quantum approximate optimization algorithms and related quantum heuristics, and into their implementation on hardware realizable in the near term.

Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance

PubMed Central

Li, Zhaokai; Yung, Man-Hong; Chen, Hongwei; Lu, Dawei; Whitfield, James D.; Peng, Xinhua; Aspuru-Guzik, Alán; Du, Jiangfeng

2011-01-01

Quantum ground-state problems are computationally hard problems for general many-body Hamiltonians; there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10−5 decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wave functions than classical computers PMID:22355607

Boosting quantum annealer performance via sample persistence

NASA Astrophysics Data System (ADS)

Karimi, Hamed; Rosenberg, Gili

2017-07-01

We propose a novel method for reducing the number of variables in quadratic unconstrained binary optimization problems, using a quantum annealer (or any sampler) to fix the value of a large portion of the variables to values that have a high probability of being optimal. The resulting problems are usually much easier for the quantum annealer to solve, due to their being smaller and consisting of disconnected components. This approach significantly increases the success rate and number of observations of the best known energy value in samples obtained from the quantum annealer, when compared with calling the quantum annealer without using it, even when using fewer annealing cycles. Use of the method results in a considerable improvement in success metrics even for problems with high-precision couplers and biases, which are more challenging for the quantum annealer to solve. The results are further enhanced by applying the method iteratively and combining it with classical pre-processing. We present results for both Chimera graph-structured problems and embedded problems from a real-world application.

Research on Quantum Authentication Methods for the Secure Access Control Among Three Elements of Cloud Computing

NASA Astrophysics Data System (ADS)

Dong, Yumin; Xiao, Shufen; Ma, Hongyang; Chen, Libo

2016-12-01

Cloud computing and big data have become the developing engine of current information technology (IT) as a result of the rapid development of IT. However, security protection has become increasingly important for cloud computing and big data, and has become a problem that must be solved to develop cloud computing. The theft of identity authentication information remains a serious threat to the security of cloud computing. In this process, attackers intrude into cloud computing services through identity authentication information, thereby threatening the security of data from multiple perspectives. Therefore, this study proposes a model for cloud computing protection and management based on quantum authentication, introduces the principle of quantum authentication, and deduces the quantum authentication process. In theory, quantum authentication technology can be applied in cloud computing for security protection. This technology cannot be cloned; thus, it is more secure and reliable than classical methods.

Asymptotic inference in system identification for the atom maser.

PubMed

Catana, Catalin; van Horssen, Merlijn; Guta, Madalin

2012-11-28

System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However, for quantum dynamical systems such as quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input that may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators, and the connection to large deviations is briefly discussed.

Atoms and molecules in cavities, from weak to strong coupling in quantum-electrodynamics (QED) chemistry

PubMed Central

Flick, Johannes; Ruggenthaler, Michael; Appel, Heiko

2017-01-01

In this work, we provide an overview of how well-established concepts in the fields of quantum chemistry and material sciences have to be adapted when the quantum nature of light becomes important in correlated matter–photon problems. We analyze model systems in optical cavities, where the matter–photon interaction is considered from the weak- to the strong-coupling limit and for individual photon modes as well as for the multimode case. We identify fundamental changes in Born–Oppenheimer surfaces, spectroscopic quantities, conical intersections, and efficiency for quantum control. We conclude by applying our recently developed quantum-electrodynamical density-functional theory to spontaneous emission and show how a straightforward approximation accurately describes the correlated electron–photon dynamics. This work paves the way to describe matter–photon interactions from first principles and addresses the emergence of new states of matter in chemistry and material science. PMID:28275094

Elucidating Reaction Mechanisms on Quantum Computers

NASA Astrophysics Data System (ADS)

Wiebe, Nathan; Reiher, Markus; Svore, Krysta; Wecker, Dave; Troyer, Matthias

We show how a quantum computer can be employed to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical-computer simulations for such problems, to significantly increase their accuracy and enable hitherto intractable simulations. Detailed resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. This demonstrates that quantum computers will realistically be able to tackle important problems in chemistry that are both scientifically and economically significant.

Quantum speedup of the traveling-salesman problem for bounded-degree graphs

NASA Astrophysics Data System (ADS)

Moylett, Dominic J.; Linden, Noah; Montanaro, Ashley

2017-03-01

The traveling-salesman problem is one of the most famous problems in graph theory. However, little is currently known about the extent to which quantum computers could speed up algorithms for the problem. In this paper, we prove a quadratic quantum speedup when the degree of each vertex is at most 3 by applying a quantum backtracking algorithm to a classical algorithm by Xiao and Nagamochi. We then use similar techniques to accelerate a classical algorithm for when the degree of each vertex is at most 4, before speeding up higher-degree graphs via reductions to these instances.

DOE pushes for useful quantum computing

NASA Astrophysics Data System (ADS)

Cho, Adrian

2018-01-01

The U.S. Department of Energy (DOE) is joining the quest to develop quantum computers, devices that would exploit quantum mechanics to crack problems that overwhelm conventional computers. The initiative comes as Google and other companies race to build a quantum computer that can demonstrate "quantum supremacy" by beating classical computers on a test problem. But reaching that milestone will not mean practical uses are at hand, and the new $40 million DOE effort is intended to spur the development of useful quantum computing algorithms for its work in chemistry, materials science, nuclear physics, and particle physics. With the resources at its 17 national laboratories, DOE could play a key role in developing the machines, researchers say, although finding problems with which quantum computers can help isn't so easy.

Truth Values of Quantum Phenomena

NASA Astrophysics Data System (ADS)

Bolotin, Arkady

2018-04-01

In the paper, the idea of describing not-yet-verified properties of quantum objects with logical many-valuedness is scrutinized. As it is argued, to promote such an idea, the following two foundational problems of many-valued quantum logic must be decided: the problem of choosing a proper system of many-valued logic and the problem of the emergence of bivalence from logical many-valuedness. Difficulties accompanying solutions of these problems are discussed.

Quantum cryptography as a retrodiction problem.

PubMed

Werner, A H; Franz, T; Werner, R F

2009-11-27

We propose a quantum key distribution protocol based on a quantum retrodiction protocol, known as the Mean King problem. The protocol uses a two way quantum channel. We show security against coherent attacks in a transmission-error free scenario, even if Eve is allowed to attack both transmissions. This establishes a connection between retrodiction and key distribution.

Human development VIII: a theory of "deep" quantum chemistry and cell consciousness: quantum chemistry controls genes and biochemistry to give cells and higher organisms consciousness and complex behavior.

PubMed

Ventegodt, Søren; Hermansen, Tyge Dahl; Flensborg-Madsen, Trine; Nielsen, Maj Lyck; Merrick, Joav

2006-11-14

Deep quantum chemistry is a theory of deeply structured quantum fields carrying the biological information of the cell, making it able to remember, intend, represent the inner and outer world for comparison, understand what it "sees", and make choices on its structure, form, behavior and division. We suggest that deep quantum chemistry gives the cell consciousness and all the qualities and abilities related to consciousness. We use geometric symbolism, which is a pre-mathematical and philosophical approach to problems that cannot yet be handled mathematically. Using Occam's razor we have started with the simplest model that works; we presume this to be a many-dimensional, spiral fractal. We suggest that all the electrons of the large biological molecules' orbitals make one huge "cell-orbital", which is structured according to the spiral fractal nature of quantum fields. Consciousness of single cells, multi cellular structures as e.g. organs, multi-cellular organisms and multi-individual colonies (like ants) and human societies can thus be explained by deep quantum chemistry. When biochemical activity is strictly controlled by the quantum-mechanical super-orbital of the cell, this orbital can deliver energetic quanta as biological information, distributed through many fractal levels of the cell to guide form and behavior of an individual single or a multi-cellular organism. The top level of information is the consciousness of the cell or organism, which controls all the biochemical processes. By this speculative work inspired by Penrose and Hameroff we hope to inspire other researchers to formulate more strict and mathematically correct hypothesis on the complex and coherence nature of matter, life and consciousness.

Human Development VIII: A Theory of “Deep” Quantum Chemistry and Cell Consciousness: Quantum Chemistry Controls Genes and Biochemistry to Give Cells and Higher Organisms Consciousness and Complex Behavior

PubMed Central

Ventegodt, Søren; Hermansen, Tyge Dahl; Flensborg-Madsen, Trine; Nielsen, Maj Lyck; Merrick, Joav

2006-01-01

Deep quantum chemistry is a theory of deeply structured quantum fields carrying the biological information of the cell, making it able to remember, intend, represent the inner and outer world for comparison, understand what it “sees”, and make choices on its structure, form, behavior and division. We suggest that deep quantum chemistry gives the cell consciousness and all the qualities and abilities related to consciousness. We use geometric symbolism, which is a pre-mathematical and philosophical approach to problems that cannot yet be handled mathematically. Using Occams razor we have started with the simplest model that works; we presume this to be a many-dimensional, spiral fractal. We suggest that all the electrons of the large biological molecules orbitals make one huge “cell-orbital”, which is structured according to the spiral fractal nature of quantum fields. Consciousness of single cells, multi cellular structures as e.g. organs, multi-cellular organisms and multi-individual colonies (like ants) and human societies can thus be explained by deep quantum chemistry. When biochemical activity is strictly controlled by the quantum-mechanical super-orbital of the cell, this orbital can deliver energetic quanta as biological information, distributed through many fractal levels of the cell to guide form and behavior of an individual single or a multi-cellular organism. The top level of information is the consciousness of the cell or organism, which controls all the biochemical processes. By this speculative work inspired by Penrose and Hameroff we hope to inspire other researchers to formulate more strict and mathematically correct hypothesis on the complex and coherence nature of matter, life and consciousness. PMID:17115084

Compiling quantum circuits to realistic hardware architectures using temporal planners

NASA Astrophysics Data System (ADS)

Venturelli, Davide; Do, Minh; Rieffel, Eleanor; Frank, Jeremy

2018-04-01

To run quantum algorithms on emerging gate-model quantum hardware, quantum circuits must be compiled to take into account constraints on the hardware. For near-term hardware, with only limited means to mitigate decoherence, it is critical to minimize the duration of the circuit. We investigate the application of temporal planners to the problem of compiling quantum circuits to newly emerging quantum hardware. While our approach is general, we focus on compiling to superconducting hardware architectures with nearest neighbor constraints. Our initial experiments focus on compiling Quantum Alternating Operator Ansatz (QAOA) circuits whose high number of commuting gates allow great flexibility in the order in which the gates can be applied. That freedom makes it more challenging to find optimal compilations but also means there is a greater potential win from more optimized compilation than for less flexible circuits. We map this quantum circuit compilation problem to a temporal planning problem, and generated a test suite of compilation problems for QAOA circuits of various sizes to a realistic hardware architecture. We report compilation results from several state-of-the-art temporal planners on this test set. This early empirical evaluation demonstrates that temporal planning is a viable approach to quantum circuit compilation.

Exploring the quantum speed limit with computer games

NASA Astrophysics Data System (ADS)

Sørensen, Jens Jakob W. H.; Pedersen, Mads Kock; Munch, Michael; Haikka, Pinja; Jensen, Jesper Halkjær; Planke, Tilo; Andreasen, Morten Ginnerup; Gajdacz, Miroslav; Mølmer, Klaus; Lieberoth, Andreas; Sherson, Jacob F.

2016-04-01

Humans routinely solve problems of immense computational complexity by intuitively forming simple, low-dimensional heuristic strategies. Citizen science (or crowd sourcing) is a way of exploiting this ability by presenting scientific research problems to non-experts. ‘Gamification’—the application of game elements in a non-game context—is an effective tool with which to enable citizen scientists to provide solutions to research problems. The citizen science games Foldit, EteRNA and EyeWire have been used successfully to study protein and RNA folding and neuron mapping, but so far gamification has not been applied to problems in quantum physics. Here we report on Quantum Moves, an online platform gamifying optimization problems in quantum physics. We show that human players are able to find solutions to difficult problems associated with the task of quantum computing. Players succeed where purely numerical optimization fails, and analyses of their solutions provide insights into the problem of optimization of a more profound and general nature. Using player strategies, we have thus developed a few-parameter heuristic optimization method that efficiently outperforms the most prominent established numerical methods. The numerical complexity associated with time-optimal solutions increases for shorter process durations. To understand this better, we produced a low-dimensional rendering of the optimization landscape. This rendering reveals why traditional optimization methods fail near the quantum speed limit (that is, the shortest process duration with perfect fidelity). Combined analyses of optimization landscapes and heuristic solution strategies may benefit wider classes of optimization problems in quantum physics and beyond.

Exploring the quantum speed limit with computer games.

PubMed

Sørensen, Jens Jakob W H; Pedersen, Mads Kock; Munch, Michael; Haikka, Pinja; Jensen, Jesper Halkjær; Planke, Tilo; Andreasen, Morten Ginnerup; Gajdacz, Miroslav; Mølmer, Klaus; Lieberoth, Andreas; Sherson, Jacob F

2016-04-14

Humans routinely solve problems of immense computational complexity by intuitively forming simple, low-dimensional heuristic strategies. Citizen science (or crowd sourcing) is a way of exploiting this ability by presenting scientific research problems to non-experts. 'Gamification'--the application of game elements in a non-game context--is an effective tool with which to enable citizen scientists to provide solutions to research problems. The citizen science games Foldit, EteRNA and EyeWire have been used successfully to study protein and RNA folding and neuron mapping, but so far gamification has not been applied to problems in quantum physics. Here we report on Quantum Moves, an online platform gamifying optimization problems in quantum physics. We show that human players are able to find solutions to difficult problems associated with the task of quantum computing. Players succeed where purely numerical optimization fails, and analyses of their solutions provide insights into the problem of optimization of a more profound and general nature. Using player strategies, we have thus developed a few-parameter heuristic optimization method that efficiently outperforms the most prominent established numerical methods. The numerical complexity associated with time-optimal solutions increases for shorter process durations. To understand this better, we produced a low-dimensional rendering of the optimization landscape. This rendering reveals why traditional optimization methods fail near the quantum speed limit (that is, the shortest process duration with perfect fidelity). Combined analyses of optimization landscapes and heuristic solution strategies may benefit wider classes of optimization problems in quantum physics and beyond.

Experimental realization of a one-way quantum computer algorithm solving Simon's problem.

PubMed

Tame, M S; Bell, B A; Di Franco, C; Wadsworth, W J; Rarity, J G

2014-11-14

We report an experimental demonstration of a one-way implementation of a quantum algorithm solving Simon's problem-a black-box period-finding problem that has an exponential gap between the classical and quantum runtime. Using an all-optical setup and modifying the bases of single-qubit measurements on a five-qubit cluster state, key representative functions of the logical two-qubit version's black box can be queried and solved. To the best of our knowledge, this work represents the first experimental realization of the quantum algorithm solving Simon's problem. The experimental results are in excellent agreement with the theoretical model, demonstrating the successful performance of the algorithm. With a view to scaling up to larger numbers of qubits, we analyze the resource requirements for an n-qubit version. This work helps highlight how one-way quantum computing provides a practical route to experimentally investigating the quantum-classical gap in the query complexity model.

Demonstration of quantum advantage in machine learning

NASA Astrophysics Data System (ADS)

Ristè, Diego; da Silva, Marcus P.; Ryan, Colm A.; Cross, Andrew W.; Córcoles, Antonio D.; Smolin, John A.; Gambetta, Jay M.; Chow, Jerry M.; Johnson, Blake R.

2017-04-01

The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle, whose structure encodes the solution. One measure of the algorithmic performance is the query complexity, i.e., the scaling of the number of oracle calls needed to find the solution with a given probability. Few-qubit demonstrations of quantum algorithms, such as Deutsch-Jozsa and Grover, have been implemented across diverse physical systems such as nuclear magnetic resonance, trapped ions, optical systems, and superconducting circuits. However, at the small scale, these problems can already be solved classically with a few oracle queries, limiting the obtained advantage. Here we solve an oracle-based problem, known as learning parity with noise, on a five-qubit superconducting processor. Executing classical and quantum algorithms using the same oracle, we observe a large gap in query count in favor of quantum processing. We find that this gap grows by orders of magnitude as a function of the error rates and the problem size. This result demonstrates that, while complex fault-tolerant architectures will be required for universal quantum computing, a significant quantum advantage already emerges in existing noisy systems.

An implementation problem for boson fields and quantum Girsanov transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr; Obata, Nobuaki, E-mail: obata@math.is.tohoku.ac.jp

2016-08-15

We study an implementation problem for quadratic functions of annihilation and creation operators on a boson field in terms of quantum white noise calculus. The implementation problem is shown to be equivalent to a linear differential equation for white noise operators containing quantum white noise derivatives. The solution is explicitly obtained and turns out to form a class of white noise operators including generalized Fourier–Gauss and Fourier–Mehler transforms, Bogoliubov transform, and a quantum extension of the Girsanov transform.

Portfolios of quantum algorithms.

PubMed

Maurer, S M; Hogg, T; Huberman, B A

2001-12-17

Quantum computation holds promise for the solution of many intractable problems. However, since many quantum algorithms are stochastic in nature they can find the solution of hard problems only probabilistically. Thus the efficiency of the algorithms has to be characterized by both the expected time to completion and the associated variance. In order to minimize both the running time and its uncertainty, we show that portfolios of quantum algorithms analogous to those of finance can outperform single algorithms when applied to the NP-complete problems such as 3-satisfiability.

Gaussian Boson Sampling.

PubMed

Hamilton, Craig S; Kruse, Regina; Sansoni, Linda; Barkhofen, Sonja; Silberhorn, Christine; Jex, Igor

2017-10-27

Boson sampling has emerged as a tool to explore the advantages of quantum over classical computers as it does not require universal control over the quantum system, which favors current photonic experimental platforms. Here, we introduce Gaussian Boson sampling, a classically hard-to-solve problem that uses squeezed states as a nonclassical resource. We relate the probability to measure specific photon patterns from a general Gaussian state in the Fock basis to a matrix function called the Hafnian, which answers the last remaining question of sampling from Gaussian states. Based on this result, we design Gaussian Boson sampling, a #P hard problem, using squeezed states. This demonstrates that Boson sampling from Gaussian states is possible, with significant advantages in the photon generation probability, compared to existing protocols.

Controlling the sign problem in finite-density quantum field theory

NASA Astrophysics Data System (ADS)

Garron, Nicolas; Langfeld, Kurt

2017-07-01

Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analog. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor signal to noise ratio. We study three alternatives for this integration: the Gaussian approximation, the "telegraphic" approximation, and a novel expansion in terms of theory-dependent moments and universal coefficients. We have tested the methods for QCD at finite densities of heavy quarks. We find that for two of the approximations the results are extremely close—if not identical—to the full answer in the strong sign-problem regime.

An improved quantum watermarking scheme using small-scale quantum circuits and color scrambling

NASA Astrophysics Data System (ADS)

Li, Panchi; Zhao, Ya; Xiao, Hong; Cao, Maojun

2017-05-01

In order to solve the problem of embedding the watermark into the quantum color image, in this paper, an improved scheme of using small-scale quantum circuits and color scrambling is proposed. Both color carrier image and color watermark image are represented using novel enhanced quantum representation. The image sizes for carrier and watermark are assumed to be 2^{n+1}× 2^{n+2} and 2n× 2n, respectively. At first, the color of pixels in watermark image is scrambled using the controlled rotation gates, and then, the scrambled watermark with 2^n× 2^n image size and 24-qubit gray scale is expanded to an image with 2^{n+1}× 2^{n+2} image size and 3-qubit gray scale. Finally, the expanded watermark image is embedded into the carrier image by the controlled-NOT gates. The extraction of watermark is the reverse process of embedding it into carrier image, which is achieved by applying operations in the reverse order. Simulation-based experimental results show that the proposed scheme is superior to other similar algorithms in terms of three items, visual quality, scrambling effect of watermark image, and noise resistibility.

Quantum speedup in solving the maximal-clique problem

NASA Astrophysics Data System (ADS)

Chang, Weng-Long; Yu, Qi; Li, Zhaokai; Chen, Jiahui; Peng, Xinhua; Feng, Mang

2018-03-01

The maximal-clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry, and bioinformatics to social networks. Here we develop a quantum algorithm to solve the maximal-clique problem for any graph G with n vertices with quadratic speedup over its classical counterparts, where the time and spatial complexities are reduced to, respectively, O (√{2n}) and O (n2) . With respect to oracle-related quantum algorithms for the NP-complete problems, we identify our algorithm as optimal. To justify the feasibility of the proposed quantum algorithm, we successfully solve a typical clique problem for a graph G with two vertices and one edge by carrying out a nuclear magnetic resonance experiment involving four qubits.

Quantum proofs can be verified using only single-qubit measurements

NASA Astrophysics Data System (ADS)

Morimae, Tomoyuki; Nagaj, Daniel; Schuch, Norbert

2016-02-01

Quantum Merlin Arthur (QMA) is the class of problems which, though potentially hard to solve, have a quantum solution that can be verified efficiently using a quantum computer. It thus forms a natural quantum version of the classical complexity class NP (and its probabilistic variant MA, Merlin-Arthur games), where the verifier has only classical computational resources. In this paper, we study what happens when we restrict the quantum resources of the verifier to the bare minimum: individual measurements on single qubits received as they come, one by one. We find that despite this grave restriction, it is still possible to soundly verify any problem in QMA for the verifier with the minimum quantum resources possible, without using any quantum memory or multiqubit operations. We provide two independent proofs of this fact, based on measurement-based quantum computation and the local Hamiltonian problem. The former construction also applies to QMA1, i.e., QMA with one-sided error.

Resonator reset in circuit QED by optimal control for large open quantum systems

NASA Astrophysics Data System (ADS)

Boutin, Samuel; Andersen, Christian Kraglund; Venkatraman, Jayameenakshi; Ferris, Andrew J.; Blais, Alexandre

2017-10-01

We study an implementation of the open GRAPE (gradient ascent pulse engineering) algorithm well suited for large open quantum systems. While typical implementations of optimal control algorithms for open quantum systems rely on explicit matrix exponential calculations, our implementation avoids these operations, leading to a polynomial speedup of the open GRAPE algorithm in cases of interest. This speedup, as well as the reduced memory requirements of our implementation, are illustrated by comparison to a standard implementation of open GRAPE. As a practical example, we apply this open-system optimization method to active reset of a readout resonator in circuit QED. In this problem, the shape of a microwave pulse is optimized such as to empty the cavity from measurement photons as fast as possible. Using our open GRAPE implementation, we obtain pulse shapes, leading to a reset time over 4 times faster than passive reset.

QUANTUM CONTROL OF LIGHT: From Slow Light and FAST CARS to Nuclear γ-ray Spectroscopy

NASA Astrophysics Data System (ADS)

Scully, Marlan

2007-06-01

In recent work we have demonstrated strong coherent backward wave oscillation using forward propagating fields only. This surprising result is achieved by applying laser fields to an ultra-dispersive medium with proper chosen detunings to excite a molecular vibrational coherence that corresponds to a backward propagating wave [PRL, 97, 113001 (2006)]. The physics then has much in common with propagation of ultra-slow light. Applications of coherent scattering and remote sensing to the detection of bio and chemical pathogens (e.g., anthrax) via Coherent Anti-Raman Scattering together with Femtosecond Adaptive Spectroscopic Techniques (FAST CARS [Opt. Comm., 244, 423 (2005)]) will be discussed. Furthermore, the interplay between quantum optics (Dicke super and sub-radiant states) and nuclear physics (forward scattering of γ radiation) provides interesting problems and insights into the quantum control of scattered light [PRL, 96, 010501 (2005)].

`Relativistic' corrections to the mass of a plucked guitar string

NASA Astrophysics Data System (ADS)

Kolodrubetz, Michael; Polkovnikov, Anatoli

Quantum systems respond non-adiabaticity when parameters controlling them are ramped at a finite rate. If the parameters themselves are dynamical - for instance the position of a box that defines the boundary of a quantum field - the feedback of these excitations gives rise to effective Newtonian equations of motion for the parameter. For the age old problem of photons in a box, this correction gives rise to a mass proportional to the energy of the photons. We show that a similar correction arises for a classical guitar string plucked with energy E; moving clamps at the ends of the string requires inertial mass m = 2 E /cs2 , where cs is the speed of sound. This quasi-relativistic effect should be observable in freshman physics level experiments. We then comment on how these simple methods have been readily extended to treat problems such as ramps and quenches of strongly-interacting superconductors and dynamical trapping near a quantum critical point.

Applications of Atomic Systems in Quantum Simulation, Quantum Computation and Topological Phases of Matter

NASA Astrophysics Data System (ADS)

Wang, Shengtao

The ability to precisely and coherently control atomic systems has improved dramatically in the last two decades, driving remarkable advancements in quantum computation and simulation. In recent years, atomic and atom-like systems have also been served as a platform to study topological phases of matter and non-equilibrium many-body physics. Integrated with rapid theoretical progress, the employment of these systems is expanding the realm of our understanding on a range of physical phenomena. In this dissertation, I draw on state-of-the-art experimental technology to develop several new ideas for controlling and applying atomic systems. In the first part of this dissertation, we propose several novel schemes to realize, detect, and probe topological phases in atomic and atom-like systems. We first theoretically study the intriguing properties of Hopf insulators, a peculiar type of topological insulators beyond the standard classification paradigm of topological phases. Using a solid-state quantum simulator, we report the first experimental observation of Hopf insulators. We demonstrate the Hopf fibration with fascinating topological links in the experiment, showing clear signals of topological phase transitions for the underlying Hamiltonian. Next, we propose a feasible experimental scheme to realize the chiral topological insulator in three dimensions. They are a type of topological insulators protected by the chiral symmetry and have thus far remained unobserved in experiment. We then introduce a method to directly measure topological invariants in cold-atom experiments. This detection scheme is general and applicable to probe of different topological insulators in any spatial dimension. In another study, we theoretically discover a new type of topological gapless rings, dubbed a Weyl exceptional ring, in three-dimensional dissipative cold atomic systems. In the second part of this dissertation, we focus on the application of atomic systems in quantum computation and simulation. Trapped atomic ions are one of the leading platforms to build a scalable, universal quantum computer. The common one-dimensional setup, however, greatly limits the system's scalability. By solving the critical problem of micromotion, we propose a two-dimensional architecture for scalable trapped-ion quantum computation. Hamiltonian tomography for many-body quantum systems is essential for benchmarking quantum computation and simulation. By employing dynamical decoupling, we propose a scalable scheme for full Hamiltonian tomography. The required number of measurements increases only polynomially with the system size, in contrast to an exponential scaling in common methods. Finally, we work toward the goal of demonstrating quantum supremacy. A number of sampling tasks, such as the boson sampling problem, have been proposed to be classically intractable under mild assumptions. An intermediate quantum computer can efficiently solve the sampling problem, but the correct operation of the device is not known to be classically verifiable. Toward practical verification, we present an experimental friendly scheme to extract useful and robust information from the quantum boson samplers based on coarse-grained measurements. In a separate study, we introduce a new model built from translation-invariant Ising-interacting spins. This model possesses several advantageous properties, catalyzing the ultimate experimental demonstration of quantum supremacy.

A synchronous game for binary constraint systems

NASA Astrophysics Data System (ADS)

Kim, Se-Jin; Paulsen, Vern; Schafhauser, Christopher

2018-03-01

Recently, Slofstra proved that the set of quantum correlations is not closed. We prove that the set of synchronous quantum correlations is not closed, which implies his result, by giving an example of a synchronous game that has a perfect quantum approximate strategy but no perfect quantum strategy. We also exhibit a graph for which the quantum independence number and the quantum approximate independence number are different. We prove new characterisations of synchronous quantum approximate correlations and synchronous quantum spatial correlations. We solve the synchronous approximation problem of Dykema and the second author, which yields a new equivalence of Connes' embedding problem in terms of synchronous correlations.

Instantons in Quantum Annealing: Thermally Assisted Tunneling Vs Quantum Monte Carlo Simulations

NASA Technical Reports Server (NTRS)

Jiang, Zhang; Smelyanskiy, Vadim N.; Boixo, Sergio; Isakov, Sergei V.; Neven, Hartmut; Mazzola, Guglielmo; Troyer, Matthias

2015-01-01

Recent numerical result (arXiv:1512.02206) from Google suggested that the D-Wave quantum annealer may have an asymptotic speed-up than simulated annealing, however, the asymptotic advantage disappears when it is compared to quantum Monte Carlo (a classical algorithm despite its name). We show analytically that the asymptotic scaling of quantum tunneling is exactly the same as the escape rate in quantum Monte Carlo for a class of problems. Thus, the Google result might be explained in our framework. We also found that the transition state in quantum Monte Carlo corresponds to the instanton solution in quantum tunneling problems, which is observed in numerical simulations.

The Quantum Logical Challenge: Peter Mittelstaedt's Contributions to Logic and Philosophy of Science

NASA Astrophysics Data System (ADS)

Beltrametti, E.; Dalla Chiara, M. L.; Giuntini, R.

2017-12-01

Peter Mittelstaedt's contributions to quantum logic and to the foundational problems of quantum theory have significantly realized the most authentic spirit of the International Quantum Structures Association: an original research about hard technical problems, which are often "entangled" with the emergence of important changes in our general world-conceptions. During a time where both the logical and the physical community often showed a skeptical attitude towards Birkhoff and von Neumann's quantum logic, Mittelstaedt brought into light the deeply innovating features of a quantum logical thinking that allows us to overcome some strong and unrealistic assumptions of classical logical arguments. Later on his intense research on the unsharp approach to quantum theory and to the measurement problem stimulated the increasing interest for unsharp forms of quantum logic, creating a fruitful interaction between the work of quantum logicians and of many-valued logicians. Mittelstaedt's general views about quantum logic and quantum theory seem to be inspired by a conjecture that is today more and more confirmed: there is something universal in the quantum theoretic formalism that goes beyond the limits of microphysics, giving rise to interesting applications to a number of different fields.

Programming and Tuning a Quantum Annealing Device to Solve Real World Problems

NASA Astrophysics Data System (ADS)

Perdomo-Ortiz, Alejandro; O'Gorman, Bryan; Fluegemann, Joseph; Smelyanskiy, Vadim

2015-03-01

Solving real-world applications with quantum algorithms requires overcoming several challenges, ranging from translating the computational problem at hand to the quantum-machine language to tuning parameters of the quantum algorithm that have a significant impact on the performance of the device. In this talk, we discuss these challenges, strategies developed to enhance performance, and also a more efficient implementation of several applications. Although we will focus on applications of interest to NASA's Quantum Artificial Intelligence Laboratory, the methods and concepts presented here apply to a broader family of hard discrete optimization problems, including those that occur in many machine-learning algorithms.

Experimental two-dimensional quantum walk on a photonic chip

PubMed Central

Lin, Xiao-Feng; Feng, Zhen; Chen, Jing-Yuan; Gao, Jun; Sun, Ke; Wang, Chao-Yue; Lai, Peng-Cheng; Xu, Xiao-Yun; Wang, Yao; Qiao, Lu-Feng; Yang, Ai-Lin

2018-01-01

Quantum walks, in virtue of the coherent superposition and quantum interference, have exponential superiority over their classical counterpart in applications of quantum searching and quantum simulation. The quantum-enhanced power is highly related to the state space of quantum walks, which can be expanded by enlarging the photon number and/or the dimensions of the evolution network, but the former is considerably challenging due to probabilistic generation of single photons and multiplicative loss. We demonstrate a two-dimensional continuous-time quantum walk by using the external geometry of photonic waveguide arrays, rather than the inner degree of freedoms of photons. Using femtosecond laser direct writing, we construct a large-scale three-dimensional structure that forms a two-dimensional lattice with up to 49 × 49 nodes on a photonic chip. We demonstrate spatial two-dimensional quantum walks using heralded single photons and single photon–level imaging. We analyze the quantum transport properties via observing the ballistic evolution pattern and the variance profile, which agree well with simulation results. We further reveal the transient nature that is the unique feature for quantum walks of beyond one dimension. An architecture that allows a quantum walk to freely evolve in all directions and at a large scale, combining with defect and disorder control, may bring up powerful and versatile quantum walk machines for classically intractable problems. PMID:29756040

Experimental two-dimensional quantum walk on a photonic chip.

PubMed

Tang, Hao; Lin, Xiao-Feng; Feng, Zhen; Chen, Jing-Yuan; Gao, Jun; Sun, Ke; Wang, Chao-Yue; Lai, Peng-Cheng; Xu, Xiao-Yun; Wang, Yao; Qiao, Lu-Feng; Yang, Ai-Lin; Jin, Xian-Min

2018-05-01

Quantum walks, in virtue of the coherent superposition and quantum interference, have exponential superiority over their classical counterpart in applications of quantum searching and quantum simulation. The quantum-enhanced power is highly related to the state space of quantum walks, which can be expanded by enlarging the photon number and/or the dimensions of the evolution network, but the former is considerably challenging due to probabilistic generation of single photons and multiplicative loss. We demonstrate a two-dimensional continuous-time quantum walk by using the external geometry of photonic waveguide arrays, rather than the inner degree of freedoms of photons. Using femtosecond laser direct writing, we construct a large-scale three-dimensional structure that forms a two-dimensional lattice with up to 49 × 49 nodes on a photonic chip. We demonstrate spatial two-dimensional quantum walks using heralded single photons and single photon-level imaging. We analyze the quantum transport properties via observing the ballistic evolution pattern and the variance profile, which agree well with simulation results. We further reveal the transient nature that is the unique feature for quantum walks of beyond one dimension. An architecture that allows a quantum walk to freely evolve in all directions and at a large scale, combining with defect and disorder control, may bring up powerful and versatile quantum walk machines for classically intractable problems.

Exploring quantum computing application to satellite data assimilation

NASA Astrophysics Data System (ADS)

Cheung, S.; Zhang, S. Q.

2015-12-01

This is an exploring work on potential application of quantum computing to a scientific data optimization problem. On classical computational platforms, the physical domain of a satellite data assimilation problem is represented by a discrete variable transform, and classical minimization algorithms are employed to find optimal solution of the analysis cost function. The computation becomes intensive and time-consuming when the problem involves large number of variables and data. The new quantum computer opens a very different approach both in conceptual programming and in hardware architecture for solving optimization problem. In order to explore if we can utilize the quantum computing machine architecture, we formulate a satellite data assimilation experimental case in the form of quadratic programming optimization problem. We find a transformation of the problem to map it into Quadratic Unconstrained Binary Optimization (QUBO) framework. Binary Wavelet Transform (BWT) will be applied to the data assimilation variables for its invertible decomposition and all calculations in BWT are performed by Boolean operations. The transformed problem will be experimented as to solve for a solution of QUBO instances defined on Chimera graphs of the quantum computer.

Construction of a single atom trap for quantum information protocols

NASA Astrophysics Data System (ADS)

Shea, Margaret E.; Baker, Paul M.; Gauthier, Daniel J.; Duke Physics Department Team

2016-05-01

The field of quantum information science addresses outstanding problems such as achieving fundamentally secure communication and solving computationally hard problems. Great progress has been made in the field, particularly using photons coupled to ions and super conducting qubits. Neutral atoms are also interesting for these applications and though the technology for control of neutrals lags behind that of trapped ions, they offer some key advantages: primarily coupling to optical frequencies closer to the telecom band than trapped ions or superconducting qubits. Here we report progress on constructing a single atom trap for 87 Rb. This system is a promising platform for studying the technical problems facing neutral atom quantum computing. For example, most protocols destroy the trap when reading out the neutral atom's state; we will investigate an alternative non-destructive state detection scheme. We detail the experimental systems involved and the challenges addressed in trapping a single atom. All of our hardware components are off the shelf and relatively inexpensive. Unlike many other systems, we place a high numerical aperture lens inside our vacuum system to increase photon collection efficiency. We gratefully acknowledge the financial support of the ARO through Grant # W911NF1520047.

Quantum Machine Learning

NASA Technical Reports Server (NTRS)

Biswas, Rupak

2018-01-01

Quantum computing promises an unprecedented ability to solve intractable problems by harnessing quantum mechanical effects such as tunneling, superposition, and entanglement. The Quantum Artificial Intelligence Laboratory (QuAIL) at NASA Ames Research Center is the space agency's primary facility for conducting research and development in quantum information sciences. QuAIL conducts fundamental research in quantum physics but also explores how best to exploit and apply this disruptive technology to enable NASA missions in aeronautics, Earth and space sciences, and space exploration. At the same time, machine learning has become a major focus in computer science and captured the imagination of the public as a panacea to myriad big data problems. In this talk, we will discuss how classical machine learning can take advantage of quantum computing to significantly improve its effectiveness. Although we illustrate this concept on a quantum annealer, other quantum platforms could be used as well. If explored fully and implemented efficiently, quantum machine learning could greatly accelerate a wide range of tasks leading to new technologies and discoveries that will significantly change the way we solve real-world problems.

Solving search problems by strongly simulating quantum circuits

PubMed Central

Johnson, T. H.; Biamonte, J. D.; Clark, S. R.; Jaksch, D.

2013-01-01

Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several efficient strong simulation techniques are known for restricted families of quantum circuits and we develop an additional technique in this article. Further, we show that strong simulation algorithms perform another fundamental task: solving search problems. Efficient strong simulation techniques allow solutions to a class of search problems to be counted and found efficiently. This enhances the utility of strong simulation methods, known or yet to be discovered, and extends the class of search problems known to be efficiently simulable. Relating strong simulation to search problems also bounds the computational power of efficiently strongly simulable circuits; if they could solve all problems in P this would imply that all problems in NP and #P could be solved in polynomial time. PMID:23390585

Probing for quantum speedup in spin-glass problems with planted solutions

NASA Astrophysics Data System (ADS)

Hen, Itay; Job, Joshua; Albash, Tameem; Rønnow, Troels F.; Troyer, Matthias; Lidar, Daniel A.

2015-10-01

The availability of quantum annealing devices with hundreds of qubits has made the experimental demonstration of a quantum speedup for optimization problems a coveted, albeit elusive goal. Going beyond earlier studies of random Ising problems, here we introduce a method to construct a set of frustrated Ising-model optimization problems with tunable hardness. We study the performance of a D-Wave Two device (DW2) with up to 503 qubits on these problems and compare it to a suite of classical algorithms, including a highly optimized algorithm designed to compete directly with the DW2. The problems are generated around predetermined ground-state configurations, called planted solutions, which makes them particularly suitable for benchmarking purposes. The problem set exhibits properties familiar from constraint satisfaction (SAT) problems, such as a peak in the typical hardness of the problems, determined by a tunable clause density parameter. We bound the hardness regime where the DW2 device either does not or might exhibit a quantum speedup for our problem set. While we do not find evidence for a speedup for the hardest and most frustrated problems in our problem set, we cannot rule out that a speedup might exist for some of the easier, less frustrated problems. Our empirical findings pertain to the specific D-Wave processor and problem set we studied and leave open the possibility that future processors might exhibit a quantum speedup on the same problem set.

Projected regression method for solving Fredholm integral equations arising in the analytic continuation problem of quantum physics

NASA Astrophysics Data System (ADS)

Arsenault, Louis-François; Neuberg, Richard; Hannah, Lauren A.; Millis, Andrew J.

2017-11-01

We present a supervised machine learning approach to the inversion of Fredholm integrals of the first kind as they arise, for example, in the analytic continuation problem of quantum many-body physics. The approach provides a natural regularization for the ill-conditioned inverse of the Fredholm kernel, as well as an efficient and stable treatment of constraints. The key observation is that the stability of the forward problem permits the construction of a large database of outputs for physically meaningful inputs. Applying machine learning to this database generates a regression function of controlled complexity, which returns approximate solutions for previously unseen inputs; the approximate solutions are then projected onto the subspace of functions satisfying relevant constraints. Under standard error metrics the method performs as well or better than the Maximum Entropy method for low input noise and is substantially more robust to increased input noise. We suggest that the methodology will be similarly effective for other problems involving a formally ill-conditioned inversion of an integral operator, provided that the forward problem can be efficiently solved.

Ultrafast adiabatic quantum algorithm for the NP-complete exact cover problem

PubMed Central

Wang, Hefeng; Wu, Lian-Ao

2016-01-01

An adiabatic quantum algorithm may lose quantumness such as quantum coherence entirely in its long runtime, and consequently the expected quantum speedup of the algorithm does not show up. Here we present a general ultrafast adiabatic quantum algorithm. We show that by applying a sequence of fast random or regular signals during evolution, the runtime can be reduced substantially, whereas advantages of the adiabatic algorithm remain intact. We also propose a randomized Trotter formula and show that the driving Hamiltonian and the proposed sequence of fast signals can be implemented simultaneously. We illustrate the algorithm by solving the NP-complete 3-bit exact cover problem (EC3), where NP stands for nondeterministic polynomial time, and put forward an approach to implementing the problem with trapped ions. PMID:26923834

Playing distributed two-party quantum games on quantum networks

NASA Astrophysics Data System (ADS)

Liu, Bo-Yang; Dai, Hong-Yi; Zhang, Ming

2017-12-01

This paper investigates quantum games between two remote players on quantum networks. We propose two schemes for distributed remote quantum games: the client-server scheme based on states transmission between nodes of the network and the peer-to-peer scheme devised upon remote quantum operations. Following these schemes, we construct two designs of the distributed prisoners' dilemma game on quantum entangling networks, where concrete methods are employed for teleportation and nonlocal two-qubits unitary gates, respectively. It seems to us that the requirement for playing distributed quantum games on networks is still an open problem. We explore this problem by comparing and characterizing the two schemes from the viewpoints of network structures, quantum and classical operations, experimental realization and simplification.

Perfect quantum multiple-unicast network coding protocol

NASA Astrophysics Data System (ADS)

Li, Dan-Dan; Gao, Fei; Qin, Su-Juan; Wen, Qiao-Yan

2018-01-01

In order to realize long-distance and large-scale quantum communication, it is natural to utilize quantum repeater. For a general quantum multiple-unicast network, it is still puzzling how to complete communication tasks perfectly with less resources such as registers. In this paper, we solve this problem. By applying quantum repeaters to multiple-unicast communication problem, we give encoding-decoding schemes for source nodes, internal ones and target ones, respectively. Source-target nodes share EPR pairs by using our encoding-decoding schemes over quantum multiple-unicast network. Furthermore, quantum communication can be accomplished perfectly via teleportation. Compared with existed schemes, our schemes can reduce resource consumption and realize long-distance transmission of quantum information.

The Role of Frame Force in Quantum Detection

DTIC Science & Technology

2007-01-01

42040) 10. C. H. Bennett, Quantum cryptography using any two nonorthogonal states, Phys. Rev. Lett. 68 (1992), no. 21, 3121–3124. MR 1 163 546 11. S ...SUBTITLE The Role of Frame Force in Quantum Detection 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR( S ) 5d. PROJECT...equivalent to a quantum detection problem from quantum mechanics. To this end we first reformulate Problem 1.2 in terms of orthonormal bases instead of 1

Philosophical perspectives on quantum chaos: Models and interpretations

NASA Astrophysics Data System (ADS)

Bokulich, Alisa Nicole

2001-09-01

The problem of quantum chaos is a special case of the larger problem of understanding how the classical world emerges from quantum mechanics. While we have learned that chaos is pervasive in classical systems, it appears to be almost entirely absent in quantum systems. The aim of this dissertation is to determine what implications the interpretation of quantum mechanics has for attempts to explain the emergence of classical chaos. There are three interpretations of quantum mechanics that have set out programs for solving the problem of quantum chaos: the standard interpretation, the statistical interpretation, and the deBroglie-Bohm causal interpretation. One of the main conclusions of this dissertation is that an interpretation alone is insufficient for solving the problem of quantum chaos and that the phenomenon of decoherence must be taken into account. Although a completely satisfactory solution of the problem of quantum chaos is still outstanding, I argue that the deBroglie-Bohm interpretation with the help of decoherence outlines the most promising research program to pursue. In addition to making a contribution to the debate in the philosophy of physics concerning the interpretation of quantum mechanics, this dissertation reveals two important methodological lessons for the philosophy of science. First, issues of reductionism and intertheoretic relations cannot be divorced from questions concerning the interpretation of the theories involved. Not only is the exploration of intertheoretic relations a central part of the articulation and interpretation of an individual theory, but the very terms used to discuss intertheoretic relations, such as `state' and `classical limit', are themselves defined by particular interpretations of the theory. The second lesson that emerges is that, when it comes to characterizing the relationship between classical chaos and quantum mechanics, the traditional approaches to intertheoretic relations, namely reductionism and theoretical pluralism, are inadequate. The fruitful ways in which models have been used in quantum chaos research point to the need for a new framework for addressing intertheoretic relations that focuses on models rather than laws.

Quantum algorithm for solving some discrete mathematical problems by probing their energy spectra

NASA Astrophysics Data System (ADS)

Wang, Hefeng; Fan, Heng; Li, Fuli

2014-01-01

When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum algorithm for solving discrete mathematical problems based on the circuit model. Our algorithm has favorable scaling properties in solving some discrete mathematical problems.

Characteristic operator functions for quantum input-plant-output models and coherent control

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gough, John E.

We introduce the characteristic operator as the generalization of the usual concept of a transfer function of linear input-plant-output systems to arbitrary quantum nonlinear Markovian input-output models. This is intended as a tool in the characterization of quantum feedback control systems that fits in with the general theory of networks. The definition exploits the linearity of noise differentials in both the plant Heisenberg equations of motion and the differential form of the input-output relations. Mathematically, the characteristic operator is a matrix of dimension equal to the number of outputs times the number of inputs (which must coincide), but with entriesmore » that are operators of the plant system. In this sense, the characteristic operator retains details of the effective plant dynamical structure and is an essentially quantum object. We illustrate the relevance to model reduction and simplification definition by showing that the convergence of the characteristic operator in adiabatic elimination limit models requires the same conditions and assumptions appearing in the work on limit quantum stochastic differential theorems of Bouten and Silberfarb [Commun. Math. Phys. 283, 491-505 (2008)]. This approach also shows in a natural way that the limit coefficients of the quantum stochastic differential equations in adiabatic elimination problems arise algebraically as Schur complements and amounts to a model reduction where the fast degrees of freedom are decoupled from the slow ones and eliminated.« less

A random walk approach to quantum algorithms.

PubMed

Kendon, Vivien M

2006-12-15

The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial; pure quantum dynamics is deterministic, so randomness only enters during the measurement phase, i.e. when converting the quantum information into classical information. The outcome of a quantum random walk is very different from the corresponding classical random walk owing to the interference between the different possible paths. The upshot is that quantum walkers find themselves further from their starting point than a classical walker on average, and this forms the basis of a quantum speed up, which can be exploited to solve problems faster. Surprisingly, the effect of making the walk slightly less than perfectly quantum can optimize the properties of the quantum walk for algorithmic applications. Looking to the future, even with a small quantum computer available, the development of quantum walk algorithms might proceed more rapidly than it has, especially for solving real problems.

Toward a new culture in verified quantum operations

NASA Astrophysics Data System (ADS)

Flammia, Steve

Measuring error rates of quantum operations has become an indispensable component in any aspiring platform for quantum computation. As the quality of controlled quantum operations increases, the demands on the accuracy and precision with which we measure these error rates also grows. However, well-meaning scientists that report these error measures are faced with a sea of non-standardized methodologies and are often asked during publication for only coarse information about how their estimates were obtained. Moreover, there are serious incentives to use methodologies and measures that will continually produce numbers that improve with time to show progress. These problems will only get exacerbated as our typical error rates go from 1 in 100 to 1 in 1000 or less. This talk will survey existing challenges presented by the current paradigm and offer some suggestions for solutions than can help us move toward fair and standardized methods for error metrology in quantum computing experiments, and towards a culture that values full disclose of methodologies and higher standards for data analysis.

Robust quantum optimizer with full connectivity.

PubMed

Nigg, Simon E; Lörch, Niels; Tiwari, Rakesh P

2017-04-01

Quantum phenomena have the potential to speed up the solution of hard optimization problems. For example, quantum annealing, based on the quantum tunneling effect, has recently been shown to scale exponentially better with system size than classical simulated annealing. However, current realizations of quantum annealers with superconducting qubits face two major challenges. First, the connectivity between the qubits is limited, excluding many optimization problems from a direct implementation. Second, decoherence degrades the success probability of the optimization. We address both of these shortcomings and propose an architecture in which the qubits are robustly encoded in continuous variable degrees of freedom. By leveraging the phenomenon of flux quantization, all-to-all connectivity with sufficient tunability to implement many relevant optimization problems is obtained without overhead. Furthermore, we demonstrate the robustness of this architecture by simulating the optimal solution of a small instance of the nondeterministic polynomial-time hard (NP-hard) and fully connected number partitioning problem in the presence of dissipation.

Students' Conceptual Difficulties in Quantum Mechanics: Potential Well Problems

ERIC Educational Resources Information Center

Ozcan, Ozgur; Didis, Nilufer; Tasar, Mehmet Fatih

2009-01-01

In this study, students' conceptual difficulties about some basic concepts in quantum mechanics like one-dimensional potential well problems and probability density of tunneling particles were identified. For this aim, a multiple choice instrument named Quantum Mechanics Conceptual Test has been developed by one of the researchers of this study…

Improved mapping of the travelling salesman problem for quantum annealing

NASA Astrophysics Data System (ADS)

Troyer, Matthias; Heim, Bettina; Brown, Ethan; Wecker, David

2015-03-01

We consider the quantum adiabatic algorithm as applied to the travelling salesman problem (TSP). We introduce a novel mapping of TSP to an Ising spin glass Hamiltonian and compare it to previous known mappings. Through direct perturbative analysis, unitary evolution, and simulated quantum annealing, we show this new mapping to be significantly superior. We discuss how this advantage can translate to actual physical implementations of TSP on quantum annealers.

Large-scale semidefinite programming for many-electron quantum mechanics.

PubMed

Mazziotti, David A

2011-02-25

The energy of a many-electron quantum system can be approximated by a constrained optimization of the two-electron reduced density matrix (2-RDM) that is solvable in polynomial time by semidefinite programming (SDP). Here we develop a SDP method for computing strongly correlated 2-RDMs that is 10-20 times faster than previous methods [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)]. We illustrate with (i) the dissociation of N(2) and (ii) the metal-to-insulator transition of H(50). For H(50) the SDP problem has 9.4×10(6) variables. This advance also expands the feasibility of large-scale applications in quantum information, control, statistics, and economics. © 2011 American Physical Society

Large-Scale Semidefinite Programming for Many-Electron Quantum Mechanics

NASA Astrophysics Data System (ADS)

Mazziotti, David A.

2011-02-01

The energy of a many-electron quantum system can be approximated by a constrained optimization of the two-electron reduced density matrix (2-RDM) that is solvable in polynomial time by semidefinite programming (SDP). Here we develop a SDP method for computing strongly correlated 2-RDMs that is 10-20 times faster than previous methods [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)PRLTAO0031-900710.1103/PhysRevLett.93.213001]. We illustrate with (i) the dissociation of N2 and (ii) the metal-to-insulator transition of H50. For H50 the SDP problem has 9.4×106 variables. This advance also expands the feasibility of large-scale applications in quantum information, control, statistics, and economics.

Two Quantum Protocols for Oblivious Set-member Decision Problem

NASA Astrophysics Data System (ADS)

Shi, Run-Hua; Mu, Yi; Zhong, Hong; Cui, Jie; Zhang, Shun

2015-10-01

In this paper, we defined a new secure multi-party computation problem, called Oblivious Set-member Decision problem, which allows one party to decide whether a secret of another party belongs to his private set in an oblivious manner. There are lots of important applications of Oblivious Set-member Decision problem in fields of the multi-party collaborative computation of protecting the privacy of the users, such as private set intersection and union, anonymous authentication, electronic voting and electronic auction. Furthermore, we presented two quantum protocols to solve the Oblivious Set-member Decision problem. Protocol I takes advantage of powerful quantum oracle operations so that it needs lower costs in both communication and computation complexity; while Protocol II takes photons as quantum resources and only performs simple single-particle projective measurements, thus it is more feasible with the present technology.

Two Quantum Protocols for Oblivious Set-member Decision Problem

PubMed Central

Shi, Run-hua; Mu, Yi; Zhong, Hong; Cui, Jie; Zhang, Shun

2015-01-01

In this paper, we defined a new secure multi-party computation problem, called Oblivious Set-member Decision problem, which allows one party to decide whether a secret of another party belongs to his private set in an oblivious manner. There are lots of important applications of Oblivious Set-member Decision problem in fields of the multi-party collaborative computation of protecting the privacy of the users, such as private set intersection and union, anonymous authentication, electronic voting and electronic auction. Furthermore, we presented two quantum protocols to solve the Oblivious Set-member Decision problem. Protocol I takes advantage of powerful quantum oracle operations so that it needs lower costs in both communication and computation complexity; while Protocol II takes photons as quantum resources and only performs simple single-particle projective measurements, thus it is more feasible with the present technology. PMID:26514668

Two Quantum Protocols for Oblivious Set-member Decision Problem.

PubMed

Shi, Run-Hua; Mu, Yi; Zhong, Hong; Cui, Jie; Zhang, Shun

2015-10-30

In this paper, we defined a new secure multi-party computation problem, called Oblivious Set-member Decision problem, which allows one party to decide whether a secret of another party belongs to his private set in an oblivious manner. There are lots of important applications of Oblivious Set-member Decision problem in fields of the multi-party collaborative computation of protecting the privacy of the users, such as private set intersection and union, anonymous authentication, electronic voting and electronic auction. Furthermore, we presented two quantum protocols to solve the Oblivious Set-member Decision problem. Protocol I takes advantage of powerful quantum oracle operations so that it needs lower costs in both communication and computation complexity; while Protocol II takes photons as quantum resources and only performs simple single-particle projective measurements, thus it is more feasible with the present technology.

Dynamical control of a quantum Kapitza pendulum in a spin-1 BEC

NASA Astrophysics Data System (ADS)

Hoang, Thai; Gerving, Corey; Land, Ben; Anquez, Martin; Hamley, Chris; Chapman, Michael

2013-05-01

We demonstrate dynamic stabilization of an unstable strongly interacting quantum many-body system by periodic manipulation of the phase of the collective states. The experiment employs a spin-1 atomic Bose condensate that has spin dynamics analogous to a non-rigid pendulum in the mean-field limit. The condensate spin is initialized to an unstable (hyperbolic) fixed point of the phase space, where subsequent free evolution gives rise to spin-nematic squeezing and quantum spin mixing. To stabilize the system, periodic microwave pulses are applied that manipulate the spin-nematic fluctuations and limit their growth. The range of pulse periods and phase shifts with which the condensate can be stabilized is measured and compares well with a linear stability analysis of the problem. C.D. Hamley, et al., ``Spin-Nematic Squeezed Vacuum in a Quantum Gas,'' Nature Physics 8, 305-308 (2012).

Emergence of coherence and the dynamics of quantum phase transitions

PubMed Central

Braun, Simon; Friesdorf, Mathis; Hodgman, Sean S.; Schreiber, Michael; Ronzheimer, Jens Philipp; Riera, Arnau; del Rey, Marco; Bloch, Immanuel; Eisert, Jens

2015-01-01

The dynamics of quantum phase transitions pose one of the most challenging problems in modern many-body physics. Here, we study a prototypical example in a clean and well-controlled ultracold atom setup by observing the emergence of coherence when crossing the Mott insulator to superfluid quantum phase transition. In the 1D Bose–Hubbard model, we find perfect agreement between experimental observations and numerical simulations for the resulting coherence length. We, thereby, perform a largely certified analog quantum simulation of this strongly correlated system reaching beyond the regime of free quasiparticles. Experimentally, we additionally explore the emergence of coherence in higher dimensions, where no classical simulations are available, as well as for negative temperatures. For intermediate quench velocities, we observe a power-law behavior of the coherence length, reminiscent of the Kibble–Zurek mechanism. However, we find nonuniversal exponents that cannot be captured by this mechanism or any other known model. PMID:25775515

Quantum biological channel modeling and capacity calculation.

PubMed

Djordjevic, Ivan B

2012-12-10

Quantum mechanics has an important role in photosynthesis, magnetoreception, and evolution. There were many attempts in an effort to explain the structure of genetic code and transfer of information from DNA to protein by using the concepts of quantum mechanics. The existing biological quantum channel models are not sufficiently general to incorporate all relevant contributions responsible for imperfect protein synthesis. Moreover, the problem of determination of quantum biological channel capacity is still an open problem. To solve these problems, we construct the operator-sum representation of biological channel based on codon basekets (basis vectors), and determine the quantum channel model suitable for study of the quantum biological channel capacity and beyond. The transcription process, DNA point mutations, insertions, deletions, and translation are interpreted as the quantum noise processes. The various types of quantum errors are classified into several broad categories: (i) storage errors that occur in DNA itself as it represents an imperfect storage of genetic information, (ii) replication errors introduced during DNA replication process, (iii) transcription errors introduced during DNA to mRNA transcription, and (iv) translation errors introduced during the translation process. By using this model, we determine the biological quantum channel capacity and compare it against corresponding classical biological channel capacity. We demonstrate that the quantum biological channel capacity is higher than the classical one, for a coherent quantum channel model, suggesting that quantum effects have an important role in biological systems. The proposed model is of crucial importance towards future study of quantum DNA error correction, developing quantum mechanical model of aging, developing the quantum mechanical models for tumors/cancer, and study of intracellular dynamics in general.

An approach to quantum-computational hydrologic inverse analysis

DOE PAGES

O'Malley, Daniel

2018-05-02

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealermore » to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.« less

An approach to quantum-computational hydrologic inverse analysis.

PubMed

O'Malley, Daniel

2018-05-02

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealer to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.

An approach to quantum-computational hydrologic inverse analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

O'Malley, Daniel

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealermore » to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.« less

Quantum digital-to-analog conversion algorithm using decoherence

NASA Astrophysics Data System (ADS)

SaiToh, Akira

2015-08-01

We consider the problem of mapping digital data encoded on a quantum register to analog amplitudes in parallel. It is shown to be unlikely that a fully unitary polynomial-time quantum algorithm exists for this problem; NP becomes a subset of BQP if it exists. In the practical point of view, we propose a nonunitary linear-time algorithm using quantum decoherence. It tacitly uses an exponentially large physical resource, which is typically a huge number of identical molecules. Quantumness of correlation appearing in the process of the algorithm is also discussed.

Device-Independent Tests of Classical and Quantum Dimensions

NASA Astrophysics Data System (ADS)

Gallego, Rodrigo; Brunner, Nicolas; Hadley, Christopher; Acín, Antonio

2010-12-01

We address the problem of testing the dimensionality of classical and quantum systems in a “black-box” scenario. We develop a general formalism for tackling this problem. This allows us to derive lower bounds on the classical dimension necessary to reproduce given measurement data. Furthermore, we generalize the concept of quantum dimension witnesses to arbitrary quantum systems, allowing one to place a lower bound on the Hilbert space dimension necessary to reproduce certain data. Illustrating these ideas, we provide simple examples of classical and quantum dimension witnesses.

A different Deutsch-Jozsa

NASA Astrophysics Data System (ADS)

Bera, Debajyoti

2015-06-01

One of the early achievements of quantum computing was demonstrated by Deutsch and Jozsa (Proc R Soc Lond A Math Phys Sci 439(1907):553, 1992) regarding classification of a particular type of Boolean functions. Their solution demonstrated an exponential speedup compared to classical approaches to the same problem; however, their solution was the only known quantum algorithm for that specific problem so far. This paper demonstrates another quantum algorithm for the same problem, with the same exponential advantage compared to classical algorithms. The novelty of this algorithm is the use of quantum amplitude amplification, a technique that is the key component of another celebrated quantum algorithm developed by Grover (Proceedings of the twenty-eighth annual ACM symposium on theory of computing, ACM Press, New York, 1996). A lower bound for randomized (classical) algorithms is also presented which establishes a sound gap between the effectiveness of our quantum algorithm and that of any randomized algorithm with similar efficiency.

String theory, quantum phase transitions, and the emergent Fermi liquid.

PubMed

Cubrović, Mihailo; Zaanen, Jan; Schalm, Koenraad

2009-07-24

A central problem in quantum condensed matter physics is the critical theory governing the zero-temperature quantum phase transition between strongly renormalized Fermi liquids as found in heavy fermion intermetallics and possibly in high-critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the anti-de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid.

Optimal quantum cloning based on the maximin principle by using a priori information

NASA Astrophysics Data System (ADS)

Kang, Peng; Dai, Hong-Yi; Wei, Jia-Hua; Zhang, Ming

2016-10-01

We propose an optimal 1 →2 quantum cloning method based on the maximin principle by making full use of a priori information of amplitude and phase about the general cloned qubit input set, which is a simply connected region enclosed by a "longitude-latitude grid" on the Bloch sphere. Theoretically, the fidelity of the optimal quantum cloning machine derived from this method is the largest in terms of the maximin principle compared with that of any other machine. The problem solving is an optimization process that involves six unknown complex variables, six vectors in an uncertain-dimensional complex vector space, and four equality constraints. Moreover, by restricting the structure of the quantum cloning machine, the optimization problem is simplified as a three-real-parameter suboptimization problem with only one equality constraint. We obtain the explicit formula for a suboptimal quantum cloning machine. Additionally, the fidelity of our suboptimal quantum cloning machine is higher than or at least equal to that of universal quantum cloning machines and phase-covariant quantum cloning machines. It is also underlined that the suboptimal cloning machine outperforms the "belt quantum cloning machine" for some cases.

Quantum Metropolis sampling.

PubMed

Temme, K; Osborne, T J; Vollbrecht, K G; Poulin, D; Verstraete, F

2011-03-03

The original motivation to build a quantum computer came from Feynman, who imagined a machine capable of simulating generic quantum mechanical systems--a task that is believed to be intractable for classical computers. Such a machine could have far-reaching applications in the simulation of many-body quantum physics in condensed-matter, chemical and high-energy systems. Part of Feynman's challenge was met by Lloyd, who showed how to approximately decompose the time evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibbs states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm, a method that has basically acquired a monopoly on the simulation of interacting particles. Here we demonstrate how to implement a quantum version of the Metropolis algorithm. This algorithm permits sampling directly from the eigenstates of the Hamiltonian, and thus evades the sign problem present in classical simulations. A small-scale implementation of this algorithm should be achievable with today's technology.

Some Thoughts Regarding Practical Quantum Computing

NASA Astrophysics Data System (ADS)

Ghoshal, Debabrata; Gomez, Richard; Lanzagorta, Marco; Uhlmann, Jeffrey

2006-03-01

Quantum computing has become an important area of research in computer science because of its potential to provide more efficient algorithmic solutions to certain problems than are possible with classical computing. The ability of performing parallel operations over an exponentially large computational space has proved to be the main advantage of the quantum computing model. In this regard, we are particularly interested in the potential applications of quantum computers to enhance real software systems of interest to the defense, industrial, scientific and financial communities. However, while much has been written in popular and scientific literature about the benefits of the quantum computational model, several of the problems associated to the practical implementation of real-life complex software systems in quantum computers are often ignored. In this presentation we will argue that practical quantum computation is not as straightforward as commonly advertised, even if the technological problems associated to the manufacturing and engineering of large-scale quantum registers were solved overnight. We will discuss some of the frequently overlooked difficulties that plague quantum computing in the areas of memories, I/O, addressing schemes, compilers, oracles, approximate information copying, logical debugging, error correction and fault-tolerant computing protocols.

Quantum Corral Wave-function Engineering

NASA Astrophysics Data System (ADS)

Correa, Alfredo; Reboredo, Fernando; Balseiro, Carlos

2005-03-01

We present a theoretical method for the design and optimization of quantum corrals[1] with specific electronic properties. Taking advantage that spins are subject to a RKKY interaction that is directly controlled by the scattering of the quantum corral, we design corral structures that reproduce spin Hamiltonians with coupling constants determined a priori[2]. We solve exactly the bi-dimensional scattering problem for each corral configuration within the s-wave approximation[3] and subsequently the geometry of the quantum corral is optimized by means of simulated annealing[4] and genetic algorithms[5]. We demonstrate the possibility of automatic design of structures with complicated target electronic properties[6]. This work was performed under the auspices of the US Department of Energy by the University of California at the LLNL under contract no W-7405-Eng-48. [1] M. F. Crommie, C. P. Lutz and D. M. Eigler, Nature 403, 512 (2000) [2] D. P. DiVincenzo et al., Nature 408, 339 (2000) [3] G. A. Fiete and E. J. Heller, Rev. Mod. Phys. 75, 933 (2003) [4] M. R. A. T. N. Metropolis et al., J. Chem. Phys. 1087 (1953) [5] E. Aarts and J. K. Lenstra, eds. Local search in combinatorial problems (Princeton University Press, 1997) [6] A. A. Correa, F. Reboredo and C. Balseiro, Phys. Rev. B (in press).

Review of the inverse scattering problem at fixed energy in quantum mechanics

NASA Technical Reports Server (NTRS)

Sabatier, P. C.

1972-01-01

Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantum mechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.

Quantum mechanics and hidden superconformal symmetry

NASA Astrophysics Data System (ADS)

Bonezzi, R.; Corradini, O.; Latini, E.; Waldron, A.

2017-12-01

Solvability of the ubiquitous quantum harmonic oscillator relies on a spectrum generating osp (1 |2 ) superconformal symmetry. We study the problem of constructing all quantum mechanical models with a hidden osp (1 |2 ) symmetry on a given space of states. This problem stems from interacting higher spin models coupled to gravity. In one dimension, we show that the solution to this problem is the Vasiliev-Plyushchay family of quantum mechanical models with hidden superconformal symmetry obtained by viewing the harmonic oscillator as a one dimensional Dirac system, so that Grassmann parity equals wave function parity. These models—both oscillator and particlelike—realize all possible unitary irreducible representations of osp (1 |2 ).

Faster than classical quantum algorithm for dense formulas of exact satisfiability and occupation problems

NASA Astrophysics Data System (ADS)

Mandrà, Salvatore; Giacomo Guerreschi, Gian; Aspuru-Guzik, Alán

2016-07-01

We present an exact quantum algorithm for solving the Exact Satisfiability problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts: the first step consists in the identification and efficient characterization of a restricted subspace that contains all the valid assignments of the Exact Satisfiability; while the second part performs a quantum search in such restricted subspace. The quantum algorithm can be used either to find a valid assignment (or to certify that no solution exists) or to count the total number of valid assignments. The query complexities for the worst-case are respectively bounded by O(\\sqrt{{2}n-{M\\prime }}) and O({2}n-{M\\prime }), where n is the number of variables and {M}\\prime the number of linearly independent clauses. Remarkably, the proposed quantum algorithm results to be faster than any known exact classical algorithm to solve dense formulas of Exact Satisfiability. As a concrete application, we provide the worst-case complexity for the Hamiltonian cycle problem obtained after mapping it to a suitable Occupation problem. Specifically, we show that the time complexity for the proposed quantum algorithm is bounded by O({2}n/4) for 3-regular undirected graphs, where n is the number of nodes. The same worst-case complexity holds for (3,3)-regular bipartite graphs. As a reference, the current best classical algorithm has a (worst-case) running time bounded by O({2}31n/96). Finally, when compared to heuristic techniques for Exact Satisfiability problems, the proposed quantum algorithm is faster than the classical WalkSAT and Adiabatic Quantum Optimization for random instances with a density of constraints close to the satisfiability threshold, the regime in which instances are typically the hardest to solve. The proposed quantum algorithm can be straightforwardly extended to the generalized version of the Exact Satisfiability known as Occupation problem. The general version of the algorithm is presented and analyzed.

A position-dependent mass harmonic oscillator and deformed space

NASA Astrophysics Data System (ADS)

da Costa, Bruno G.; Borges, Ernesto P.

2018-04-01

We consider canonically conjugated generalized space and linear momentum operators x^ q and p^ q in quantum mechanics, associated with a generalized translation operator which produces infinitesimal deformed displacements controlled by a deformation parameter q. A canonical transformation (x ^ ,p ^ ) →(x^ q,p^ q ) leads the Hamiltonian of a position-dependent mass particle in usual space to another Hamiltonian of a particle with constant mass in a conservative force field of the deformed space. The equation of motion for the classical phase space (x, p) may be expressed in terms of the deformed (dual) q-derivative. We revisit the problem of a q-deformed oscillator in both classical and quantum formalisms. Particularly, this canonical transformation leads a particle with position-dependent mass in a harmonic potential to a particle with constant mass in a Morse potential. The trajectories in phase spaces (x, p) and (xq, pq) are analyzed for different values of the deformation parameter. Finally, we compare the results of the problem in classical and quantum formalisms through the principle of correspondence and the WKB approximation.

Error suppression and correction for quantum annealing

NASA Astrophysics Data System (ADS)

Lidar, Daniel

While adiabatic quantum computing and quantum annealing enjoy a certain degree of inherent robustness against excitations and control errors, there is no escaping the need for error correction or suppression. In this talk I will give an overview of our work on the development of such error correction and suppression methods. We have experimentally tested one such method combining encoding, energy penalties and decoding, on a D-Wave Two processor, with encouraging results. Mean field theory shows that this can be explained in terms of a softening of the closing of the gap due to the energy penalty, resulting in protection against excitations that occur near the quantum critical point. Decoding recovers population from excited states and enhances the success probability of quantum annealing. Moreover, we have demonstrated that using repetition codes with increasing code distance can lower the effective temperature of the annealer. References: K.L. Pudenz, T. Albash, D.A. Lidar, ``Error corrected quantum annealing with hundreds of qubits'', Nature Commun. 5, 3243 (2014). K.L. Pudenz, T. Albash, D.A. Lidar, ``Quantum annealing correction for random Ising problems'', Phys. Rev. A. 91, 042302 (2015). S. Matsuura, H. Nishimori, T. Albash, D.A. Lidar, ``Mean Field Analysis of Quantum Annealing Correction''. arXiv:1510.07709. W. Vinci et al., in preparation.

A general method for controlling and resolving rotational orientation of molecules in molecule-surface collisions

PubMed Central

Godsi, Oded; Corem, Gefen; Alkoby, Yosef; Cantin, Joshua T.; Krems, Roman V.; Somers, Mark F.; Meyer, Jörg; Kroes, Geert-Jan; Maniv, Tsofar; Alexandrowicz, Gil

2017-01-01

The outcome of molecule–surface collisions can be modified by pre-aligning the molecule; however, experiments accomplishing this are rare because of the difficulty of preparing molecules in aligned quantum states. Here we present a general solution to this problem based on magnetic manipulation of the rotational magnetic moment of the incident molecule. We apply the technique to the scattering of H2 from flat and stepped copper surfaces. We demonstrate control of the molecule's initial quantum state, allowing a direct comparison of differences in the stereodynamic scattering from the two surfaces. Our results show that a stepped surface exhibits a much larger dependence of the corrugation of the interaction on the alignment of the molecule than the low-index surface. We also demonstrate an extension of the technique that transforms the set-up into an interferometer, which is sensitive to molecular quantum states both before and after the scattering event. PMID:28480890

Quantum annealing correction with minor embedding

NASA Astrophysics Data System (ADS)

Vinci, Walter; Albash, Tameem; Paz-Silva, Gerardo; Hen, Itay; Lidar, Daniel A.

2015-10-01

Quantum annealing provides a promising route for the development of quantum optimization devices, but the usefulness of such devices will be limited in part by the range of implementable problems as dictated by hardware constraints. To overcome constraints imposed by restricted connectivity between qubits, a larger set of interactions can be approximated using minor embedding techniques whereby several physical qubits are used to represent a single logical qubit. However, minor embedding introduces new types of errors due to its approximate nature. We introduce and study quantum annealing correction schemes designed to improve the performance of quantum annealers in conjunction with minor embedding, thus leading to a hybrid scheme defined over an encoded graph. We argue that this scheme can be efficiently decoded using an energy minimization technique provided the density of errors does not exceed the per-site percolation threshold of the encoded graph. We test the hybrid scheme using a D-Wave Two processor on problems for which the encoded graph is a two-level grid and the Ising model is known to be NP-hard. The problems we consider are frustrated Ising model problem instances with "planted" (a priori known) solutions. Applied in conjunction with optimized energy penalties and decoding techniques, we find that this approach enables the quantum annealer to solve minor embedded instances with significantly higher success probability than it would without error correction. Our work demonstrates that quantum annealing correction can and should be used to improve the robustness of quantum annealing not only for natively embeddable problems but also when minor embedding is used to extend the connectivity of physical devices.

Quantum probability and Hilbert's sixth problem

NASA Astrophysics Data System (ADS)

Accardi, Luigi

2018-04-01

With the birth of quantum mechanics, the two disciplines that Hilbert proposed to axiomatize, probability and mechanics, became entangled and a new probabilistic model arose in addition to the classical one. Thus, to meet Hilbert's challenge, an axiomatization should account deductively for the basic features of all three disciplines. This goal was achieved within the framework of quantum probability. The present paper surveys the quantum probabilistic axiomatization. This article is part of the themed issue `Hilbert's sixth problem'.

Entanglement and the fermion sign problem in auxiliary field quantum Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Broecker, Peter; Trebst, Simon

2016-08-01

Quantum Monte Carlo simulations of fermions are hampered by the notorious sign problem whose most striking manifestation is an exponential growth of sampling errors with the number of particles. With the sign problem known to be an NP-hard problem and any generic solution thus highly elusive, the Monte Carlo sampling of interacting many-fermion systems is commonly thought to be restricted to a small class of model systems for which a sign-free basis has been identified. Here we demonstrate that entanglement measures, in particular the so-called Rényi entropies, can intrinsically exhibit a certain robustness against the sign problem in auxiliary-field quantum Monte Carlo approaches and possibly allow for the identification of global ground-state properties via their scaling behavior even in the presence of a strong sign problem. We corroborate these findings via numerical simulations of fermionic quantum phase transitions of spinless fermions on the honeycomb lattice at and below half filling.

Colloquium: Non-Markovian dynamics in open quantum systems

NASA Astrophysics Data System (ADS)

Breuer, Heinz-Peter; Laine, Elsi-Mari; Piilo, Jyrki; Vacchini, Bassano

2016-04-01

The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry, and quantum information. In close analogy to a classical Markovian stochastic process, the interaction of an open quantum system with a noisy environment is often modeled phenomenologically by means of a dynamical semigroup with a corresponding time-independent generator in Lindblad form, which describes a memoryless dynamics of the open system typically leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence, correlations, and entanglement. Here recent theoretical results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of quantum memory effects. The general theory is illustrated by a series of physical examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely, to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This Colloquium further explores the various physical sources of non-Markovian quantum dynamics, such as structured environmental spectral densities, nonlocal correlations between environmental degrees of freedom, and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments addressing the detection, quantification, and control of non-Markovian quantum dynamics are also briefly discussed.

A Generalization of the Simultaneous Diagonalization of Hermitian Matrices and its Relation to Quantum Estimation Theory

NASA Astrophysics Data System (ADS)

Nagaoka, Hiroshi

We study the problem of minimizing a quadratic quantity defined for given two Hermitian matrices X, Y and a positive-definite Hermitian matrix. This problem is reduced to the simultaneous diagonalization of X, Y when XY = YX. We derive a lower bound for the quantity, and in some special cases solve the problem by showing that the lower bound is achievable. This problem is closely related to a simultaneous measurement of quantum mechanical observables which are not commuting and has an application in the theory of quantum state estimation.

Quantum Zeno Effect in the Measurement Problem

NASA Technical Reports Server (NTRS)

Namiki, Mikio; Pasaczio, Saverio

1996-01-01

Critically analyzing the so-called quantum Zeno effect in the measurement problem, we show that observation of this effect does not necessarily mean experimental evidence for the naive notion of wave-function collapse by measurement (the simple projection rule). We also examine what kind of limitation the uncertainty relation and others impose on the observation of the quantum Zeno effect.

Quantum Bio-Informatics II From Quantum Information to Bio-Informatics

NASA Astrophysics Data System (ADS)

Accardi, L.; Freudenberg, Wolfgang; Ohya, Masanori

2009-02-01

The problem of quantum-like representation in economy cognitive science, and genetics / L. Accardi, A. Khrennikov and M. Ohya -- Chaotic behavior observed in linea dynamics / M. Asano, T. Yamamoto and Y. Togawa -- Complete m-level quantum teleportation based on Kossakowski-Ohya scheme / M. Asano, M. Ohya and Y. Tanaka -- Towards quantum cybernetics: optimal feedback control in quantum bio informatics / V. P. Belavkin -- Quantum entanglement and circulant states / D. Chruściński -- The compound Fock space and its application in brain models / K. -H. Fichtner and W. Freudenberg -- Characterisation of beam splitters / L. Fichtner and M. Gäbler -- Application of entropic chaos degree to a combined quantum baker's map / K. Inoue, M. Ohya and I. V. Volovich -- On quantum algorithm for multiple alignment of amino acid sequences / S. Iriyama and M. Ohya --Quantum-like models for decision making in psychology and cognitive science / A. Khrennikov -- On completely positive non-Markovian evolution of a d-level system / A. Kossakowski and R. Rebolledo -- Measures of entanglement - a Hilbert space approach / W. A. Majewski -- Some characterizations of PPT states and their relation / T. Matsuoka -- On the dynamics of entanglement and characterization ofentangling properties of quantum evolutions / M. Michalski -- Perspective from micro-macro duality - towards non-perturbative renormalization scheme / I. Ojima -- A simple symmetric algorithm using a likeness with Introns behavior in RNA sequences / M. Regoli -- Some aspects of quadratic generalized white noise functionals / Si Si and T. Hida -- Analysis of several social mobility data using measure of departure from symmetry / K. Tahata ... [et al.] -- Time in physics and life science / I. V. Volovich -- Note on entropies in quantum processes / N. Watanabe -- Basics of molecular simulation and its application to biomolecules / T. Ando and I. Yamato -- Theory of proton-induced superionic conduction in hydrogen-bonded systems / H. Kamimura -- Massive collection of full-length complementary DNA clones and microarray analyses: keys to rice transcriptome analysis / S. Kikuchi -- Changes of influenza A(H5) viruses by means of entropic chaos degree / K. Sato and M. Ohya -- Basics of genome sequence analysis in bioinformatics - its fundamental ideas and problems / T. Suzuki and S. Miyazaki -- A basic introduction to gene expression studies using microarray expression data analysis / D. Wanke and J. Kilian -- Integrating biological perspectives: a quantum leap for microarray expression analysis / D. Wanke ... [et al.].

Improving security of the ping-pong protocol

NASA Astrophysics Data System (ADS)

Zawadzki, Piotr

2013-01-01

A security layer for the asymptotically secure ping-pong protocol is proposed and analyzed in the paper. The operation of the improvement exploits inevitable errors introduced by the eavesdropping in the control and message modes. Its role is similar to the privacy amplification algorithms known from the quantum key distribution schemes. Messages are processed in blocks which guarantees that an eavesdropper is faced with a computationally infeasible problem as long as the system parameters are within reasonable limits. The introduced additional information preprocessing does not require quantum memory registers and confidential communication is possible without prior key agreement or some shared secret.

Relativistic particle in a box: Klein-Gordon versus Dirac equations

NASA Astrophysics Data System (ADS)

Alberto, Pedro; Das, Saurya; Vagenas, Elias C.

2018-03-01

The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantised energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one- and three-dimensional box using the Klein-Gordon equation in the Feshbach-Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect.

Robust quantum optimizer with full connectivity

PubMed Central

Nigg, Simon E.; Lörch, Niels; Tiwari, Rakesh P.

2017-01-01

Quantum phenomena have the potential to speed up the solution of hard optimization problems. For example, quantum annealing, based on the quantum tunneling effect, has recently been shown to scale exponentially better with system size than classical simulated annealing. However, current realizations of quantum annealers with superconducting qubits face two major challenges. First, the connectivity between the qubits is limited, excluding many optimization problems from a direct implementation. Second, decoherence degrades the success probability of the optimization. We address both of these shortcomings and propose an architecture in which the qubits are robustly encoded in continuous variable degrees of freedom. By leveraging the phenomenon of flux quantization, all-to-all connectivity with sufficient tunability to implement many relevant optimization problems is obtained without overhead. Furthermore, we demonstrate the robustness of this architecture by simulating the optimal solution of a small instance of the nondeterministic polynomial-time hard (NP-hard) and fully connected number partitioning problem in the presence of dissipation. PMID:28435880

Experimental quantum annealing: case study involving the graph isomorphism problem.

PubMed

Zick, Kenneth M; Shehab, Omar; French, Matthew

2015-06-08

Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N(2) to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers.

Experimental quantum annealing: case study involving the graph isomorphism problem

PubMed Central

Zick, Kenneth M.; Shehab, Omar; French, Matthew

2015-01-01

Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N2 to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers. PMID:26053973

Quantum-enhanced reinforcement learning for finite-episode games with discrete state spaces

NASA Astrophysics Data System (ADS)

Neukart, Florian; Von Dollen, David; Seidel, Christian; Compostella, Gabriele

2017-12-01

Quantum annealing algorithms belong to the class of metaheuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum annealing machines produced by D-Wave Systems, have been subject to multiple analyses in research, with the aim of characterizing the technology's usefulness for optimization and sampling tasks. Here, we present a way to partially embed both Monte Carlo policy iteration for finding an optimal policy on random observations, as well as how to embed n sub-optimal state-value functions for approximating an improved state-value function given a policy for finite horizon games with discrete state spaces on a D-Wave 2000Q quantum processing unit (QPU). We explain how both problems can be expressed as a quadratic unconstrained binary optimization (QUBO) problem, and show that quantum-enhanced Monte Carlo policy evaluation allows for finding equivalent or better state-value functions for a given policy with the same number episodes compared to a purely classical Monte Carlo algorithm. Additionally, we describe a quantum-classical policy learning algorithm. Our first and foremost aim is to explain how to represent and solve parts of these problems with the help of the QPU, and not to prove supremacy over every existing classical policy evaluation algorithm.

Elucidating reaction mechanisms on quantum computers.

PubMed

Reiher, Markus; Wiebe, Nathan; Svore, Krysta M; Wecker, Dave; Troyer, Matthias

2017-07-18

With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.

Elucidating reaction mechanisms on quantum computers

PubMed Central

Reiher, Markus; Wiebe, Nathan; Svore, Krysta M.; Wecker, Dave; Troyer, Matthias

2017-01-01

With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources. PMID:28674011

An Introduction to Multi-player, Multi-choice Quantum Games: Quantum Minority Games & Kolkata Restaurant Problems

NASA Astrophysics Data System (ADS)

Sharif, Puya; Heydari, Hoshang

We give a self contained introduction to a few quantum game protocols, starting with the quantum version of the two-player two-choice game of Prisoners dilemma, followed by an n-player generalization trough the quantum minority games, and finishing with a contribution towards an n-player m-choice generalization with a quantum version of a three-player Kolkata restaurant problem. We have omitted some technical details accompanying these protocols, and instead laid the focus on presenting some general aspects of the field as a whole. This review contains an introduction to the formalism of quantum information theory, as well as to important game theoretical concepts, and is aimed to work as a review suiting economists and game theorists with limited knowledge of quantum physics as well as to physicists with limited knowledge of game theory.

Elucidating reaction mechanisms on quantum computers

NASA Astrophysics Data System (ADS)

Reiher, Markus; Wiebe, Nathan; Svore, Krysta M.; Wecker, Dave; Troyer, Matthias

2017-07-01

With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.

Dynamics of a Landau-Zener non-dissipative system with fluctuating energy levels

NASA Astrophysics Data System (ADS)

Fai, L. C.; Diffo, J. T.; Ateuafack, M. E.; Tchoffo, M.; Fouokeng, G. C.

2014-12-01

This paper considers a Landau-Zener (two-level) system influenced by a three-dimensional Gaussian and non-Gaussian coloured noise and finds a general form of the time dependent diabatic quantum bit (qubit) flip transition probabilities in the fast, intermediate and slow noise limits. The qubit flip probability is observed to mimic (for low-frequencies noise) that of the standard LZ problem. The qubit flip probability is also observed to be the measure of quantum coherence of states. The transition probability is observed to be tailored by non-Gaussian low-frequency noise and otherwise by Gaussian low-frequency coloured noise. Intermediate and fast noise limits are observed to alter the memory of the system in time and found to improve and control quantum information processing.

Performance of quantum annealing on random Ising problems implemented using the D-Wave Two

NASA Astrophysics Data System (ADS)

Wang, Zhihui; Job, Joshua; Rønnow, Troels F.; Troyer, Matthias; Lidar, Daniel A.; USC Collaboration; ETH Collaboration

2014-03-01

Detecting a possible speedup of quantum annealing compared to classical algorithms is a pressing task in experimental adiabatic quantum computing. In this talk, we discuss the performance of the D-Wave Two quantum annealing device on Ising spin glass problems. The expected time to solution for the device to solve random instances with up to 503 spins and with specified coupling ranges is evaluated while carefully addressing the issue of statistical errors. We perform a systematic comparison of the expected time to solution between the D-Wave Two and classical stochastic solvers, specifically simulated annealing, and simulated quantum annealing based on quantum Monte Carlo, and discuss the question of speedup.

Strange Bedfellows: Quantum Mechanics and Data Mining

NASA Astrophysics Data System (ADS)

Weinstein, Marvin

2010-02-01

Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.

Optimum testing of multiple hypotheses in quantum detection theory

NASA Technical Reports Server (NTRS)

Yuen, H. P.; Kennedy, R. S.; Lax, M.

1975-01-01

The problem of specifying the optimum quantum detector in multiple hypotheses testing is considered for application to optical communications. The quantum digital detection problem is formulated as a linear programming problem on an infinite-dimensional space. A necessary and sufficient condition is derived by the application of a general duality theorem specifying the optimum detector in terms of a set of linear operator equations and inequalities. Existence of the optimum quantum detector is also established. The optimality of commuting detection operators is discussed in some examples. The structure and performance of the optimal receiver are derived for the quantum detection of narrow-band coherent orthogonal and simplex signals. It is shown that modal photon counting is asymptotically optimum in the limit of a large signaling alphabet and that the capacity goes to infinity in the absence of a bandwidth limitation.

Quantum-Enhanced Machine Learning

NASA Astrophysics Data System (ADS)

Dunjko, Vedran; Taylor, Jacob M.; Briegel, Hans J.

2016-09-01

The emerging field of quantum machine learning has the potential to substantially aid in the problems and scope of artificial intelligence. This is only enhanced by recent successes in the field of classical machine learning. In this work we propose an approach for the systematic treatment of machine learning, from the perspective of quantum information. Our approach is general and covers all three main branches of machine learning: supervised, unsupervised, and reinforcement learning. While quantum improvements in supervised and unsupervised learning have been reported, reinforcement learning has received much less attention. Within our approach, we tackle the problem of quantum enhancements in reinforcement learning as well, and propose a systematic scheme for providing improvements. As an example, we show that quadratic improvements in learning efficiency, and exponential improvements in performance over limited time periods, can be obtained for a broad class of learning problems.

Recall Performance for Content-Addressable Memory Using Adiabatic Quantum Optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Imam, Neena; Humble, Travis S.; McCaskey, Alex

A content-addressable memory (CAM) stores key-value associations such that the key is recalled by providing its associated value. While CAM recall is traditionally performed using recurrent neural network models, we show how to solve this problem using adiabatic quantum optimization. Our approach maps the recurrent neural network to a commercially available quantum processing unit by taking advantage of the common underlying Ising spin model. We then assess the accuracy of the quantum processor to store key-value associations by quantifying recall performance against an ensemble of problem sets. We observe that different learning rules from the neural network community influence recallmore » accuracy but performance appears to be limited by potential noise in the processor. The strong connection established between quantum processors and neural network problems supports the growing intersection of these two ideas.« less

Connes' embedding problem and winning strategies for quantum XOR games

NASA Astrophysics Data System (ADS)

Harris, Samuel J.

2017-12-01

We consider quantum XOR games, defined in the work of Regev and Vidick [ACM Trans. Comput. Theory 7, 43 (2015)], from the perspective of unitary correlations defined in the work of Harris and Paulsen [Integr. Equations Oper. Theory 89, 125 (2017)]. We show that the winning bias of a quantum XOR game in the tensor product model (respectively, the commuting model) is equal to the norm of its associated linear functional on the unitary correlation set from the appropriate model. We show that Connes' embedding problem has a positive answer if and only if every quantum XOR game has entanglement bias equal to the commuting bias. In particular, the embedding problem is equivalent to determining whether every quantum XOR game G with a winning strategy in the commuting model also has a winning strategy in the approximate finite-dimensional model.

Quantum-Inspired Maximizer

NASA Technical Reports Server (NTRS)

Zak, Michail

2008-01-01

A report discusses an algorithm for a new kind of dynamics based on a quantum- classical hybrid-quantum-inspired maximizer. The model is represented by a modified Madelung equation in which the quantum potential is replaced by different, specially chosen 'computational' potential. As a result, the dynamics attains both quantum and classical properties: it preserves superposition and entanglement of random solutions, while allowing one to measure its state variables, using classical methods. Such optimal combination of characteristics is a perfect match for quantum-inspired computing. As an application, an algorithm for global maximum of an arbitrary integrable function is proposed. The idea of the proposed algorithm is very simple: based upon the Quantum-inspired Maximizer (QIM), introduce a positive function to be maximized as the probability density to which the solution is attracted. Then the larger value of this function will have the higher probability to appear. Special attention is paid to simulation of integer programming and NP-complete problems. It is demonstrated that the problem of global maximum of an integrable function can be found in polynomial time by using the proposed quantum- classical hybrid. The result is extended to a constrained maximum with applications to integer programming and TSP (Traveling Salesman Problem).

Semiclassical approach to finite-temperature quantum annealing with trapped ions

NASA Astrophysics Data System (ADS)

Raventós, David; Graß, Tobias; Juliá-Díaz, Bruno; Lewenstein, Maciej

2018-05-01

Recently it has been demonstrated that an ensemble of trapped ions may serve as a quantum annealer for the number-partitioning problem [Nat. Commun. 7, 11524 (2016), 10.1038/ncomms11524]. This hard computational problem may be addressed by employing a tunable spin-glass architecture. Following the proposal of the trapped-ion annealer, we study here its robustness against thermal effects; that is, we investigate the role played by thermal phonons. For the efficient description of the system, we use a semiclassical approach, and benchmark it against the exact quantum evolution. The aim is to understand better and characterize how the quantum device approaches a solution of an otherwise difficult to solve NP-hard problem.

XY vs X Mixer in Quantum Alternating Operator Ansatz for Optimization Problems with Constraints

NASA Technical Reports Server (NTRS)

Wang, Zhihui; Rubin, Nicholas; Rieffel, Eleanor G.

2018-01-01

Quantum Approximate Optimization Algorithm, further generalized as Quantum Alternating Operator Ansatz (QAOA), is a family of algorithms for combinatorial optimization problems. It is a leading candidate to run on emerging universal quantum computers to gain insight into quantum heuristics. In constrained optimization, penalties are often introduced so that the ground state of the cost Hamiltonian encodes the solution (a standard practice in quantum annealing). An alternative is to choose a mixing Hamiltonian such that the constraint corresponds to a constant of motion and the quantum evolution stays in the feasible subspace. Better performance of the algorithm is speculated due to a much smaller search space. We consider problems with a constant Hamming weight as the constraint. We also compare different methods of generating the generalized W-state, which serves as a natural initial state for the Hamming-weight constraint. Using graph-coloring as an example, we compare the performance of using XY model as a mixer that preserves the Hamming weight with the performance of adding a penalty term in the cost Hamiltonian.

Preserving electron spin coherence in solids by optimal dynamical decoupling.

PubMed

Du, Jiangfeng; Rong, Xing; Zhao, Nan; Wang, Ya; Yang, Jiahui; Liu, R B

2009-10-29

To exploit the quantum coherence of electron spins in solids in future technologies such as quantum computing, it is first vital to overcome the problem of spin decoherence due to their coupling to the noisy environment. Dynamical decoupling, which uses stroboscopic spin flips to give an average coupling to the environment that is effectively zero, is a particularly promising strategy for combating decoherence because it can be naturally integrated with other desired functionalities, such as quantum gates. Errors are inevitably introduced in each spin flip, so it is desirable to minimize the number of control pulses used to realize dynamical decoupling having a given level of precision. Such optimal dynamical decoupling sequences have recently been explored. The experimental realization of optimal dynamical decoupling in solid-state systems, however, remains elusive. Here we use pulsed electron paramagnetic resonance to demonstrate experimentally optimal dynamical decoupling for preserving electron spin coherence in irradiated malonic acid crystals at temperatures from 50 K to room temperature. Using a seven-pulse optimal dynamical decoupling sequence, we prolonged the spin coherence time to about 30 mus; it would otherwise be about 0.04 mus without control or 6.2 mus under one-pulse control. By comparing experiments with microscopic theories, we have identified the relevant electron spin decoherence mechanisms in the solid. Optimal dynamical decoupling may be applied to other solid-state systems, such as diamonds with nitrogen-vacancy centres, and so lay the foundation for quantum coherence control of spins in solids at room temperature.

The Quantum Binding Problem in the Context of Associative Memory

PubMed Central

Wichert, Andreas

2016-01-01

We present a method to solve the binding problem by using a quantum algorithm for the retrieval of associations from associative memory during visual scene analysis. The problem is solved by mapping the information representing different objects into superposition by using entanglement and Grover’s amplification algorithm. PMID:27603782

Protecting software agents from malicious hosts using quantum computing

NASA Astrophysics Data System (ADS)

Reisner, John; Donkor, Eric

2000-07-01

We evaluate how quantum computing can be applied to security problems for software agents. Agent-based computing, which merges technological advances in artificial intelligence and mobile computing, is a rapidly growing domain, especially in applications such as electronic commerce, network management, information retrieval, and mission planning. System security is one of the more eminent research areas in agent-based computing, and the specific problem of protecting a mobile agent from a potentially hostile host is one of the most difficult of these challenges. In this work, we describe our agent model, and discuss the capabilities and limitations of classical solutions to the malicious host problem. Quantum computing may be extremely helpful in addressing the limitations of classical solutions to this problem. This paper highlights some of the areas where quantum computing could be applied to agent security.

Quantum simulation of the integer factorization problem: Bell states in a Penning trap

NASA Astrophysics Data System (ADS)

Rosales, Jose Luis; Martin, Vicente

2018-03-01

The arithmetic problem of factoring an integer N can be translated into the physics of a quantum device, a result that supports Pólya's and Hilbert's conjecture to demonstrate Riemann's hypothesis. The energies of this system, being univocally related to the factors of N , are the eigenvalues of a bounded Hamiltonian. Here we solve the quantum conditions and show that the histogram of the discrete energies, provided by the spectrum of the system, should be interpreted in number theory as the relative probability for a prime to be a factor candidate of N . This is equivalent to a quantum sieve that is shown to require only o (ln√{N}) 3 energy measurements to solve the problem, recovering Shor's complexity result. Hence the outcome can be seen as a probability map that a pair of primes solve the given factorization problem. Furthermore, we show that a possible embodiment of this quantum simulator corresponds to two entangled particles in a Penning trap. The possibility to build the simulator experimentally is studied in detail. The results show that factoring numbers, many orders of magnitude larger than those computed with experimentally available quantum computers, is achievable using typical parameters in Penning traps.

Inexact trajectory planning and inverse problems in the Hamilton–Pontryagin framework

PubMed Central

Burnett, Christopher L.; Holm, Darryl D.; Meier, David M.

2013-01-01

We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control, motivated by potential applications in computational anatomy and quantum control. Reduction by symmetry in such problems naturally summons methods from Lie group theory and Riemannian geometry. A geometrically illuminating form of the Euler–Lagrange equations is obtained from a higher-order Hamilton–Pontryagin variational formulation. In this context, the previously known node equations are recovered with a new interpretation as Legendre–Ostrogradsky momenta possessing certain conservation properties. Three example applications are discussed as well as a numerical integration scheme that follows naturally from the Hamilton–Pontryagin principle and preserves the geometric properties of the continuous-time solution. PMID:24353467

Quo vadis: Hydrologic inverse analyses using high-performance computing and a D-Wave quantum annealer

NASA Astrophysics Data System (ADS)

O'Malley, D.; Vesselinov, V. V.

2017-12-01

Classical microprocessors have had a dramatic impact on hydrology for decades, due largely to the exponential growth in computing power predicted by Moore's law. However, this growth is not expected to continue indefinitely and has already begun to slow. Quantum computing is an emerging alternative to classical microprocessors. Here, we demonstrated cutting edge inverse model analyses utilizing some of the best available resources in both worlds: high-performance classical computing and a D-Wave quantum annealer. The classical high-performance computing resources are utilized to build an advanced numerical model that assimilates data from O(10^5) observations, including water levels, drawdowns, and contaminant concentrations. The developed model accurately reproduces the hydrologic conditions at a Los Alamos National Laboratory contamination site, and can be leveraged to inform decision-making about site remediation. We demonstrate the use of a D-Wave 2X quantum annealer to solve hydrologic inverse problems. This work can be seen as an early step in quantum-computational hydrology. We compare and contrast our results with an early inverse approach in classical-computational hydrology that is comparable to the approach we use with quantum annealing. Our results show that quantum annealing can be useful for identifying regions of high and low permeability within an aquifer. While the problems we consider are small-scale compared to the problems that can be solved with modern classical computers, they are large compared to the problems that could be solved with early classical CPUs. Further, the binary nature of the high/low permeability problem makes it well-suited to quantum annealing, but challenging for classical computers.

Effective optimization using sample persistence: A case study on quantum annealers and various Monte Carlo optimization methods

NASA Astrophysics Data System (ADS)

Karimi, Hamed; Rosenberg, Gili; Katzgraber, Helmut G.

2017-10-01

We present and apply a general-purpose, multistart algorithm for improving the performance of low-energy samplers used for solving optimization problems. The algorithm iteratively fixes the value of a large portion of the variables to values that have a high probability of being optimal. The resulting problems are smaller and less connected, and samplers tend to give better low-energy samples for these problems. The algorithm is trivially parallelizable since each start in the multistart algorithm is independent, and could be applied to any heuristic solver that can be run multiple times to give a sample. We present results for several classes of hard problems solved using simulated annealing, path-integral quantum Monte Carlo, parallel tempering with isoenergetic cluster moves, and a quantum annealer, and show that the success metrics and the scaling are improved substantially. When combined with this algorithm, the quantum annealer's scaling was substantially improved for native Chimera graph problems. In addition, with this algorithm the scaling of the time to solution of the quantum annealer is comparable to the Hamze-de Freitas-Selby algorithm on the weak-strong cluster problems introduced by Boixo et al. Parallel tempering with isoenergetic cluster moves was able to consistently solve three-dimensional spin glass problems with 8000 variables when combined with our method, whereas without our method it could not solve any.

Quantum cryptography and applications in the optical fiber network

NASA Astrophysics Data System (ADS)

Luo, Yuhui

2005-09-01

Quantum cryptography, as part of quantum information and communications, can provide absolute security for information transmission because it is established on the fundamental laws of quantum theory, such as the principle of uncertainty, No-cloning theorem and quantum entanglement. In this thesis research, a novel scheme to implement quantum key distribution based on multiphoton entanglement with a new protocol is proposed. Its advantages are: a larger information capacity can be obtained with a longer transmission distance and the detection of multiple photons is easier than that of a single photon. The security and attacks pertaining to such a system are also studied. Next, a quantum key distribution over wavelength division multiplexed (WDM) optical fiber networks is realized. Quantum key distribution in networks is a long-standing problem for practical applications. Here we combine quantum cryptography and WDM to solve this problem because WDM technology is universally deployed in the current and next generation fiber networks. The ultimate target is to deploy quantum key distribution over commercial networks. The problems arising from the networks are also studied in this part. Then quantum key distribution in multi-access networks using wavelength routing technology is investigated in this research. For the first time, quantum cryptography for multiple individually targeted users has been successfully implemented in sharp contrast to that using the indiscriminating broadcasting structure. It overcomes the shortcoming that every user in the network can acquire the quantum key signals intended to be exchanged between only two users. Furthermore, a more efficient scheme of quantum key distribution is adopted, hence resulting in a higher key rate. Lastly, a quantum random number generator based on quantum optics has been experimentally demonstrated. This device is a key component for quantum key distribution as it can create truly random numbers, which is an essential requirement to perform quantum key distribution. This new generator is composed of a single optical fiber coupler with fiber pigtails, which can be easily used in optical fiber communications.

An Early Quantum Computing Proposal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Stephen Russell; Alexander, Francis Joseph; Barros, Kipton Marcos

The D-Wave 2X is the third generation of quantum processing created by D-Wave. NASA (with Google and USRA) and Lockheed Martin (with USC), both own D-Wave systems. Los Alamos National Laboratory (LANL) purchased a D-Wave 2X in November 2015. The D-Wave 2X processor contains (nominally) 1152 quantum bits (or qubits) and is designed to specifically perform quantum annealing, which is a well-known method for finding a global minimum of an optimization problem. This methodology is based on direct execution of a quantum evolution in experimental quantum hardware. While this can be a powerful method for solving particular kinds of problems,more » it also means that the D-Wave 2X processor is not a general computing processor and cannot be programmed to perform a wide variety of tasks. It is a highly specialized processor, well beyond what NNSA currently thinks of as an “advanced architecture.”A D-Wave is best described as a quantum optimizer. That is, it uses quantum superposition to find the lowest energy state of a system by repeated doses of power and settling stages. The D-Wave produces multiple solutions to any suitably formulated problem, one of which is the lowest energy state solution (global minimum). Mapping problems onto the D-Wave requires defining an objective function to be minimized and then encoding that function in the Hamiltonian of the D-Wave system. The quantum annealing method is then used to find the lowest energy configuration of the Hamiltonian using the current D-Wave Two, two-level, quantum processor. This is not always an easy thing to do, and the D-Wave Two has significant limitations that restrict problem sizes that can be run and algorithmic choices that can be made. Furthermore, as more people are exploring this technology, it has become clear that it is very difficult to come up with general approaches to optimization that can both utilize the D-Wave and that can do better than highly developed algorithms on conventional computers for specific applications. These are all fundamental challenges that must be overcome for the D-Wave, or similar, quantum computing technology to be broadly applicable.« less

Bose-Einstein Condensation and Bose Glasses in an S = 1 Organo-metallic quantum magnet

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zapf, Vivien

2012-06-01

I will speak about Bose-Einstein condensation (BEC) in quantum magnets, in particular the compound NiCl2-4SC(NH2)2. Here a magnetic field-induced quantum phase transition to XY antiferromagnetism can be mapped onto BEC of the spins. The tuning parameter for BEC transition is the magnetic field rather than the temperature. Some interesting phenomena arise, for example the fact that the mass of the bosons that condense can be strongly renormalized by quantum fluctuations. I will discuss the utility of this mapping for both understanding the nature of the quantum magnetism and testing the thermodynamic limit of Bose-Einstein Condensation. Furthermore we can dope themore » system in a clean and controlled way to create the long sought-after Bose Glass transition, which is the bosonic analogy of Anderson localization. I will present experiments and simulations showing evidence for a new scaling exponent, which finally makes contact between theory and experiments. Thus we take a small step towards the difficult problem of understanding the effect of disorder on bosonic wave functions.« less

Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning

NASA Technical Reports Server (NTRS)

Smelyanskiy, V. N.; Toussaint, U. V.; Timucin, D. A.

2002-01-01

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap. g min, = O(n 2(exp -n/2), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to 'the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.

Space and time in the quantum universe.

NASA Astrophysics Data System (ADS)

Smolin, L.

This paper is devoted to the problem of constructing a quantum theory that could describe a closed system - a quantum cosmology. The author argues that this problem is an aspect of a much older problem - that of how to eliminate from the physical theories "ideal elements", which are elements of the mathematical structure whose interpretation requires the existence of things outside the dynamical system described by the theory. This discussion is aimed at uncovering criteria that a theory of quantum cosmology must satisfy, if it is to give physically sensible predictions. The author proposes three such criteria and shows that conventional quantum cosmology can only satisfy them, if there is an intrinsic time coordinate on the phase space of the theory. It is shown that approaches based on correlations in the wave function, that do not use an inner product, cannot satisfy these criteria. As example, the author discusses the problem of quantizing a class of relational dynamical models invented by Barbour and Bertotti. The dynamical structure of these theories is closely analogous to general relativity, and the problem of their measurement theory is also similar. It is concluded that these theories can only be sensibly quantized if they contain an intrinsic time.

Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning

NASA Technical Reports Server (NTRS)

Smelyanskiy, Vadius; vonToussaint, Udo V.; Timucin, Dogan A.; Clancy, Daniel (Technical Monitor)

2002-01-01

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum exitation gap, gmin = O(n2(sup -n/2)), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.

Loop Quantum Gravity and Asymptotically Flat Spaces

NASA Astrophysics Data System (ADS)

Arnsdorf, Matthias

2002-12-01

Remarkable progress has been made in the field of non-perturbative (loop) quantum gravity in the last decade or so and it is now a rigorously defined kinematical theory (c.f. [5] for a review and references). We are now at the stage where physical applications of loop quantum gravity can be studied and used to provide checks for the consistency of the quantisation programme. Equally, old fundamental problems of canonical quantum gravity such as the problem of time or the interpretation of quantum cosmology need to be reevaluated seriously. These issues can be addressed most profitably in the asymptotically flat sector of quantum gravity. Indeed, it is likely that we should obtain a quantum theory for this special case even if it is not possible to quantise full general relativity. The purpose of this summary is to advertise the extension of loop quantum gravity to this sector that was developed in [1]...

Time-dependent perturbation of a two-state quantum mechanical system

NASA Technical Reports Server (NTRS)

Dion, D. R.

1974-01-01

A two- (nondegenerate) level quantum system interacting with a classical monochromatic radiation field is described. The existing work on this problem is reviewed and some novel aspects of the problems are presented.

Physics: Quantum problems solved through games

NASA Astrophysics Data System (ADS)

Maniscalco, Sabrina

2016-04-01

Humans are better than computers at performing certain tasks because of their intuition and superior visual processing. Video games are now being used to channel these abilities to solve problems in quantum physics. See Letter p.210

Generation of quantum entangled states in nonlinear plasmonic structures and metamaterials (Presentation Recording)

NASA Astrophysics Data System (ADS)

Poddubny, Alexander N.; Sukhorukov, Andrey A.

2015-09-01

The practical development of quantum plasmonic circuits incorporating non-classical interference [1] and sources of entangled states calls for a versatile quantum theoretical framework which can fully describe the generation and detection of entangled photons and plasmons. However, majority of the presently used theoretical approaches are typically limited to the toy models assuming loss-less and nondispersive elements or including just a few resonant modes. Here, we present a rigorous Green function approach describing entangled photon-plasmon state generation through spontaneous wave mixing in realistic metal-dielectric nanostructures. Our approach is based on the local Huttner-Barnett quantization scheme [2], which enables problem formulation in terms of a Hermitian Hamiltonian where the losses and dispersion are fully encoded in the electromagnetic Green functions. Hence, the problem can be addressed by the standard quantum mechanical perturbation theory, overcoming mathematical difficulties associated with other quantization schemes. We derive explicit expressions with clear physical meaning for the spatially dependent two-photon detection probability, single-photon detection probability and single-photon density matrix. In the limiting case of low-loss nondispersive waveguides our approach reproduces the previous results [3,4]. Importantly, our technique is far more general and can quantitatively describe generation and detection of spatially-entangled photons in arbitrary metal-dielectric structures taking into account actual losses and dispersion. This is essential to perform the design and optimization of plasmonic structures for generation and control of quantum entangled states. [1] J.S. Fakonas, H. Lee, Y.A. Kelaita and H.A. Atwater, Nature Photonics 8, 317(2014) [2] W. Vogel and D.-G. Welsch, Quantum Optics, Wiley (2006). [3] D.A. Antonosyan, A.S. Solntsev and A.A. Sukhorukov, Phys. Rev. A 90 043845 (2014) [4] L.-G. Helt, J.E. Sipe and M.J. Steel, arXiv: 1407.4219

Recent progress of quantum annealing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suzuki, Sei

2015-03-10

We review the recent progress of quantum annealing. Quantum annealing was proposed as a method to solve generic optimization problems. Recently a Canadian company has drawn a great deal of attention, as it has commercialized a quantum computer based on quantum annealing. Although the performance of quantum annealing is not sufficiently understood, it is likely that quantum annealing will be a practical method both on a conventional computer and on a quantum computer.

Quantum dice rolling: a multi-outcome generalization of quantum coin flipping

NASA Astrophysics Data System (ADS)

Aharon, N.; Silman, J.

2010-03-01

The problem of quantum dice rolling (DR)—a generalization of the problem of quantum coin flipping (CF) to more than two outcomes and parties—is studied in both its weak and strong variants. We prove by construction that quantum mechanics allows for (i) weak N-sided DR admitting arbitrarily small bias for any N and (ii) two-party strong N-sided DR saturating Kitaev's bound for any N. To derive (ii) we also prove by construction that quantum mechanics allows for (iii) strong imbalanced CF saturating Kitaev's bound for any degree of imbalance. Furthermore, as a corollary of (ii) we introduce a family of optimal 2m-party strong nm-sided DR protocols for any pair m and n.

Verifiable fault tolerance in measurement-based quantum computation

NASA Astrophysics Data System (ADS)

Fujii, Keisuke; Hayashi, Masahito

2017-09-01

Quantum systems, in general, cannot be simulated efficiently by a classical computer, and hence are useful for solving certain mathematical problems and simulating quantum many-body systems. This also implies, unfortunately, that verification of the output of the quantum systems is not so trivial, since predicting the output is exponentially hard. As another problem, the quantum system is very delicate for noise and thus needs an error correction. Here, we propose a framework for verification of the output of fault-tolerant quantum computation in a measurement-based model. In contrast to existing analyses on fault tolerance, we do not assume any noise model on the resource state, but an arbitrary resource state is tested by using only single-qubit measurements to verify whether or not the output of measurement-based quantum computation on it is correct. Verifiability is equipped by a constant time repetition of the original measurement-based quantum computation in appropriate measurement bases. Since full characterization of quantum noise is exponentially hard for large-scale quantum computing systems, our framework provides an efficient way to practically verify the experimental quantum error correction.

The "Hard Problem" and the Quantum Physicists. Part 1: The First Generation

ERIC Educational Resources Information Center

Smith, C. U. M.

2006-01-01

All four of the most important figures in the early twentieth-century development of quantum physics--Niels Bohr, Erwin Schroedinger, Werner Heisenberg and Wolfgang Pauli--had strong interests in the traditional mind--brain, or "hard," problem. This paper reviews their approach to this problem, showing the influence of Bohr's complementarity…

Replicating the benefits of Deutschian closed timelike curves without breaking causality

NASA Astrophysics Data System (ADS)

Yuan, Xiao; Assad, Syed M.; Thompson, Jayne; Haw, Jing Yan; Vedral, Vlatko; Ralph, Timothy C.; Lam, Ping Koy; Weedbrook, Christian; Gu, Mile

2015-11-01

In general relativity, closed timelike curves can break causality with remarkable and unsettling consequences. At the classical level, they induce causal paradoxes disturbing enough to motivate conjectures that explicitly prevent their existence. At the quantum level such problems can be resolved through the Deutschian formalism, however this induces radical benefits—from cloning unknown quantum states to solving problems intractable to quantum computers. Instinctively, one expects these benefits to vanish if causality is respected. Here we show that in harnessing entanglement, we can efficiently solve NP-complete problems and clone arbitrary quantum states—even when all time-travelling systems are completely isolated from the past. Thus, the many defining benefits of Deutschian closed timelike curves can still be harnessed, even when causality is preserved. Our results unveil a subtle interplay between entanglement and general relativity, and significantly improve the potential of probing the radical effects that may exist at the interface between relativity and quantum theory.

Probing for quantum speedup on D-Wave Two

NASA Astrophysics Data System (ADS)

Rønnow, Troels F.; Wang, Zhihui; Job, Joshua; Isakov, Sergei V.; Boixo, Sergio; Lidar, Daniel; Martinis, John; Troyer, Matthias

2014-03-01

Quantum speedup refers to the advantage quantum devices can have over classical ones in solving classes of computational problems. In this talk we show how to correctly define and measure quantum speedup in experimental devices. We show how to avoid issues that might mask or fake quantum speedup.

Hybrid Methods in Quantum Information

NASA Astrophysics Data System (ADS)

Marshall, Kevin

Today, the potential power of quantum information processing comes as no surprise to physicist or science-fiction writer alike. However, the grand promises of this field remain unrealized, despite significant strides forward, due to the inherent difficulties of manipulating quantum systems. Simply put, it turns out that it is incredibly difficult to interact, in a controllable way, with the quantum realm when we seem to live our day to day lives in a classical world. In an effort to solve this challenge, people are exploring a variety of different physical platforms, each with their strengths and weaknesses, in hopes of developing new experimental methods that one day might allow us to control a quantum system. One path forward rests in combining different quantum systems in novel ways to exploit the benefits of different systems while circumventing their respective weaknesses. In particular, quantum systems come in two different flavours: either discrete-variable systems or continuous-variable ones. The field of hybrid quantum information seeks to combine these systems, in clever ways, to help overcome the challenges blocking the path between what is theoretically possible and what is achievable in a laboratory. In this thesis we explore four topics in the context of hybrid methods in quantum information, in an effort to contribute to the resolution of existing challenges and to stimulate new avenues of research. First, we explore the manipulation of a continuous-variable quantum system consisting of phonons in a linear chain of trapped ions where we use the discretized internal levels to mediate interactions. Using our proposed interaction we are able to implement, for example, the acoustic equivalent of a beam splitter with modest experimental resources. Next we propose an experimentally feasible implementation of the cubic phase gate, a primitive non-Gaussian gate required for universal continuous-variable quantum computation, based off sequential photon subtraction. We then discuss the notion of embedding a finite dimensional state into a continuous-variable system, and propose a method of performing quantum computations on encrypted continuous-variable states. This protocol allows for a client, of limited quantum ability, to outsource a computation while hiding their information. Next, we discuss the possibility of performing universal quantum computation on discrete-variable logical states encoded in mixed continuous-variable quantum states. Finally, we present an account of open problems related to our results, and possible future avenues of research.

Composition in the Quantum World

NASA Astrophysics Data System (ADS)

Hall, Edward Jonathan

This thesis presents a problem for the foundations of quantum mechanics. It arises from the way that theory describes the composition of larger systems in terms of smaller ones, and renders untenable a wide range of interpretations of quantum mechanics. That quantum mechanics is difficult to interpret is old news, given the well-known Measurement Problem. But the problem I raise is quite different, and in important respects more fundamental. In brief: The physical world exhibits mereological structure: physical objects have parts, which in turn have parts, and so on. A natural way to try to represent this structure is by means of a particle theory, according to which the physical world consists entirely enduring physical objects which themselves have no proper parts, but aggregates of which are, or compose, all physical objects. Elementary, non-relativistic quantum mechanics can be cast in this mold--at least, according to the usual expositions of that theory. But herein lies the problem: the standard attempt to give a systematic particle interpretation to elementary quantum mechanics results in nonsense, thanks to the well-established principle of Permutation Invariance, which constrains the quantum -mechanical description of systems containing identical particles. Specifically, it follows from the most minimal principles of a particle interpretation (much weaker than those needed to generate the Measurement Problem), together with Permutation Invariance, that systems identical in composition must have the same physical state. In other words, systems which merely have the same numbers of the same types of particles are therefore, at all times, perfect physical duplicates. This conclusion is absurd: e.g., it is quite plausible that some of those particles which compose my body make up a system identical in composition to some pepperoni pizza. Yet no part of me is a qualitative physical duplicate of any pepperoni pizza. Perhaps "you are what you eat" --but not in this sense! In what follows I develop the principles needed to explore this problem, contrast it with the Measurement Problem, and consider, finally, how it should influence our judgments of the relative merits of the many extant interpretations of quantum mechanics.

Preface of the special issue quantum foundations: information approach

PubMed Central

2016-01-01

This special issue is based on the contributions of a group of top experts in quantum foundations and quantum information and probability. It enlightens a number of interpretational, mathematical and experimental problems of quantum theory. PMID:27091161

Dynamics of DNA breathing: weak noise analysis, finite time singularity, and mapping onto the quantum Coulomb problem.

PubMed

Fogedby, Hans C; Metzler, Ralf

2007-12-01

We study the dynamics of denaturation bubbles in double-stranded DNA on the basis of the Poland-Scheraga model. We show that long time distributions for the survival of DNA bubbles and the size autocorrelation function can be derived from an asymptotic weak noise approach. In particular, below the melting temperature the bubble closure corresponds to a noisy finite time singularity. We demonstrate that the associated Fokker-Planck equation is equivalent to a quantum Coulomb problem. Below the melting temperature, the bubble lifetime is associated with the continuum of scattering states of the repulsive Coulomb potential; at the melting temperature, the Coulomb potential vanishes and the underlying first exit dynamics exhibits a long time power law tail; above the melting temperature, corresponding to an attractive Coulomb potential, the long time dynamics is controlled by the lowest bound state. Correlations and finite size effects are discussed.

Resonant transition-based quantum computation

NASA Astrophysics Data System (ADS)

Chiang, Chen-Fu; Hsieh, Chang-Yu

2017-05-01

In this article we assess a novel quantum computation paradigm based on the resonant transition (RT) phenomenon commonly associated with atomic and molecular systems. We thoroughly analyze the intimate connections between the RT-based quantum computation and the well-established adiabatic quantum computation (AQC). Both quantum computing frameworks encode solutions to computational problems in the spectral properties of a Hamiltonian and rely on the quantum dynamics to obtain the desired output state. We discuss how one can adapt any adiabatic quantum algorithm to a corresponding RT version and the two approaches are limited by different aspects of Hamiltonians' spectra. The RT approach provides a compelling alternative to the AQC under various circumstances. To better illustrate the usefulness of the novel framework, we analyze the time complexity of an algorithm for 3-SAT problems and discuss straightforward methods to fine tune its efficiency.

Exotic Quantum Phases and Phase Transitions of Strongly Interacting Electrons in Low-Dimensional Systems

NASA Astrophysics Data System (ADS)

Mishmash, Ryan V.

Experiments on strongly correlated quasi-two-dimensional electronic materials---for example, the high-temperature cuprate superconductors and the putative quantum spin liquids kappa-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2---routinely reveal highly mysterious quantum behavior which cannot be explained in terms of weakly interacting degrees of freedom. Theoretical progress thus requires the introduction of completely new concepts and machinery beyond the traditional framework of the band theory of solids and its interacting counterpart, Landau's Fermi liquid theory. In full two dimensions, controlled and reliable analytical approaches to such problems are severely lacking, as are numerical simulations of even the simplest of model Hamiltonians due to the infamous fermionic sign problem. Here, we attempt to circumvent some of these difficulties by studying analogous problems in quasi-one dimension. In this lower dimensional setting, theoretical and numerical tractability are on much stronger footing due to the methods of bosonization and the density matrix renormalization group, respectively. Using these techniques, we attack two problems: (1) the Mott transition between a Fermi liquid metal and a quantum spin liquid as potentially directly relevant to the organic compounds kappa-(BEDT-TTF)2Cu 2(CN)3 and EtMe3Sb[Pd(dmit)2] 2 and (2) non-Fermi liquid metals as strongly motivated by the strange metal phase observed in the cuprates. In both cases, we are able to realize highly exotic quantum phases as ground states of reasonable microscopic models. This lends strong credence to respective underlying slave-particle descriptions of the low-energy physics, which are inherently strongly interacting and also unconventional in comparison to weakly interacting alternatives. Finally, working in two dimensions directly, we propose a new slave-particle theory which explains in a universal way many of the intriguing experimental results of the triangular lattice organic spin liquid candidates kappa-(BEDT-TTF) 2Cu2(CN)3 and EtMe3Sb[Pd(dmit) 2]2. With use of large-scale variational Monte Carlo calculations, we show that this new state has very competitive trial energy in an effective spin model thought to describe the essential features of the real materials.

Area-Preserving Diffeomorphisms, W∞ and { U}q [sl(2)] in Chern-Simons Theory and the Quantum Hall System

NASA Astrophysics Data System (ADS)

Kogan, Ian I.

We discuss a quantum { U}q [sl(2)] symmetry in the Landau problem, which naturally arises due to the relation between { U}q [sl(2)] and the group of magnetic translations. The latter is connected with W∞ and area-preserving (symplectic) diffeomorphisms which are the canonical transformations in the two-dimensional phase space. We shall discuss the hidden quantum symmetry in a 2 + 1 gauge theory with the Chern-Simons term and in a quantum Hall system, which are both connected with the Landau problem.

Quantum self-gravitating collapsing matter in a quantum geometry

NASA Astrophysics Data System (ADS)

Campiglia, Miguel; Gambini, Rodolfo; Olmedo, Javier; Pullin, Jorge

2016-09-01

The problem of how space-time responds to gravitating quantum matter in full quantum gravity has been one of the main questions that any program of quantization of gravity should address. Here we analyze this issue by considering the quantization of a collapsing null shell coupled to spherically symmetric loop quantum gravity. We show that the constraint algebra of canonical gravity is Abelian both classically and when quantized using loop quantum gravity techniques. The Hamiltonian constraint is well defined and suitable Dirac observables characterizing the problem were identified at the quantum level. We can write the metric as a parameterized Dirac observable at the quantum level and study the physics of the collapsing shell and black hole formation. We show how the singularity inside the black hole is eliminated by loop quantum gravity and how the shell can traverse it. The construction is compatible with a scenario in which the shell tunnels into a baby universe inside the black hole or one in which it could emerge through a white hole.

Emerging interpretations of quantum mechanics and recent progress in quantum measurement

NASA Astrophysics Data System (ADS)

Clarke, M. L.

2014-01-01

The focus of this paper is to provide a brief discussion on the quantum measurement process, by reviewing select examples highlighting recent progress towards its understanding. The areas explored include an outline of the measurement problem, the standard interpretation of quantum mechanics, quantum to classical transition, types of measurement (including weak and projective measurements) and newly emerging interpretations of quantum mechanics (decoherence theory, objective reality, quantum Darwinism and quantum Bayesianism).

Detection of Biochemical Pathogens, Laser Stand-off Spectroscopy, Quantum Coherence, and Many Body Quantum Optics

DTIC Science & Technology

2012-02-24

AND SUBTITLE Detection of Biochemical Pathogens, Laser Stand-off Spectroscopy, Quantum Coherence, and Many Body Quantum Optics 6. AUTHORS Marian O...Maximum 200 words) Results of our earlier research in the realm of quantum optics were extended in order to solve the challenging technical problems of...efficient methods of generating UV light via quantum coherence. 14. SUBJECT TERMS Quantum coherence, quantum optics, lasers 15. NUMBER OF PAGES 15

Discrete-time Quantum Walks via Interchange Framework and Memory in Quantum Evolution

NASA Astrophysics Data System (ADS)

Dimcovic, Zlatko

One of the newer and rapidly developing approaches in quantum computing is based on "quantum walks," which are quantum processes on discrete space that evolve in either discrete or continuous time and are characterized by mixing of components at each step. The idea emerged in analogy with the classical random walks and stochastic techniques, but these unitary processes are very different even as they have intriguing similarities. This thesis is concerned with study of discrete-time quantum walks. The original motivation from classical Markov chains required for discrete-time quantum walks that one adds an auxiliary Hilbert space, unrelated to the one in which the system evolves, in order to be able to mix components in that space and then take the evolution steps accordingly (based on the state in that space). This additional, "coin," space is very often an internal degree of freedom like spin. We have introduced a general framework for construction of discrete-time quantum walks in a close analogy with the classical random walks with memory that is rather different from the standard "coin" approach. In this method there is no need to bring in a different degree of freedom, while the full state of the system is still described in the direct product of spaces (of states). The state can be thought of as an arrow pointing from the previous to the current site in the evolution, representing the one-step memory. The next step is then controlled by a single local operator assigned to each site in the space, acting quite like a scattering operator. This allows us to probe and solve some problems of interest that have not had successful approaches with "coined" walks. We construct and solve a walk on the binary tree, a structure of great interest but until our result without an explicit discrete time quantum walk, due to difficulties in managing coin spaces necessary in the standard approach. Beyond algorithmic interests, the model based on memory allows one to explore effects of history on the quantum evolution and the subtle emergence of classical features as "memory" is explicitly kept for additional steps. We construct and solve a walk with an additional correlation step, finding interesting new features. On the other hand, the fact that the evolution is driven entirely by a local operator, not involving additional spaces, enables us to choose the Fourier transform as an operator completely controlling the evolution. This in turn allows us to combine the quantum walk approach with Fourier transform based techniques, something decidedly not possible in classical computational physics. We are developing a formalism for building networks manageable by walks constructed with this framework, based on the surprising efficiency of our framework in discovering internals of a simple network that we so far solved. Finally, in line with our expectation that the field of quantum walks can take cues from the rich history of development of the classical stochastic techniques, we establish starting points for the work on non-Abelian quantum walks, with a particular quantum-walk analog of the classical "card shuffling," the walk on the permutation group. In summary, this thesis presents a new framework for construction of discrete time quantum walks, employing and exploring memoried nature of unitary evolution. It is applied to fully solving the problems of: A walk on the binary tree and exploration of the quantum-to-classical transition with increased correlation length (history). It is then used for simple network discovery, and to lay the groundwork for analysis of complex networks, based on combined power of efficient exploration of the Hilbert space (as a walk mixing components) and Fourier transformation (since we can choose this for the evolution operator). We hope to establish this as a general technique as its power would be unmatched by any approaches available in the classical computing. We also looked at the promising and challenging prospect of walks on non-Abelian structures by setting up the problem of "quantum card shuffling," a quantum walk on the permutation group. Relation to other work is thoroughly discussed throughout, along with examination of the context of our work and overviews of our current and future work.

Quantum communication and information processing

NASA Astrophysics Data System (ADS)

Beals, Travis Roland

Quantum computers enable dramatically more efficient algorithms for solving certain classes of computational problems, but, in doing so, they create new problems. In particular, Shor's Algorithm allows for efficient cryptanalysis of many public-key cryptosystems. As public key cryptography is a critical component of present-day electronic commerce, it is crucial that a working, secure replacement be found. Quantum key distribution (QKD), first developed by C.H. Bennett and G. Brassard, offers a partial solution, but many challenges remain, both in terms of hardware limitations and in designing cryptographic protocols for a viable large-scale quantum communication infrastructure. In Part I, I investigate optical lattice-based approaches to quantum information processing. I look at details of a proposal for an optical lattice-based quantum computer, which could potentially be used for both quantum communications and for more sophisticated quantum information processing. In Part III, I propose a method for converting and storing photonic quantum bits in the internal state of periodically-spaced neutral atoms by generating and manipulating a photonic band gap and associated defect states. In Part II, I present a cryptographic protocol which allows for the extension of present-day QKD networks over much longer distances without the development of new hardware. I also present a second, related protocol which effectively solves the authentication problem faced by a large QKD network, thus making QKD a viable, information-theoretic secure replacement for public key cryptosystems.

Limits on efficient computation in the physical world

NASA Astrophysics Data System (ADS)

Aaronson, Scott Joel

More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be jettisoned in the light of modern physics, many others emerge nearly unscathed; and I use powerful tools from computational complexity theory to help determine which are which. In the first part of the thesis, I attack the common belief that quantum computing resembles classical exponential parallelism, by showing that quantum computers would face serious limitations on a wider range of problems than was previously known. In particular, any quantum algorithm that solves the collision problem---that of deciding whether a sequence of n integers is one-to-one or two-to-one---must query the sequence O (n1/5) times. This resolves a question that was open for years; previously no lower bound better than constant was known. A corollary is that there is no "black-box" quantum algorithm to break cryptographic hash functions or solve the Graph Isomorphism problem in polynomial time. I also show that relative to an oracle, quantum computers could not solve NP-complete problems in polynomial time, even with the help of nonuniform "quantum advice states"; and that any quantum algorithm needs O (2n/4/n) queries to find a local minimum of a black-box function on the n-dimensional hypercube. Surprisingly, the latter result also leads to new classical lower bounds for the local search problem. Finally, I give new lower bounds on quantum one-way communication complexity, and on the quantum query complexity of total Boolean functions and recursive Fourier sampling. The second part of the thesis studies the relationship of the quantum computing model to physical reality. I first examine the arguments of Leonid Levin, Stephen Wolfram, and others who believe quantum computing to be fundamentally impossible. I find their arguments unconvincing without a "Sure/Shor separator"---a criterion that separates the already-verified quantum states from those that appear in Shor's factoring algorithm. I argue that such a separator should be based on a complexity classification of quantum states, and go on to create such a classification. Next I ask what happens to the quantum computing model if we take into account that the speed of light is finite---and in particular, whether Grover's algorithm still yields a quadratic speedup for searching a database. Refuting a claim by Benioff, I show that the surprising answer is yes. Finally, I analyze hypothetical models of computation that go even beyond quantum computing. I show that many such models would be as powerful as the complexity class PP, and use this fact to give a simple, quantum computing based proof that PP is closed under intersection. On the other hand, I also present one model---wherein we could sample the entire history of a hidden variable---that appears to be more powerful than standard quantum computing, but only slightly so.

Compiling Planning into Quantum Optimization Problems: A Comparative Study

DTIC Science & Technology

2015-06-07

and Sipser, M. 2000. Quantum computation by adiabatic evolution. arXiv:quant- ph/0001106. Fikes, R. E., and Nilsson, N. J. 1972. STRIPS: A new...become available: quantum annealing. Quantum annealing is one of the most accessible quantum algorithms for a computer sci- ence audience not versed...in quantum computing because of its close ties to classical optimization algorithms such as simulated annealing. While large-scale universal quantum

A New Ontological View of the Quantum Measurement Problem

DTIC Science & Technology

2005-06-13

broader issues in the foundations of quantum mechanics as well. In this scenario, a quantum measurement is a nonequilibrium phase transition in a...the foundations of quantum mechan - ics as well. In this scenario a quantum measurement is a non-equilibrium phase transition in a “resonant cavity...ontology, and the probabilistic element is removed from the foundations of quantum mechanics , its apparent presence in the quantum measurement being solely

27-Year R&D 100 Awards Winning Streak - Continuum Magazine | NREL

Science.gov Websites

the real-time quantum efficiency system. Photo by Dennis Schroeder, NREL 27-Year R&D 100 Awards Mehta, and Peter Rupnowski at the controls of the Optical Cavity Furnace. Photo by Dennis Schroeder signals in solar cells used with Innovalight's Silicon Ink. Photo by Dennis Schroeder, NREL Problem: For

Quantum Statistical Properties of the Codirectional Kerr Nonlinear Coupler in Terms of su (2 ) Lie Group in Interaction with a Two-level Atom

NASA Astrophysics Data System (ADS)

Abdalla, M. Sebawe; Khalil, E. M.; Obada, A. S.-F.

2017-08-01

The problem of the codirectional Kerr coupler has been considered several times from different point of view. In the present paper we introduce the interaction between a two-level atom and the codirectional Kerr nonlinear coupler in terms of su (2 ) Lie algebra. Under certain conditions we have adjusted the Kerr coupler and consequently we have managed to handle the problem. The wave function is obtained by using the evolution operator where the Heisnberg equation of motion is invoked to get the constants of the motion. We note that the Kerr parameter χ as well as the quantum number j plays the role of controlling the atomic inversion behavior. Also the maximum entanglement occurs after a short period of time when χ = 0. On the other hand for the entropy and the variance squeezing we observe that there is exchange between the quadrature variances. Furthermore, the variation in the quantum number j as well as in the parameter χ leads to increase or decrease in the number of fluctuations. Finally we examined the second order correlation function where classical and nonclassical phenomena are observed.

On the 'principle of the quantumness', the quantumness of Relativity, and the computational grand-unification

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Ariano, Giacomo Mauro

2010-05-04

I will argue that the proposal of establishing operational foundations of Quantum Theory should have top-priority, and that the Lucien Hardy's program on Quantum Gravity should be paralleled by an analogous program on Quantum Field Theory (QFT), which needs to be reformulated, notwithstanding its experimental success. In this paper, after reviewing recently suggested operational 'principles of the quantumness', I address the problem on whether Quantum Theory and Special Relativity are unrelated theories, or instead, if the one implies the other. I show how Special Relativity can be indeed derived from causality of Quantum Theory, within the computational paradigm 'the universemore » is a huge quantum computer', reformulating QFT as a Quantum-Computational Field Theory (QCFT). In QCFT Special Relativity emerges from the fabric of the computational network, which also naturally embeds gauge invariance. In this scheme even the quantization rule and the Planck constant can in principle be derived as emergent from the underlying causal tapestry of space-time. In this way Quantum Theory remains the only theory operating the huge computer of the universe.Is the computational paradigm only a speculative tautology (theory as simulation of reality), or does it have a scientific value? The answer will come from Occam's razor, depending on the mathematical simplicity of QCFT. Here I will just start scratching the surface of QCFT, analyzing simple field theories, including Dirac's. The number of problems and unmotivated recipes that plague QFT strongly motivates us to undertake the QCFT project, since QCFT makes all such problems manifest, and forces a re-foundation of QFT.« less

Quantum snake walk on graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosmanis, Ansis

2011-02-15

I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, whichmore » asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.« less

The Quantum Measurement Problem and Physical reality: A Computation Theoretic Perspective

NASA Astrophysics Data System (ADS)

Srikanth, R.

2006-11-01

Is the universe computable? If yes, is it computationally a polynomial place? In standard quantum mechanics, which permits infinite parallelism and the infinitely precise specification of states, a negative answer to both questions is not ruled out. On the other hand, empirical evidence suggests that NP-complete problems are intractable in the physical world. Likewise, computational problems known to be algorithmically uncomputable do not seem to be computable by any physical means. We suggest that this close correspondence between the efficiency and power of abstract algorithms on the one hand, and physical computers on the other, finds a natural explanation if the universe is assumed to be algorithmic; that is, that physical reality is the product of discrete sub-physical information processing equivalent to the actions of a probabilistic Turing machine. This assumption can be reconciled with the observed exponentiality of quantum systems at microscopic scales, and the consequent possibility of implementing Shor's quantum polynomial time algorithm at that scale, provided the degree of superposition is intrinsically, finitely upper-bounded. If this bound is associated with the quantum-classical divide (the Heisenberg cut), a natural resolution to the quantum measurement problem arises. From this viewpoint, macroscopic classicality is an evidence that the universe is in BPP, and both questions raised above receive affirmative answers. A recently proposed computational model of quantum measurement, which relates the Heisenberg cut to the discreteness of Hilbert space, is briefly discussed. A connection to quantum gravity is noted. Our results are compatible with the philosophy that mathematical truths are independent of the laws of physics.

Strategies in a symmetric quantum Kolkata restaurant problem

NASA Astrophysics Data System (ADS)

Sharif, Puya; Heydari, Hoshang

2012-12-01

The Quantum Kolkata restaurant problem is a multiple-choice version of the quantum minority game, where a set of n non-communicating players have to chose between one of m choices. A payoff is granted to the players that make a unique choice. It has previously been shown that shared entanglement and quantum operations can aid the players to coordinate their actions and acquire higher payoffs than is possible with classical randomization. In this paper the initial quantum state is expanded to a family of GHZ-type states and strategies are discussed in terms of possible final outcomes. It is shown that the players individually seek outcomes that maximize the collective good.

NP-hardness of decoding quantum error-correction codes

NASA Astrophysics Data System (ADS)

Hsieh, Min-Hsiu; Le Gall, François

2011-05-01

Although the theory of quantum error correction is intimately related to classical coding theory and, in particular, one can construct quantum error-correction codes (QECCs) from classical codes with the dual-containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expects degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or nondegenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.

A variational eigenvalue solver on a photonic quantum processor

PubMed Central

Peruzzo, Alberto; McClean, Jarrod; Shadbolt, Peter; Yung, Man-Hong; Zhou, Xiao-Qi; Love, Peter J.; Aspuru-Guzik, Alán; O’Brien, Jeremy L.

2014-01-01

Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the physical dimension grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estimation algorithm efficiently finds the eigenvalue of a given eigenvector but requires fully coherent evolution. Here we present an alternative approach that greatly reduces the requirements for coherent evolution and combine this method with a new approach to state preparation based on ansätze and classical optimization. We implement the algorithm by combining a highly reconfigurable photonic quantum processor with a conventional computer. We experimentally demonstrate the feasibility of this approach with an example from quantum chemistry—calculating the ground-state molecular energy for He–H+. The proposed approach drastically reduces the coherence time requirements, enhancing the potential of quantum resources available today and in the near future. PMID:25055053

Quasi-Solid-State Single-Atom Transistors.

PubMed

Xie, Fangqing; Peukert, Andreas; Bender, Thorsten; Obermair, Christian; Wertz, Florian; Schmieder, Philipp; Schimmel, Thomas

2018-06-21

The single-atom transistor represents a quantum electronic device at room temperature, allowing the switching of an electric current by the controlled and reversible relocation of one single atom within a metallic quantum point contact. So far, the device operates by applying a small voltage to a control electrode or "gate" within the aqueous electrolyte. Here, the operation of the atomic device in the quasi-solid state is demonstrated. Gelation of pyrogenic silica transforms the electrolyte into the quasi-solid state, exhibiting the cohesive properties of a solid and the diffusive properties of a liquid, preventing the leakage problem and avoiding the handling of a liquid system. The electrolyte is characterized by cyclic voltammetry, conductivity measurements, and rotation viscometry. Thus, a first demonstration of the single-atom transistor operating in the quasi-solid-state is given. The silver single-atom and atomic-scale transistors in the quasi-solid-state allow bistable switching between zero and quantized conductance levels, which are integer multiples of the conductance quantum G 0  = 2e 2 /h. Source-drain currents ranging from 1 to 8 µA are applied in these experiments. Any obvious influence of the gelation of the aqueous electrolyte on the electron transport within the quantum point contact is not observed. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Performance improvement of continuous-variable quantum key distribution with an entangled source in the middle via photon subtraction

NASA Astrophysics Data System (ADS)

Guo, Ying; Liao, Qin; Wang, Yijun; Huang, Duan; Huang, Peng; Zeng, Guihua

2017-03-01

A suitable photon-subtraction operation can be exploited to improve the maximal transmission of continuous-variable quantum key distribution (CVQKD) in point-to-point quantum communication. Unfortunately, the photon-subtraction operation faces solving the improvement transmission problem of practical quantum networks, where the entangled source is located in the third part, which may be controlled by a malicious eavesdropper, instead of in one of the trusted parts, controlled by Alice or Bob. In this paper, we show that a solution can come from using a non-Gaussian operation, in particular, the photon-subtraction operation, which provides a method to enhance the performance of entanglement-based (EB) CVQKD. Photon subtraction not only can lengthen the maximal transmission distance by increasing the signal-to-noise rate but also can be easily implemented with existing technologies. Security analysis shows that CVQKD with an entangled source in the middle (ESIM) from applying photon subtraction can well increase the secure transmission distance in both direct and reverse reconciliations of the EB-CVQKD scheme, even if the entangled source originates from an untrusted part. Moreover, it can defend against the inner-source attack, which is a specific attack by an untrusted entangled source in the framework of ESIM.

Schroedinger's immortal cat

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peres, A.

1988-01-01

The purpose of this paper is to review and clarify the quantum measurement problem. The latter originates in the ambivalent nature of the observer: Although the observer is not described by the Schroedinger equation, it should nevertheless be possible to quantize him and include him in the wave function if quantum theory is universally valid. The problem is to prove that no contradiction may arise in these two conflicting descriptions. The proof invokes the notion of irreversibility. The validity of the latter is questionable, because the standard rationale for classical irreversibility, namely mixing and coarse graining, does not apply tomore » quantum theory. There is no chaos in a closed, finite quantum system. However, when a system is large enough, it cannot be perfectly isolated from it environment, namely from external (or even internal) degrees of freedom which are not fully accounted for in the Hamiltonian of that system. As a consequence, the long-range evolution of such a quantum system is essentially unpredictable. It follows that the notion of irreversibility is a valid one in quantum theory and the measurement problem can be brought to a satisfactory solution.« less

Computational Role of Tunneling in a Programmable Quantum Annealer

NASA Technical Reports Server (NTRS)

Boixo, Sergio; Smelyanskiy, Vadim; Shabani, Alireza; Isakov, Sergei V.; Dykman, Mark; Amin, Mohammad; Mohseni, Masoud; Denchev, Vasil S.; Neven, Hartmut

2016-01-01

Quantum tunneling is a phenomenon in which a quantum state tunnels through energy barriers above the energy of the state itself. Tunneling has been hypothesized as an advantageous physical resource for optimization. Here we present the first experimental evidence of a computational role of multiqubit quantum tunneling in the evolution of a programmable quantum annealer. We developed a theoretical model based on a NIBA Quantum Master Equation to describe the multi-qubit dissipative cotunneling effects under the complex noise characteristics of such quantum devices.We start by considering a computational primitive, the simplest non-convex optimization problem consisting of just one global and one local minimum. The quantum evolutions enable tunneling to the global minimum while the corresponding classical paths are trapped in a false minimum. In our study the non-convex potentials are realized by frustrated networks of qubit clusters with strong intra-cluster coupling. We show that the collective effect of the quantum environment is suppressed in the critical phase during the evolution where quantum tunneling decides the right path to solution. In a later stage dissipation facilitates the multiqubit cotunneling leading to the solution state. The predictions of the model accurately describe the experimental data from the D-WaveII quantum annealer at NASA Ames. In our computational primitive the temperature dependence of the probability of success in the quantum model is opposite to that of the classical paths with thermal hopping. Specially, we provide an analysis of an optimization problem with sixteen qubits,demonstrating eight qubit cotunneling that increases success probabilities. Furthermore, we report results for larger problems with up to 200 qubits that contain the primitive as subproblems.

Solution to the satisfiability problem using a complete Grover search with trapped ions

NASA Astrophysics Data System (ADS)

Yang, Wan-Li; Wei, Hua; Zhou, Fei; Chang, Weng-Long; Feng, Mang

2009-07-01

The main idea in the original Grover search (1997 Phys. Rev. Lett. 79 325) is to single out a target state containing the solution to a search problem by amplifying the amplitude of the state, following the Oracle's job, i.e., a black box giving us information about the target state. We design quantum circuits to accomplish a complete Grover search involving both the Oracle's job and the amplification of the target state, which are employed to solve satisfiability (SAT) problems. We explore how to carry out the quantum circuits with currently available ion-trap quantum computing technology.

The quantum N-body problem in the mean-field and semiclassical regime

NASA Astrophysics Data System (ADS)

Golse, François

2018-04-01

The present work discusses the mean-field limit for the quantum N-body problem in the semiclassical regime. More precisely, we establish a convergence rate for the mean-field limit which is uniform as the ratio of Planck constant to the action of the typical single particle tends to zero. This convergence rate is formulated in terms of a quantum analogue of the quadratic Monge-Kantorovich or Wasserstein distance. This paper is an account of some recent collaboration with C. Mouhot, T. Paul and M. Pulvirenti. This article is part of the themed issue `Hilbert's sixth problem'.

Solution to the sign problem in a frustrated quantum impurity model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hann, Connor T., E-mail: connor.hann@yale.edu; Huffman, Emilie; Chandrasekharan, Shailesh

2017-01-15

In this work we solve the sign problem of a frustrated quantum impurity model consisting of three quantum spin-half chains interacting through an anti-ferromagnetic Heisenberg interaction at one end. We first map the model into a repulsive Hubbard model of spin-half fermions hopping on three independent one dimensional chains that interact through a triangular hopping at one end. We then convert the fermion model into an inhomogeneous one dimensional model and express the partition function as a weighted sum over fermion worldline configurations. By imposing a pairing of fermion worldlines in half the space we show that all negative weightmore » configurations can be eliminated. This pairing naturally leads to the original frustrated quantum spin model at half filling and thus solves its sign problem.« less

Quantum Optical Implementations of Current Quantum Computing Paradigms

DTIC Science & Technology

2005-05-01

Conferences and Proceedings: The results were presented at several conferences. These include: 1. M. O. Scully, " Foundations of Quantum Mechanics ", in...applications have revealed a strong connection between the fundamental aspects of quantum mechanics that governs physical systems and the informational...could be solved in polynomial time using quantum computers. Another set of problems where quantum mechanics can carry out computations substantially

Beyond Moore's law: towards competitive quantum devices

NASA Astrophysics Data System (ADS)

Troyer, Matthias

2015-05-01

A century after the invention of quantum theory and fifty years after Bell's inequality we see the first quantum devices emerge as products that aim to be competitive with the best classical computing devices. While a universal quantum computer of non-trivial size is still out of reach there exist a number commercial and experimental devices: quantum random number generators, quantum simulators and quantum annealers. In this colloquium I will present some of these devices and validation tests we performed on them. Quantum random number generators use the inherent randomness in quantum measurements to produce true random numbers, unlike classical pseudorandom number generators which are inherently deterministic. Optical lattice emulators use ultracold atomic gases in optical lattices to mimic typical models of condensed matter physics. In my talk I will focus especially on the devices built by Canadian company D-Wave systems, which are special purpose quantum simulators for solving hard classical optimization problems. I will review the controversy around the quantum nature of these devices and will compare them to state of the art classical algorithms. I will end with an outlook towards universal quantum computing and end with the question: which important problems that are intractable even for post-exa-scale classical computers could we expect to solve once we have a universal quantum computer?

Quantum harmonic oscillator in a thermal bath

NASA Technical Reports Server (NTRS)

Zhang, Yuhong

1993-01-01

The influence functional path-integral treatment of quantum Brownian motion is briefly reviewed. A newly derived exact master equation of a quantum harmonic oscillator coupled to a general environment at arbitrary temperature is discussed. It is applied to the problem of loss of quantum coherence.

Problems in particle theory. Technical report - 1993--1994

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adler, S.L.; Wilczek, F.

This report is a progress report on the work of two principal investigators in the broad area of particle physics theory, covering their personal work, that of their coworkers, and their proposed work for the future. One author has worked in the past on various topics in field theory and particle physics, among them current algebras, the physics of neutrino induced reactions, quantum electrodynamics (including strong magnetic field processes), the theory of the axial-vector current anomaly, topics in quantum gravity, and nonlinear models for quark confinement. While much of his work has been analytical, all of the projects listed abovemore » (except for the work on gravity) had phases which required considerable computer work as well. Over the next several years, he proposes to continue or initiate research on the following problems: (1) Acceleration algorithms for the Monte Carlo analysis of lattice field and gauge theories, and more generally, new research in computational neuroscience and pattern recognition. (2) Construction of quaternionic generalizations of complex quantum mechanics and field theory, and their application to composite models of quarks and leptons, and to the problem of unifying quantum theories of matter with general relativity. One author has worked on problems in exotic quantum statistics and its applications to condensed matter systems. His work has also continued on the quantum theory of black holes. This has evolved toward understanding properties of quantum field theory and string theory in incomplete regions of flat space.« less

Quantum Gauss-Jordan Elimination and Simulation of Accounting Principles on Quantum Computers

NASA Astrophysics Data System (ADS)

Diep, Do Ngoc; Giang, Do Hoang; Van Minh, Nguyen

2017-06-01

The paper is devoted to a version of Quantum Gauss-Jordan Elimination and its applications. In the first part, we construct the Quantum Gauss-Jordan Elimination (QGJE) Algorithm and estimate the complexity of computation of Reduced Row Echelon Form (RREF) of N × N matrices. The main result asserts that QGJE has computation time is of order 2 N/2. The second part is devoted to a new idea of simulation of accounting by quantum computing. We first expose the actual accounting principles in a pure mathematics language. Then, we simulate the accounting principles on quantum computers. We show that, all accounting actions are exhousted by the described basic actions. The main problems of accounting are reduced to some system of linear equations in the economic model of Leontief. In this simulation, we use our constructed Quantum Gauss-Jordan Elimination to solve the problems and the complexity of quantum computing is a square root order faster than the complexity in classical computing.

Quantum Matching Theory (with new complexity-theoretic, combinatorial and topical insights on the nature of the quantum entanglement)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gurvits, L.

2002-01-01

Classical matching theory can be defined in terms of matrices with nonnegative entries. The notion of Positive operator, central in Quantum Theory, is a natural generalization of matrices with non-negative entries. Based on this point of view, we introduce a definition of perfect Quantum (operator) matching. We show that the new notion inherits many 'classical' properties, but not all of them. This new notion goes somewhere beyound matroids. For separable bipartite quantum states this new notion coinsides with the full rank property of the intersection of two corresponding geometric matroids. In the classical situation, permanents are naturally associated with perfectsmore » matchings. We introduce an analog of permanents for positive operators, called Quantum Permanent and show how this generalization of the permanent is related to the Quantum Entanglement. Besides many other things, Quantum Permanents provide new rational inequalities necessary for the separability of bipartite quantum states. Using Quantum Permanents, we give deterministic poly-time algorithm to solve Hidden Matroids Intersection Problem and indicate some 'classical' complexity difficulties associated with the Quantum Entanglement. Finally, we prove that the weak membership problem for the convex set of separable bipartite density matrices is NP-HARD.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weinstein, Marvin; /SLAC

Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.

Quantum Resonance Approach to Combinatorial Optimization

NASA Technical Reports Server (NTRS)

Zak, Michail

1997-01-01

It is shown that quantum resonance can be used for combinatorial optimization. The advantage of the approach is in independence of the computing time upon the dimensionality of the problem. As an example, the solution to a constraint satisfaction problem of exponential complexity is demonstrated.

Degenerate quantum codes and the quantum Hamming bound

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sarvepalli, Pradeep; Klappenecker, Andreas

2010-03-15

The parameters of a nondegenerate quantum code must obey the Hamming bound. An important open problem in quantum coding theory is whether the parameters of a degenerate quantum code can violate this bound for nondegenerate quantum codes. In this article we show that Calderbank-Shor-Steane (CSS) codes, over a prime power alphabet q{>=}5, cannot beat the quantum Hamming bound. We prove a quantum version of the Griesmer bound for the CSS codes, which allows us to strengthen the Rains' bound that an [[n,k,d

About approximation of integer factorization problem by the combination fixed-point iteration method and Bayesian rounding for quantum cryptography

NASA Astrophysics Data System (ADS)

Ogorodnikov, Yuri; Khachay, Michael; Pljonkin, Anton

2018-04-01

We describe the possibility of employing the special case of the 3-SAT problem stemming from the well known integer factorization problem for the quantum cryptography. It is known, that for every instance of our 3-SAT setting the given 3-CNF is satisfiable by a unique truth assignment, and the goal is to find this assignment. Since the complexity status of the factorization problem is still undefined, development of approximation algorithms and heuristics adopts interest of numerous researchers. One of promising approaches to construction of approximation techniques is based on real-valued relaxation of the given 3-CNF followed by minimizing of the appropriate differentiable loss function, and subsequent rounding of the fractional minimizer obtained. Actually, algorithms developed this way differ by the rounding scheme applied on their final stage. We propose a new rounding scheme based on Bayesian learning. The article shows that the proposed method can be used to determine the security in quantum key distribution systems. In the quantum distribution the Shannon rules is applied and the factorization problem is paramount when decrypting secret keys.

Noise reduction in optically controlled quantum memory

NASA Astrophysics Data System (ADS)

Ma, Lijun; Slattery, Oliver; Tang, Xiao

2018-05-01

Quantum memory is an essential tool for quantum communications systems and quantum computers. An important category of quantum memory, called optically controlled quantum memory, uses a strong classical beam to control the storage and re-emission of a single-photon signal through an atomic ensemble. In this type of memory, the residual light from the strong classical control beam can cause severe noise and degrade the system performance significantly. Efficiently suppressing this noise is a requirement for the successful implementation of optically controlled quantum memories. In this paper, we briefly introduce the latest and most common approaches to quantum memory and review the various noise-reduction techniques used in implementing them.

Controlled Photon Switch Assisted by Coupled Quantum Dots

PubMed Central

Luo, Ming-Xing; Ma, Song-Ya; Chen, Xiu-Bo; Wang, Xiaojun

2015-01-01

Quantum switch is a primitive element in quantum network communication. In contrast to previous switch schemes on one degree of freedom (DOF) of quantum systems, we consider controlled switches of photon system with two DOFs. These controlled photon switches are constructed by exploring the optical selection rules derived from the quantum-dot spins in one-sided optical microcavities. Several double controlled-NOT gate on different joint systems are greatly simplified with an auxiliary DOF of the controlling photon. The photon switches show that two DOFs of photons can be independently transmitted in quantum networks. This result reduces the quantum resources for quantum network communication. PMID:26095049

Quantum histories without contrary inferences

NASA Astrophysics Data System (ADS)

Losada, Marcelo; Laura, Roberto

2014-12-01

In the consistent histories formulation of quantum theory it was shown that it is possible to retrodict contrary properties. We show that this problem do not appear in our formalism of generalized contexts for quantum histories.

Stochastic gradient ascent outperforms gamers in the Quantum Moves game

NASA Astrophysics Data System (ADS)

Sels, Dries

2018-04-01

In a recent work on quantum state preparation, Sørensen and co-workers [Nature (London) 532, 210 (2016), 10.1038/nature17620] explore the possibility of using video games to help design quantum control protocols. The authors present a game called "Quantum Moves" (https://www.scienceathome.org/games/quantum-moves/) in which gamers have to move an atom from A to B by means of optical tweezers. They report that, "players succeed where purely numerical optimization fails." Moreover, by harnessing the player strategies, they can "outperform the most prominent established numerical methods." The aim of this Rapid Communication is to analyze the problem in detail and show that those claims are untenable. In fact, without any prior knowledge and starting from a random initial seed, a simple stochastic local optimization method finds near-optimal solutions which outperform all players. Counterdiabatic driving can even be used to generate protocols without resorting to numeric optimization. The analysis results in an accurate analytic estimate of the quantum speed limit which, apart from zero-point motion, is shown to be entirely classical in nature. The latter might explain why gamers are reasonably good at the game. A simple modification of the BringHomeWater challenge is proposed to test this hypothesis.

Suppressed Kondo effect and Kosterlitz-Thouless-type phase transition induced by level difference in a triple dot device

NASA Astrophysics Data System (ADS)

Xiong, Yong-Chen; Huang, Hai-Ming; Zhao, Wen-Lei; Laref, Amel

2017-10-01

Quantum dot system provides an ideal platform for quantum information processing, within which to demonstrate the quantum states is one of the most important issue for quantum simulation and quantum computation. In this paper, we report a peculiar electron state in a parallel triple dot device where the Ruderman-Kittel-Kasuya-Yosida interaction is invalid when the level differences of the dots sweep into appropriate regime. This extraordinary tendency then results in an antiferromagnetic spin coupling between two of the dots and may lead to zero or full conductance, relying deeply on the relation of the two level spacings. e.g. when the level differences are kept equal, the Kondo effect is totally suppressed although the dots are triply occupied, since in this case a local inter-dot transport loop is found to play an important role in the transmission coefficient. By contrast, when the differences are retained symmetric, the Kondo peak reaches nearly to its unitary limit, owing to that the inter-dot transport process is significantly suppressed. To approach these problems, voltage controllable quantum phase transitions of Kosterlitz-Thouless type and first order are shown, and possible pictures related to the many-body effect and the effective Kondo model are given.

REVIEWS OF TOPICAL PROBLEMS: Concept of consciousness in the context of quantum mechanics

NASA Astrophysics Data System (ADS)

Menskii, Mikhail B.

2005-04-01

Conceptual problems of the quantum theory of measurement are considered, which are embodied in well-known paradoxes and in Bell's inequalities. Arguments are advanced in favor of the viewpoint that these problems may hardly be solved without direct inclusion of the observer's consciousness in the theoretical description of a quantum measurement. Discussed in this connection is the so-called many-worlds interpretation of quantum mechanics proposed by Everett, as is the extension of Everett's concept, which consists in the assumption that separating the quantum state components corresponding to alternative measurements is not only associated with the observer's consciousness but is completely identified with it. This approach is shown to open up qualitatively new avenues for the unification of physics and psychology and, more broadly, of the sciences and the humanities. This may lead to an extension of the theory of consciousness and shed light on significant and previously misunderstood phenomena in the sphere of consciousness.

Test-state approach to the quantum search problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sehrawat, Arun; Nguyen, Le Huy; Graduate School for Integrative Sciences and Engineering, National University of Singapore, Singapore 117597

2011-05-15

The search for 'a quantum needle in a quantum haystack' is a metaphor for the problem of finding out which one of a permissible set of unitary mappings - the oracles - is implemented by a given black box. Grover's algorithm solves this problem with quadratic speedup as compared with the analogous search for 'a classical needle in a classical haystack'. Since the outcome of Grover's algorithm is probabilistic - it gives the correct answer with high probability, not with certainty - the answer requires verification. For this purpose we introduce specific test states, one for each oracle. These testmore » states can also be used to realize 'a classical search for the quantum needle' which is deterministic - it always gives a definite answer after a finite number of steps - and 3.41 times as fast as the purely classical search. Since the test-state search and Grover's algorithm look for the same quantum needle, the average number of oracle queries of the test-state search is the classical benchmark for Grover's algorithm.« less

Density matrix reconstruction of a large angular momentum

NASA Astrophysics Data System (ADS)

Klose, Gerd

2001-10-01

A complete description of the quantum state of a physical system is the fundamental knowledge necessary to statistically predict the outcome of measurements. In turning this statement around, Wolfgang Pauli raised already in 1933 the question, whether an unknown quantum state could be uniquely determined by appropriate measurements-a problem that has gained new relevance in recent years. In order to harness the prospects of quantum computing, secure communication, teleportation, and the like, the development of techniques to accurately control and measure quantum states has now become a matter of practical as well as fundamental interest. However, there is no general answer to Pauli's very basic question, and quantum state reconstruction algorithms have been developed and experimentally demonstrated only for a few systems so far. This thesis presents a novel experimental method to measure the unknown and generally mixed quantum state for an angular momentum of arbitrary magnitude. The (2F + 1) x (2F + 1) density matrix describing the quantum state is hereby completely determined from a set of Stern-Gerlach measurements with (4F + 1) different orientations of the quantization axis. This protocol is implemented for laser cooled Cesium atoms in the 6S1/2(F = 4) hyperfine ground state manifold, and is applied to a number of test states prepared by optical pumping and Larmor precession. A comparison of the input and the measured states shows successful reconstructions with fidelities of about 0.95.

Symmetric quantum fully homomorphic encryption with perfect security

NASA Astrophysics Data System (ADS)

Liang, Min

2013-12-01

Suppose some data have been encrypted, can you compute with the data without decrypting them? This problem has been studied as homomorphic encryption and blind computing. We consider this problem in the context of quantum information processing, and present the definitions of quantum homomorphic encryption (QHE) and quantum fully homomorphic encryption (QFHE). Then, based on quantum one-time pad (QOTP), we construct a symmetric QFHE scheme, where the evaluate algorithm depends on the secret key. This scheme permits any unitary transformation on any -qubit state that has been encrypted. Compared with classical homomorphic encryption, the QFHE scheme has perfect security. Finally, we also construct a QOTP-based symmetric QHE scheme, where the evaluate algorithm is independent of the secret key.

Nonlinear dynamics and quantum entanglement in optomechanical systems.

PubMed

Wang, Guanglei; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso

2014-03-21

To search for and exploit quantum manifestations of classical nonlinear dynamics is one of the most fundamental problems in physics. Using optomechanical systems as a paradigm, we address this problem from the perspective of quantum entanglement. We uncover strong fingerprints in the quantum entanglement of two common types of classical nonlinear dynamical behaviors: periodic oscillations and quasiperiodic motion. There is a transition from the former to the latter as an experimentally adjustable parameter is changed through a critical value. Accompanying this process, except for a small region about the critical value, the degree of quantum entanglement shows a trend of continuous increase. The time evolution of the entanglement measure, e.g., logarithmic negativity, exhibits a strong dependence on the nature of classical nonlinear dynamics, constituting its signature.

Quantum Optics in Phase Space

NASA Astrophysics Data System (ADS)

Schleich, Wolfgang P.

2001-04-01

Quantum Optics in Phase Space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase space. Modern in style and didactically skillful, Quantum Optics in Phase Space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable problems at the end of each chapter. Often, the theoretical treatments are accompanied by the corresponding experiments. An exhaustive list of references provides a guide to the literature. Quantum Optics in Phase Space also serves advanced researchers as a comprehensive reference book. Starting with an extensive review of the experiments that define quantum optics and a brief summary of the foundations of quantum mechanics the author Wolfgang P. Schleich illustrates the properties of quantum states with the help of the Wigner phase space distribution function. His description of waves ala WKB connects semi-classical phase space with the Berry phase. These semi-classical techniques provide deeper insight into the timely topics of wave packet dynamics, fractional revivals and the Talbot effect. Whereas the first half of the book deals with mechanical oscillators such as ions in a trap or atoms in a standing wave the second half addresses problems where the quantization of the radiation field is of importance. Such topics extensively discussed include optical interferometry, the atom-field interaction, quantum state preparation and measurement, entanglement, decoherence, the one-atom maser and atom optics in quantized light fields. Quantum Optics in Phase Space presents the subject of quantum optics as transparently as possible. Giving wide-ranging references, it enables students to study and solve problems with modern scientific literature. The result is a remarkably concise yet comprehensive and accessible text- and reference book - an inspiring source of information and insight for students, teachers and researchers alike.

Quantum walks with tuneable self-avoidance in one dimension

PubMed Central

Camilleri, Elizabeth; Rohde, Peter P.; Twamley, Jason

2014-01-01

Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Here the walker has memory of its previous locations and preferentially avoids stepping back to locations where it has previously resided. Classical self-avoiding random walks have found numerous algorithmic applications, most notably in the modelling of protein folding. We consider the analogous problem in the quantum setting – a quantum walk in one dimension with tunable levels of self-avoidance. We complement a quantum walk with a memory register that records where the walker has previously resided. The walker is then able to avoid returning back to previously visited sites or apply more general memory conditioned operations to control the walk. We characterise this walk by examining the variance of the walker's distribution against time, the standard metric for quantifying how quantum or classical a walk is. We parameterise the strength of the memory recording and the strength of the memory back-action on the walker, and investigate their effect on the dynamics of the walk. We find that by manipulating these parameters, which dictate the degree of self-avoidance, the walk can be made to reproduce ideal quantum or classical random walk statistics, or a plethora of more elaborate diffusive phenomena. In some parameter regimes we observe a close correspondence between classical self-avoiding random walks and the quantum self-avoiding walk. PMID:24762398

Temperature dependence of long coherence times of oxide charge qubits.

PubMed

Dey, A; Yarlagadda, S

2018-02-22

The ability to maintain coherence and control in a qubit is a major requirement for quantum computation. We show theoretically that long coherence times can be achieved at easily accessible temperatures (such as boiling point of liquid helium) in small (i.e., ~10 nanometers) charge qubits of oxide double quantum dots when only optical phonons are the source of decoherence. In the regime of strong electron-phonon coupling and in the non-adiabatic region, we employ a duality transformation to make the problem tractable and analyze the dynamics through a non-Markovian quantum master equation. We find that the system decoheres after a long time, despite the fact that no energy is exchanged with the bath. Detuning the dots to a fraction of the optical phonon energy, increasing the electron-phonon coupling, reducing the adiabaticity, or decreasing the temperature enhances the coherence time.

Number-theoretic nature of communication in quantum spin systems.

PubMed

Godsil, Chris; Kirkland, Stephen; Severini, Simone; Smith, Jamie

2012-08-03

The last decade has witnessed substantial interest in protocols for transferring information on networks of quantum mechanical objects. A variety of control methods and network topologies have been proposed, on the basis that transfer with perfect fidelity-i.e., deterministic and without information loss-is impossible through unmodulated spin chains with more than a few particles. Solving the original problem formulated by Bose [Phys. Rev. Lett. 91, 207901 (2003)], we determine the exact number of qubits in unmodulated chains (with an XY Hamiltonian) that permit transfer with a fidelity arbitrarily close to 1, a phenomenon called pretty good state transfer. We prove that this happens if and only if the number of nodes is n = p - 1, 2p - 1, where p is a prime, or n = 2(m) - 1. The result highlights the potential of quantum spin system dynamics for reinterpreting questions about the arithmetic structure of integers and, in this case, primality.

Quantum neurophysics: From non-living matter to quantum neurobiology and psychopathology.

PubMed

Tarlacı, Sultan; Pregnolato, Massimo

2016-05-01

The concepts of quantum brain, quantum mind and quantum consciousness have been increasingly gaining currency in recent years, both in scientific papers and in the popular press. In fact, the concept of the quantum brain is a general framework. Included in it are basically four main sub-headings. These are often incorrectly used interchangeably. The first of these and the one which started the quantum mind/consciousness debate was the place of consciousness in the problem of measurement in quantum mechanics. Debate on the problem of quantum measurement and about the place of the conscious observer has lasted almost a century. One solution to this problem is that the participation of a conscious observer in the experiment will radically change our understanding of the universe and our relationship with the outside world. The second topic is that of quantum biology. This topic has become a popular field of research, especially in the last decade. It concerns whether or not the rules of quantum physics operate in biological structures. It has been shown in the latest research on photosynthesis, the sense of smell and magnetic direction finding in animals that the laws of quantum physics may operate in warm-wet-noisy biological structures. The third sub-heading is quantum neurobiology. This topic has not yet gained wide acceptance and is still in its early stages. Its primary purpose is directed to understand whether the laws of quantum physics are effective in the biology of the nervous system or not. A further step in brain neurobiology, toward the understanding of consciousness formation, is the research of quantum laws effects upon neural network functions. The fourth and final topic is quantum psychopathology. This topic takes its basis and its support from quantum neurobiology. It comes from the idea that if quantum physics is involved in the normal working of the brain, diseased conditions of the brain such as depression, anxiety, dementia, schizophrenia and hallucinations can be explained by quantum physical pathology. In this article, these topics will be reviewed in a general framework, and for the first time a general classification will be made for the quantum brain theory. Copyright © 2016 Elsevier B.V. All rights reserved.

Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators

DOE PAGES

Claassen, Martin; Lee, Ching-Hua; Thomale, Ronny; ...

2015-06-11

We develop a first quantization description of fractional Chern insulators that is the dual of the conventional fractional quantum Hall (FQH) problem, with the roles of position and momentum interchanged. In this picture, FQH states are described by anisotropic FQH liquids forming in momentum-space Landau levels in a fluctuating magnetic field. The fundamental quantum geometry of the problem emerges from the interplay of single-body and interaction metrics, both of which act as momentum-space duals of the geometrical picture of the anisotropic FQH effect. We then present a novel broad class of ideal Chern insulator lattice models that act as dualsmore » of the isotropic FQH effect. The interacting problem is well-captured by Haldane pseudopotentials and affords a detailed microscopic understanding of the interplay of interactions and non-trivial quantum geometry.« less

Infinite variance in fermion quantum Monte Carlo calculations.

PubMed

Shi, Hao; Zhang, Shiwei

2016-03-01

For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.

Completing the Physical Representation of Quantum Algorithms Provides a Quantitative Explanation of Their Computational Speedup

NASA Astrophysics Data System (ADS)

Castagnoli, Giuseppe

2018-03-01

The usual representation of quantum algorithms, limited to the process of solving the problem, is physically incomplete. We complete it in three steps: (i) extending the representation to the process of setting the problem, (ii) relativizing the extended representation to the problem solver to whom the problem setting must be concealed, and (iii) symmetrizing the relativized representation for time reversal to represent the reversibility of the underlying physical process. The third steps projects the input state of the representation, where the problem solver is completely ignorant of the setting and thus the solution of the problem, on one where she knows half solution (half of the information specifying it when the solution is an unstructured bit string). Completing the physical representation shows that the number of computation steps (oracle queries) required to solve any oracle problem in an optimal quantum way should be that of a classical algorithm endowed with the advanced knowledge of half solution.

Quantum Mechanics From the Cradle?

ERIC Educational Resources Information Center

Martin, John L.

1974-01-01

States that the major problem in learning quantum mechanics is often the student's ignorance of classical mechanics and that one conceptual hurdle in quantum mechanics is its statistical nature, in contrast to the determinism of classical mechanics. (MLH)

A Non-Intuitionist's Approach To The Interpretation Problem Of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Grelland, Hans Herlof

2005-02-01

A philosophy of physics called "linguistic empiricism" is presented and applied to the interpretation problem of quantum mechanics. This philosophical position is based on the works of Jacques Derrida. The main propositions are (i) that meaning, included the meaning attached to observations, are language-dependent and (ii) that mathematics in physics should be considered as a proper language, not necessary translatable to a more basic language of intuition and immediate experience. This has fundamental implications for quantum mechanics, which is a mathematically coherent and consistent theory; its interpretation problem is associated with its lack of physical images expressible in ordinary language.

Hidden symmetry in the confined hydrogen atom problem

NASA Astrophysics Data System (ADS)

Pupyshev, Vladimir I.; Scherbinin, Andrei V.

2002-07-01

The classical counterpart of the well-known quantum mechanical model of a spherically confined hydrogen atom is examined in terms of the Lenz vector, a dynamic variable featuring the conventional Kepler problem. It is shown that a conditional conservation law associated with the Lenz vector is true, in fair agreement with the corresponding quantum problem previously found to exhibit a hidden symmetry as well.

The Problem of Representation and Experience in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Ronde, Christian De

2014-03-01

In this paper we discuss the problem of representation and experience in quantum mechanics. We analyze the importance of metaphysics in physical thought and its relation to empiricism and analytic philosophy. We argue against both instrumentalism and scientific realism and claim that both perspectives tend to bypass the problem of representation and justify a "common sense" type experience. Finally, we present our expressionist conception of physics.

Fundamental Principles of Coherent-Feedback Quantum Control

DTIC Science & Technology

2014-12-08

in metrology (acceleration sensing, vibrometry, gravity wave detection) and in quantum information processing (continuous-variables quantum ...AFRL-OSR-VA-TR-2015-0009 FUNDAMENTAL PRINCIPLES OF COHERENT-FEEDBACK QUANTUM CONTROL Hideo Mabuchi LELAND STANFORD JUNIOR UNIV CA Final Report 12/08...foundations and potential applications of coherent-feedback quantum control. We have focused on potential applications in quantum -enhanced metrology and

LASER APPLICATIONS AND OTHER TOPICS IN QUANTUM ELECTRONICS On control of kinematic parameters of ultracold neutrons in waveguides

NASA Astrophysics Data System (ADS)

Rivlin, Lev A.

2010-10-01

The possibility of controlling the kinematic parameters of ultracold neutrons (UCNs) is analysed by the example of a waveguide transfer and transformation of 2D images in ultracold neutrons and by the example of an increase in the concentration and deceleration/acceleration of ultracold neutrons during their transport in the waveguide with a variable cross section. The critical parameters of the problem are estimated, which indicates both consistency of the proposed approach and the emerging experimental limitations.

CALL FOR PAPERS: Quantum control

NASA Astrophysics Data System (ADS)

Mancini, Stefano; Wiseman, Howard M.; Man'ko, Vladimir I.

2004-10-01

Over the last few decades, the achievements of highly precise technologies for manipulating systems at quantum scales have paved the way for the development of quantum control. Moreover, the proliferation of results in quantum information suggest that control theory might profitably be re-examined from this perspective. Journal of Optics B: Quantum and Semiclassical Optics will publish a topical issue devoted to quantum control. The Guest Editors invite contributions from researchers working in any area related to quantum control. Topics to be covered include: • Quantum Hamiltonian dynamics and programming control • Quantum decoherence control • Open loop control • Closed loop (feedback) control • Quantum measurement theory • Quantum noise and filtering • Estimation and decision theory • Quantum error correction • Group representation in quantum control • Coherent control in quantum optics and lasers • Coherent control in cavity QED and atom optics • Coherent control in molecular dynamics The topical issue is scheduled for publication in November 2005 and the DEADLINE for submission of contributions is 28 February 2005. All contributions will be peer-reviewed in accordance with the normal refereeing procedures and standards of Journal of Optics B: Quantum and Semiclassical Optics. Submissions should preferably be in either standard LaTeX form or Microsoft Word. Advice on publishing your work in the journal may be found at www.iop.org/journals/authors/jopb. Enquiries regarding this topical issue may be addressed to the Publisher, Dr Claire Bedrock (claire.bedrock@iop.org). There are no page charges for publication. The corresponding author of each paper published will receive a complimentary copy of the topical issue. Contributions to the topical issue should preferably be submitted electronically at www.iop.org/journals/authors/jopb or by e-mail to jopb@iop.org. Authors unable to submit online or by e-mail may send hard copy contributions (enclosing the electronic code) to: Journal of Optics B: Quantum and Semiclassical Optics, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK. All contributions should be accompanied by a readme file or covering letter, quoting `JOPB Topical Issue - Quantum control', giving the postal and e-mail addresses for correspondence. Any subsequent change of address should be notified to the publishing office. We look forward to receiving your contribution to this topical issue.

Fully adaptive propagation of the quantum-classical Liouville equation

NASA Astrophysics Data System (ADS)

Horenko, Illia; Weiser, Martin; Schmidt, Burkhard; Schütte, Christof

2004-05-01

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Fully adaptive propagation of the quantum-classical Liouville equation.

PubMed

Horenko, Illia; Weiser, Martin; Schmidt, Burkhard; Schütte, Christof

2004-05-15

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Finding Maximum Cliques on the D-Wave Quantum Annealer

DOE PAGES

Chapuis, Guillaume; Djidjev, Hristo; Hahn, Georg; ...

2018-05-03

This work assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is quite small (usually around 45 vertices), we also consider decomposition algorithms intended for larger graphs and analyze their performance. For smaller graphs that fit DW, we provide formulations of the maximum clique problem as a quadratic unconstrained binary optimization (QUBO) problem, which is one of the two input types (together with the Ising model) acceptable by the machine, andmore » compare several quantum implementations to current classical algorithms such as simulated annealing, Gurobi, and third-party clique finding heuristics. We further estimate the contributions of the quantum phase of the quantum annealer and the classical post-processing phase typically used to enhance each solution returned by DW. We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms. On the other hand, for instances specifically designed to fit well the DW qubit interconnection network, we observe substantial speed-ups in computing time over classical approaches.« less

Finding Maximum Cliques on the D-Wave Quantum Annealer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chapuis, Guillaume; Djidjev, Hristo; Hahn, Georg

This work assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is quite small (usually around 45 vertices), we also consider decomposition algorithms intended for larger graphs and analyze their performance. For smaller graphs that fit DW, we provide formulations of the maximum clique problem as a quadratic unconstrained binary optimization (QUBO) problem, which is one of the two input types (together with the Ising model) acceptable by the machine, andmore » compare several quantum implementations to current classical algorithms such as simulated annealing, Gurobi, and third-party clique finding heuristics. We further estimate the contributions of the quantum phase of the quantum annealer and the classical post-processing phase typically used to enhance each solution returned by DW. We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms. On the other hand, for instances specifically designed to fit well the DW qubit interconnection network, we observe substantial speed-ups in computing time over classical approaches.« less

Quantum annealing versus classical machine learning applied to a simplified computational biology problem

PubMed Central

Li, Richard Y.; Di Felice, Rosa; Rohs, Remo; Lidar, Daniel A.

2018-01-01

Transcription factors regulate gene expression, but how these proteins recognize and specifically bind to their DNA targets is still debated. Machine learning models are effective means to reveal interaction mechanisms. Here we studied the ability of a quantum machine learning approach to predict binding specificity. Using simplified datasets of a small number of DNA sequences derived from actual binding affinity experiments, we trained a commercially available quantum annealer to classify and rank transcription factor binding. The results were compared to state-of-the-art classical approaches for the same simplified datasets, including simulated annealing, simulated quantum annealing, multiple linear regression, LASSO, and extreme gradient boosting. Despite technological limitations, we find a slight advantage in classification performance and nearly equal ranking performance using the quantum annealer for these fairly small training data sets. Thus, we propose that quantum annealing might be an effective method to implement machine learning for certain computational biology problems. PMID:29652405

Quantum annealing with all-to-all connected nonlinear oscillators

PubMed Central

Puri, Shruti; Andersen, Christian Kraglund; Grimsmo, Arne L.; Blais, Alexandre

2017-01-01

Quantum annealing aims at solving combinatorial optimization problems mapped to Ising interactions between quantum spins. Here, with the objective of developing a noise-resilient annealer, we propose a paradigm for quantum annealing with a scalable network of two-photon-driven Kerr-nonlinear resonators. Each resonator encodes an Ising spin in a robust degenerate subspace formed by two coherent states of opposite phases. A fully connected optimization problem is mapped to local fields driving the resonators, which are connected with only local four-body interactions. We describe an adiabatic annealing protocol in this system and analyse its performance in the presence of photon loss. Numerical simulations indicate substantial resilience to this noise channel, leading to a high success probability for quantum annealing. Finally, we propose a realistic circuit QED implementation of this promising platform for implementing a large-scale quantum Ising machine. PMID:28593952

Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stottmeister, Alexander, E-mail: alexander.stottmeister@gravity.fau.de; Thiemann, Thomas, E-mail: thomas.thiemann@gravity.fau.de

2016-06-15

This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems,more » which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).« less

Quantum key distribution session with 16-dimensional photonic states.

PubMed

Etcheverry, S; Cañas, G; Gómez, E S; Nogueira, W A T; Saavedra, C; Xavier, G B; Lima, G

2013-01-01

The secure transfer of information is an important problem in modern telecommunications. Quantum key distribution (QKD) provides a solution to this problem by using individual quantum systems to generate correlated bits between remote parties, that can be used to extract a secret key. QKD with D-dimensional quantum channels provides security advantages that grow with increasing D. However, the vast majority of QKD implementations has been restricted to two dimensions. Here we demonstrate the feasibility of using higher dimensions for real-world quantum cryptography by performing, for the first time, a fully automated QKD session based on the BB84 protocol with 16-dimensional quantum states. Information is encoded in the single-photon transverse momentum and the required states are dynamically generated with programmable spatial light modulators. Our setup paves the way for future developments in the field of experimental high-dimensional QKD.

Universal Quantum Computing with Arbitrary Continuous-Variable Encoding.

PubMed

Lau, Hoi-Kwan; Plenio, Martin B

2016-09-02

Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal quantum computation with a fixed set of operations but arbitrary encoding. By storing a qubit in the parity of two or four qumodes, all computing processes can be implemented by basis state preparations, continuous-variable exponential-swap operations, and swap tests. Our formalism inherits the advantages that the quantum information is decoupled from collective noise, and logical qubits with different encodings can be brought to interact without decoding. We also propose a possible implementation of the required operations by using interactions that are available in a variety of continuous-variable systems. Our work separates the "hardware" problem of engineering quantum-computing-universal interactions, from the "software" problem of designing encodings for specific purposes. The development of quantum computer architecture could hence be simplified.

Universal Quantum Computing with Arbitrary Continuous-Variable Encoding

NASA Astrophysics Data System (ADS)

Lau, Hoi-Kwan; Plenio, Martin B.

2016-09-01

Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal quantum computation with a fixed set of operations but arbitrary encoding. By storing a qubit in the parity of two or four qumodes, all computing processes can be implemented by basis state preparations, continuous-variable exponential-swap operations, and swap tests. Our formalism inherits the advantages that the quantum information is decoupled from collective noise, and logical qubits with different encodings can be brought to interact without decoding. We also propose a possible implementation of the required operations by using interactions that are available in a variety of continuous-variable systems. Our work separates the "hardware" problem of engineering quantum-computing-universal interactions, from the "software" problem of designing encodings for specific purposes. The development of quantum computer architecture could hence be simplified.

An adaptive quantum mechanics/molecular mechanics method for the infrared spectrum of water: incorporation of the quantum effect between solute and solvent.

PubMed

Watanabe, Hiroshi C; Banno, Misa; Sakurai, Minoru

2016-03-14

Quantum effects in solute-solvent interactions, such as the many-body effect and the dipole-induced dipole, are known to be critical factors influencing the infrared spectra of species in the liquid phase. For accurate spectrum evaluation, the surrounding solvent molecules, in addition to the solute of interest, should be treated using a quantum mechanical method. However, conventional quantum mechanics/molecular mechanics (QM/MM) methods cannot handle free QM solvent molecules during molecular dynamics (MD) simulation because of the diffusion problem. To deal with this problem, we have previously proposed an adaptive QM/MM "size-consistent multipartitioning (SCMP) method". In the present study, as the first application of the SCMP method, we demonstrate the reproduction of the infrared spectrum of liquid-phase water, and evaluate the quantum effect in comparison with conventional QM/MM simulations.

Quantum key distribution session with 16-dimensional photonic states

NASA Astrophysics Data System (ADS)

Etcheverry, S.; Cañas, G.; Gómez, E. S.; Nogueira, W. A. T.; Saavedra, C.; Xavier, G. B.; Lima, G.

2013-07-01

The secure transfer of information is an important problem in modern telecommunications. Quantum key distribution (QKD) provides a solution to this problem by using individual quantum systems to generate correlated bits between remote parties, that can be used to extract a secret key. QKD with D-dimensional quantum channels provides security advantages that grow with increasing D. However, the vast majority of QKD implementations has been restricted to two dimensions. Here we demonstrate the feasibility of using higher dimensions for real-world quantum cryptography by performing, for the first time, a fully automated QKD session based on the BB84 protocol with 16-dimensional quantum states. Information is encoded in the single-photon transverse momentum and the required states are dynamically generated with programmable spatial light modulators. Our setup paves the way for future developments in the field of experimental high-dimensional QKD.

Quantum key distribution session with 16-dimensional photonic states

PubMed Central

Etcheverry, S.; Cañas, G.; Gómez, E. S.; Nogueira, W. A. T.; Saavedra, C.; Xavier, G. B.; Lima, G.

2013-01-01

The secure transfer of information is an important problem in modern telecommunications. Quantum key distribution (QKD) provides a solution to this problem by using individual quantum systems to generate correlated bits between remote parties, that can be used to extract a secret key. QKD with D-dimensional quantum channels provides security advantages that grow with increasing D. However, the vast majority of QKD implementations has been restricted to two dimensions. Here we demonstrate the feasibility of using higher dimensions for real-world quantum cryptography by performing, for the first time, a fully automated QKD session based on the BB84 protocol with 16-dimensional quantum states. Information is encoded in the single-photon transverse momentum and the required states are dynamically generated with programmable spatial light modulators. Our setup paves the way for future developments in the field of experimental high-dimensional QKD. PMID:23897033

Hybrid annealing: Coupling a quantum simulator to a classical computer

NASA Astrophysics Data System (ADS)

Graß, Tobias; Lewenstein, Maciej

2017-05-01

Finding the global minimum in a rugged potential landscape is a computationally hard task, often equivalent to relevant optimization problems. Annealing strategies, either classical or quantum, explore the configuration space by evolving the system under the influence of thermal or quantum fluctuations. The thermal annealing dynamics can rapidly freeze the system into a low-energy configuration, and it can be simulated well on a classical computer, but it easily gets stuck in local minima. Quantum annealing, on the other hand, can be guaranteed to find the true ground state and can be implemented in modern quantum simulators; however, quantum adiabatic schemes become prohibitively slow in the presence of quasidegeneracies. Here, we propose a strategy which combines ideas from simulated annealing and quantum annealing. In such a hybrid algorithm, the outcome of a quantum simulator is processed on a classical device. While the quantum simulator explores the configuration space by repeatedly applying quantum fluctuations and performing projective measurements, the classical computer evaluates each configuration and enforces a lowering of the energy. We have simulated this algorithm for small instances of the random energy model, showing that it potentially outperforms both simulated thermal annealing and adiabatic quantum annealing. It becomes most efficient for problems involving many quasidegenerate ground states.

Quantum machine learning: a classical perspective

NASA Astrophysics Data System (ADS)

Ciliberto, Carlo; Herbster, Mark; Ialongo, Alessandro Davide; Pontil, Massimiliano; Rocchetto, Andrea; Severini, Simone; Wossnig, Leonard

2018-01-01

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning (ML) techniques to impressive results in regression, classification, data generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets is motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed up classical ML algorithms. Here we review the literature in quantum ML and discuss perspectives for a mixed readership of classical ML and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in ML are identified as promising directions for the field. Practical questions, such as how to upload classical data into quantum form, will also be addressed.

Quantum machine learning: a classical perspective

PubMed Central

Ciliberto, Carlo; Herbster, Mark; Ialongo, Alessandro Davide; Pontil, Massimiliano; Severini, Simone; Wossnig, Leonard

2018-01-01

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning (ML) techniques to impressive results in regression, classification, data generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets is motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed up classical ML algorithms. Here we review the literature in quantum ML and discuss perspectives for a mixed readership of classical ML and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in ML are identified as promising directions for the field. Practical questions, such as how to upload classical data into quantum form, will also be addressed. PMID:29434508

Quantum machine learning: a classical perspective.

PubMed

Ciliberto, Carlo; Herbster, Mark; Ialongo, Alessandro Davide; Pontil, Massimiliano; Rocchetto, Andrea; Severini, Simone; Wossnig, Leonard

2018-01-01

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning (ML) techniques to impressive results in regression, classification, data generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets is motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed up classical ML algorithms. Here we review the literature in quantum ML and discuss perspectives for a mixed readership of classical ML and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in ML are identified as promising directions for the field. Practical questions, such as how to upload classical data into quantum form, will also be addressed.

EDITORIAL: CAMOP: Quantum Non-Stationary Systems CAMOP: Quantum Non-Stationary Systems

NASA Astrophysics Data System (ADS)

Dodonov, Victor V.; Man'ko, Margarita A.

2010-09-01

Although time-dependent quantum systems have been studied since the very beginning of quantum mechanics, they continue to attract the attention of many researchers, and almost every decade new important discoveries or new fields of application are made. Among the impressive results or by-products of these studies, one should note the discovery of the path integral method in the 1940s, coherent and squeezed states in the 1960-70s, quantum tunneling in Josephson contacts and SQUIDs in the 1960s, the theory of time-dependent quantum invariants in the 1960-70s, different forms of quantum master equations in the 1960-70s, the Zeno effect in the 1970s, the concept of geometric phase in the 1980s, decoherence of macroscopic superpositions in the 1980s, quantum non-demolition measurements in the 1980s, dynamics of particles in quantum traps and cavity QED in the 1980-90s, and time-dependent processes in mesoscopic quantum devices in the 1990s. All these topics continue to be the subject of many publications. Now we are witnessing a new wave of interest in quantum non-stationary systems in different areas, from cosmology (the very first moments of the Universe) and quantum field theory (particle pair creation in ultra-strong fields) to elementary particle physics (neutrino oscillations). A rapid increase in the number of theoretical and experimental works on time-dependent phenomena is also observed in quantum optics, quantum information theory and condensed matter physics. Time-dependent tunneling and time-dependent transport in nano-structures are examples of such phenomena. Another emerging direction of study, stimulated by impressive progress in experimental techniques, is related to attempts to observe the quantum behavior of macroscopic objects, such as mirrors interacting with quantum fields in nano-resonators. Quantum effects manifest themselves in the dynamics of nano-electromechanical systems; they are dominant in the quite new and very promising field of circuit QED. Another rapidly growing research field (although its origin can be traced to the beginning of the 1980s) is the quantum control of evolution at the microscopic level. These examples show that quantum non-stationary systems continue to be a living and very interesting part of quantum physics, uniting researchers from many different areas. Thus it is no mere chance that several special scientific meetings devoted to these topics have been organized recently. One was the international seminar 'Time-Dependent Phenomena in Quantum Mechanics' organized by Manfred Kleber and Tobias Kramer in 2007 at Blaubeuren, Germany. The proceedings of that event were published in 2008 as volume 99 of Journal of Physics: Conference Series. Another recent meeting was the International Workshop on Quantum Non-Stationary Systems, held on 19-23 October 2009 at the International Center for Condensed Matter Physics (ICCMP) in Brasilia, Brazil. It was organized and directed by Victor Dodonov (Institute of Physics, University of Brasilia, Brazil), Vladimir Man'ko (P N Lebedev Physical Institute, Moscow, Russia) and Salomon Mizrahi (Physics Department, Federal University of Sao Carlos, Brazil). This event was accompanied by a satellite workshop 'Quantum Dynamics in Optics and Matter', organized by Salomon Mizrahi and Victor Dodonov on 25-26 October 2009 at the Physics Department of the Federal University of Sao Carlos, Brazil. These two workshops, supported by the Brazilian federal agencies CAPES and CNPq and the local agencies FAP-DF and FAPESP, were attended by more than 120 participants from 16 countries. Almost 50 invited talks and 20 poster presentations covered a wide area of research in quantum mechanics, quantum optics and quantum information. This special issue of CAMOP/Physica Scripta contains contributions presented by some invited speakers and participants of the workshop in Brasilia. Although they do not cover all of the wide spectrum of problems related to quantum non-stationary systems, they nonetheless show some general trends. However, readers should remember that these comments represent the personal points of view of their authors. About a third of the comments are devoted to the evolution of quantum systems in the presence of dissipation or other sources of decoherence. This area, started by Landau in 1927, still contains many extremely interesting and unsolved problems. Here they are discussed in view of such different applications as the dynamics of quantum entanglement, cavity QED, optomechanics and the dynamical Casimir effect. Another group of comments deals with different (e.g. geometrical, tomographic, PT-symmetric) approaches to the dynamics of quantum systems, which have been developed in the past two decades. In particular, the problem of transition from quantum to classical description is considered and the inequalities generalizing the standard uncertainty relations are discussed in this connection. Three comments are devoted to the applications of nonclassical states, analytic representations and the algebraic techniques for resolving problems in quantum information and quantum statistical physics. The other contributions are related to different aspects of the dynamics of concrete physical systems, such as the wave-packet approach to the description of transport phenomena in mesoscopic systems, tunneling phenomena in low-dimensional semiconductor structures and resonance states of two-electron quantum dots. We thank all the authors and referees for their efforts in preparing this special issue. We hope that the comments in this collection will be useful for interested readers.

Physical theories, eternal inflation, and the quantum universe

NASA Astrophysics Data System (ADS)

Nomura, Yasunori

2011-11-01

Infinities in eternal inflation have long been plaguing cosmology, making any predictions highly sensitive to how they are regulated. The problem exists already at the level of semi-classical general relativity, and has a priori nothing to do with quantum gravity. On the other hand, we know that certain problems in semi-classical gravity, for example physics of black holes and their evaporation, have led to understanding of surprising, quantum natures of spacetime and gravity, such as the holographic principle and horizon complementarity. In this paper, we present a framework in which well-defined predictions are obtained in an eternally inflating multiverse, based on the principles of quantum mechanics. We propose that the entire multiverse is described purely from the viewpoint of a single "observer," who describes the world as a quantum state defined on his/her past light cones bounded by the (stretched) apparent horizons. We find that quantum mechanics plays an essential role in regulating infinities. The framework is "gauge invariant," i.e. predictions do not depend on how spacetime is parametrized, as it should be in a theory of quantum gravity. Our framework provides a fully unified treatment of quantum measurement processes and the multiverse. We conclude that the eternally inflating multiverse and many worlds in quantum mechanics are the same. Other important implications include: global spacetime can be viewed as a derived concept; the multiverse is a transient phenomenon during the world relaxing into a supersymmetric Minkowski state. We also present a model of "initial conditions" for the multiverse. By extrapolating our framework to the extreme, we arrive at a picture that the entire multiverse is a fluctuation in the stationary, fractal "mega-multiverse," in which an infinite sequence of multiverse productions occurs. The framework discussed here does not suffer from problems/paradoxes plaguing other measures proposed earlier, such as the youngness paradox and the Boltzmann brain problem.

Geometry of quantum state manifolds generated by the Lie algebra operators

NASA Astrophysics Data System (ADS)

Kuzmak, A. R.

2018-03-01

The Fubini-Study metric of quantum state manifold generated by the operators which satisfy the Heisenberg Lie algebra is calculated. The similar problem is studied for the manifold generated by the so(3) Lie algebra operators. Using these results, we calculate the Fubini-Study metrics of state manifolds generated by the position and momentum operators. Also the metrics of quantum state manifolds generated by some spin systems are obtained. Finally, we generalize this problem for operators of an arbitrary Lie algebra.

Quantum annealing of the traveling-salesman problem.

PubMed

Martonák, Roman; Santoro, Giuseppe E; Tosatti, Erio

2004-11-01

We propose a path-integral Monte Carlo quantum annealing scheme for the symmetric traveling-salesman problem, based on a highly constrained Ising-like representation, and we compare its performance against standard thermal simulated annealing. The Monte Carlo moves implemented are standard, and consist in restructuring a tour by exchanging two links (two-opt moves). The quantum annealing scheme, even with a drastically simple form of kinetic energy, appears definitely superior to the classical one, when tested on a 1002-city instance of the standard TSPLIB.

Adapting the traveling salesman problem to an adiabatic quantum computer

NASA Astrophysics Data System (ADS)

Warren, Richard H.

2013-04-01

We show how to guide a quantum computer to select an optimal tour for the traveling salesman. This is significant because it opens a rapid solution method for the wide range of applications of the traveling salesman problem, which include vehicle routing, job sequencing and data clustering.

The Soccer-Ball Problem

NASA Astrophysics Data System (ADS)

Hossenfelder, Sabine

2014-07-01

The idea that Lorentz-symmetry in momentum space could be modified but still remain observer-independent has received quite some attention in the recent years. This modified Lorentz-symmetry, which has been argued to arise in Loop Quantum Gravity, is being used as a phenomenological model to test possibly observable effects of quantum gravity. The most pressing problem in these models is the treatment of multi-particle states, known as the 'soccer-ball problem'. This article briefly reviews the problem and the status of existing solution attempts.

Scalable quantum information processing with photons and atoms

NASA Astrophysics Data System (ADS)

Pan, Jian-Wei

Over the past three decades, the promises of super-fast quantum computing and secure quantum cryptography have spurred a world-wide interest in quantum information, generating fascinating quantum technologies for coherent manipulation of individual quantum systems. However, the distance of fiber-based quantum communications is limited due to intrinsic fiber loss and decreasing of entanglement quality. Moreover, probabilistic single-photon source and entanglement source demand exponentially increased overheads for scalable quantum information processing. To overcome these problems, we are taking two paths in parallel: quantum repeaters and through satellite. We used the decoy-state QKD protocol to close the loophole of imperfect photon source, and used the measurement-device-independent QKD protocol to close the loophole of imperfect photon detectors--two main loopholes in quantum cryptograph. Based on these techniques, we are now building world's biggest quantum secure communication backbone, from Beijing to Shanghai, with a distance exceeding 2000 km. Meanwhile, we are developing practically useful quantum repeaters that combine entanglement swapping, entanglement purification, and quantum memory for the ultra-long distance quantum communication. The second line is satellite-based global quantum communication, taking advantage of the negligible photon loss and decoherence in the atmosphere. We realized teleportation and entanglement distribution over 100 km, and later on a rapidly moving platform. We are also making efforts toward the generation of multiphoton entanglement and its use in teleportation of multiple properties of a single quantum particle, topological error correction, quantum algorithms for solving systems of linear equations and machine learning. Finally, I will talk about our recent experiments on quantum simulations on ultracold atoms. On the one hand, by applying an optical Raman lattice technique, we realized a two-dimensional spin-obit (SO) coupling and topological bands with ultracold bosonic atoms. A controllable crossover between 2D and 1D SO couplings is studied, and the SO effects and nontrivial band topology are observe. On the other hand, utilizing a two-dimensional spin-dependent optical superlattice and a single layer of atom cloud, we directly observed the four-body ring-exchange coupling and the Anyonic fractional statistics.

Quantum information, cognition, and music.

PubMed

Dalla Chiara, Maria L; Giuntini, Roberto; Leporini, Roberto; Negri, Eleonora; Sergioli, Giuseppe

2015-01-01

Parallelism represents an essential aspect of human mind/brain activities. One can recognize some common features between psychological parallelism and the characteristic parallel structures that arise in quantum theory and in quantum computation. The article is devoted to a discussion of the following questions: a comparison between classical probabilistic Turing machines and quantum Turing machines.possible applications of the quantum computational semantics to cognitive problems.parallelism in music.

Quantum information, cognition, and music

PubMed Central

Dalla Chiara, Maria L.; Giuntini, Roberto; Leporini, Roberto; Negri, Eleonora; Sergioli, Giuseppe

2015-01-01

Parallelism represents an essential aspect of human mind/brain activities. One can recognize some common features between psychological parallelism and the characteristic parallel structures that arise in quantum theory and in quantum computation. The article is devoted to a discussion of the following questions: a comparison between classical probabilistic Turing machines and quantum Turing machines.possible applications of the quantum computational semantics to cognitive problems.parallelism in music. PMID:26539139

Quantum-enhanced Sensing and Efficient Quantum Computation

DTIC Science & Technology

2015-07-27

accuracy. The system was used to improve quantum boson sampling tests. 15. SUBJECT TERMS EOARD, Quantum Information Processing, Transition Edge Sensors...quantum  boson  sampling (QBS) problem are reported in Ref. [7]. To substantially  increase the scale of feasible tests, we developed a new variation

DOE Office of Scientific and Technical Information (OSTI.GOV)

McCaskey, Alexander J.

There is a lack of state-of-the-art HPC simulation tools for simulating general quantum computing. Furthermore, there are no real software tools that integrate current quantum computers into existing classical HPC workflows. This product, the Quantum Virtual Machine (QVM), solves this problem by providing an extensible framework for pluggable virtual, or physical, quantum processing units (QPUs). It enables the execution of low level quantum assembly codes and returns the results of such executions.

Student Understanding of Time Dependence in Quantum Mechanics

ERIC Educational Resources Information Center

Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.

2015-01-01

The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing…

Towards Quantum Cybernetics:. Optimal Feedback Control in Quantum Bio Informatics

NASA Astrophysics Data System (ADS)

Belavkin, V. P.

2009-02-01

A brief account of the quantum information dynamics and dynamical programming methods for the purpose of optimal control in quantum cybernetics with convex constraints and cońcave cost and bequest functions of the quantum state is given. Consideration is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme with continuous observations we exploit the separation theorem of filtering and control aspects for quantum stochastic micro-dynamics of the total system. This allows to start with the Belavkin quantum filtering equation and derive the generalized Hamilton-Jacobi-Bellman equation using standard arguments of classical control theory. This is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term if the control is restricted to only Hamiltonian terms in the filtering equation. A controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure quantum qubit state from a mixed one.

Adiabatic quantum computation along quasienergies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tanaka, Atushi; Nemoto, Kae; National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda ku, Tokyo 101-8430

2010-02-15

The parametric deformations of quasienergies and eigenvectors of unitary operators are applied to the design of quantum adiabatic algorithms. The conventional, standard adiabatic quantum computation proceeds along eigenenergies of parameter-dependent Hamiltonians. By contrast, discrete adiabatic computation utilizes adiabatic passage along the quasienergies of parameter-dependent unitary operators. For example, such computation can be realized by a concatenation of parameterized quantum circuits, with an adiabatic though inevitably discrete change of the parameter. A design principle of adiabatic passage along quasienergy was recently proposed: Cheon's quasienergy and eigenspace anholonomies on unitary operators is available to realize anholonomic adiabatic algorithms [A. Tanaka and M.more » Miyamoto, Phys. Rev. Lett. 98, 160407 (2007)], which compose a nontrivial family of discrete adiabatic algorithms. It is straightforward to port a standard adiabatic algorithm to an anholonomic adiabatic one, except an introduction of a parameter |v>, which is available to adjust the gaps of the quasienergies to control the running time steps. In Grover's database search problem, the costs to prepare |v> for the qualitatively different (i.e., power or exponential) running time steps are shown to be qualitatively different.« less

Superconductivity versus quantum criticality: Effects of thermal fluctuations

NASA Astrophysics Data System (ADS)

Wang, Huajia; Wang, Yuxuan; Torroba, Gonzalo

2018-02-01

We study the interplay between superconductivity and non-Fermi liquid behavior of a Fermi surface coupled to a massless SU(N ) matrix boson near the quantum critical point. The presence of thermal infrared singularities in both the fermionic self-energy and the gap equation invalidates the Eliashberg approximation, and makes the quantum-critical pairing problem qualitatively different from that at zero temperature. Taking the large N limit, we solve the gap equation beyond the Eliashberg approximation, and obtain the superconducting temperature Tc as a function of N . Our results show an anomalous scaling between the zero-temperature gap and Tc. For N greater than a critical value, we find that Tc vanishes with a Berezinskii-Kosterlitz-Thouless scaling behavior, and the system retains non-Fermi liquid behavior down to zero temperature. This confirms and extends previous renormalization-group analyses done at T =0 , and provides a controlled example of a naked quantum critical point. We discuss the crucial role of thermal fluctuations in relating our results with earlier work where superconductivity always develops due to the special role of the first Matsubara frequency.

Conditions for entangled photon emission from (111)B site-controlled pyramidal quantum dots

DOE Office of Scientific and Technical Information (OSTI.GOV)

Juska, G., E-mail: gediminas.juska@tyndall.ie; Murray, E.; Dimastrodonato, V.

A study of highly symmetric site-controlled pyramidal In{sub 0.25}Ga{sub 0.75}As quantum dots (QDs) is presented. It is discussed that polarization-entangled photons can be also obtained from pyramidal QDs of different designs from the one already reported in Juska et al. [Nat. Photonics 7, 527 (2013)]. Moreover, some of the limitations for a higher density of entangled photon emitters are addressed. Among these issues are (1) a remaining small fine-structure splitting and (2) an effective QD charging under non-resonant excitation conditions, which strongly reduce the number of useful biexciton-exciton recombination events. A possible solution of the charging problem is investigated exploitingmore » a dual-wavelength excitation technique, which allows a gradual QD charge tuning from strongly negative to positive and, eventually, efficient detection of entangled photons from QDs, which would be otherwise ineffective under a single-wavelength (non-resonant) excitation.« less

Undecidability of the spectral gap.

PubMed

Cubitt, Toby S; Perez-Garcia, David; Wolf, Michael M

2015-12-10

The spectral gap--the energy difference between the ground state and first excited state of a system--is central to quantum many-body physics. Many challenging open problems, such as the Haldane conjecture, the question of the existence of gapped topological spin liquid phases, and the Yang-Mills gap conjecture, concern spectral gaps. These and other problems are particular cases of the general spectral gap problem: given the Hamiltonian of a quantum many-body system, is it gapped or gapless? Here we prove that this is an undecidable problem. Specifically, we construct families of quantum spin systems on a two-dimensional lattice with translationally invariant, nearest-neighbour interactions, for which the spectral gap problem is undecidable. This result extends to undecidability of other low-energy properties, such as the existence of algebraically decaying ground-state correlations. The proof combines Hamiltonian complexity techniques with aperiodic tilings, to construct a Hamiltonian whose ground state encodes the evolution of a quantum phase-estimation algorithm followed by a universal Turing machine. The spectral gap depends on the outcome of the corresponding 'halting problem'. Our result implies that there exists no algorithm to determine whether an arbitrary model is gapped or gapless, and that there exist models for which the presence or absence of a spectral gap is independent of the axioms of mathematics.

Qubits in phase space: Wigner-function approach to quantum-error correction and the mean-king problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Paz, Juan Pablo; Roncaglia, Augusto Jose; Theoretical Division, LANL, MSB213, Los Alamos, New Mexico 87545

2005-07-15

We analyze and further develop a method to represent the quantum state of a system of n qubits in a phase-space grid of NxN points (where N=2{sup n}). The method, which was recently proposed by Wootters and co-workers (Gibbons et al., Phys. Rev. A 70, 062101 (2004).), is based on the use of the elements of the finite field GF(2{sup n}) to label the phase-space axes. We present a self-contained overview of the method, we give insights into some of its features, and we apply it to investigate problems which are of interest for quantum-information theory: We analyze the phase-spacemore » representation of stabilizer states and quantum error-correction codes and present a phase-space solution to the so-called mean king problem.« less

Quantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity

NASA Astrophysics Data System (ADS)

Aquilanti, Vincenzo; Bitencourt, Ana Carla P.; Ferreira, Cristiane da S.; Marzuoli, Annalisa; Ragni, Mirco

2008-11-01

The mathematical apparatus of quantum-mechanical angular momentum (re)coupling, developed originally to describe spectroscopic phenomena in atomic, molecular, optical and nuclear physics, is embedded in modern algebraic settings which emphasize the underlying combinatorial aspects. SU(2) recoupling theory, involving Wigner's 3nj symbols, as well as the related problems of their calculations, general properties, asymptotic limits for large entries, nowadays plays a prominent role also in quantum gravity and quantum computing applications. We refer to the ingredients of this theory—and of its extension to other Lie and quantum groups—by using the collective term of 'spin networks'. Recent progress is recorded about the already established connections with the mathematical theory of discrete orthogonal polynomials (the so-called Askey scheme), providing powerful tools based on asymptotic expansions, which correspond on the physical side to various levels of semi-classical limits. These results are useful not only in theoretical molecular physics but also in motivating algorithms for the computationally demanding problems of molecular dynamics and chemical reaction theory, where large angular momenta are typically involved. As for quantum chemistry, applications of these techniques include selection and classification of complete orthogonal basis sets in atomic and molecular problems, either in configuration space (Sturmian orbitals) or in momentum space. In this paper, we list and discuss some aspects of these developments—such as for instance the hyperquantization algorithm—as well as a few applications to quantum gravity and topology, thus providing evidence of a unifying background structure.

Quantum Measurement, Correlation, and Contextuality

NASA Astrophysics Data System (ADS)

Ozawa, Masanao

2011-03-01

The problem has long been discussed as to whether non-commuting observables are simultaneously measurable, since Heisenberg introduced the uncertainty principle in 1927. The problem was settled state-independently: Two observables are simultaneously measurable in every state if and only if the corresponding operators commute. However, the problem has been open for state-dependent formulation. Saying that two observables are nowhere commuting if there exist no common eigenstates, the problem at stake is whether nowhere commuting observable can be simultaneously measurable in a certain state. There have been two historical arguments claiming the case: (i) In an eigenstate of an observable A one can determine both the values of A and any other observable B . (ii) In an EPR state one can determine both the values of Q ⊗ 1 and P ⊗ 1 . In this talk, we give a necessary and sufficient condition for two observables to be simultaneously measurable in a given state, show that the above two cases actually satisfy the required mathematical conditions, and give a classification of all the possible simultaneous measurements of nowhere commuting observables for the Hilbert space with dimension 2. Related problems on quantum contextuality will also be discussed using a linguistic method based on quantum logic and quantum set theory.

Some Surprises and Paradoxes Revealed by Inverse Problem Approach and Notion about Qualitative Solutions of SCHRÖDINGER Equations “IN MIND”

NASA Astrophysics Data System (ADS)

Zakhariev, B. N.; Chabanov, V. M.

It was an important examination to give a review talk at the previous Conference on Inverse Quantum Scattering (1996, Lake Balaton) about computer visualization of this science in front of its fathers — creators, B. M. Levitan and V. A. Marchenko. We have achieved a new understanding that the discovered main rules of transformations of a single wave function bump, e.g., for the ground bound states of one dimensional quantum systems are applicable to any state of any potential with arbitrary number of bumps from finite to unlimited ones as scattering states and bound states embedded into continuum. It appeared that we need only to repeat the rule mentally the necessary number of times. That uttermost simplification and unification of physical notion of spectral, scattering and decay control for any potential have got an obligatory praise from B. M. Levitan at the conference and was a mighty stimulus for our further research After that we have written both Russian (2002) and improved English editions of “Submissive Quantum Mechanics. New Status of the Theory in Inverse Problem Approach”1 (appeared at the very end of 2007). This book was written for correction of the present defect in quantum education throughout the world. Recently the quantum IP intuition helped us to discover a new concept of permanent wave resonance with potential spatial oscillations.2 This means the constant wave swinging frequency on the whole energy intervals of spectral forbidden zones destroying physical solutions and deepening the theory of waves in periodic potentials. It also shows the other side of strengthening the fundamentally important magic structures. A ‘new language’ of wave bending will be presented to enrich our quantum intuition, e.g., the paradoxical effective attraction of barriers and repulsion of wells in multichannel systems, etc.

Team decision problems with classical and quantum signals

PubMed Central

Brandenburger, Adam; La Mura, Pierfrancesco

2016-01-01

We study team decision problems where communication is not possible, but coordination among team members can be realized via signals in a shared environment. We consider a variety of decision problems that differ in what team members know about one another's actions and knowledge. For each type of decision problem, we investigate how different assumptions on the available signals affect team performance. Specifically, we consider the cases of perfectly correlated, i.i.d., and exchangeable classical signals, as well as the case of quantum signals. We find that, whereas in perfect-recall trees (Kuhn 1950 Proc. Natl Acad. Sci. USA 36, 570–576; Kuhn 1953 In Contributions to the theory of games, vol. II (eds H Kuhn, A Tucker), pp. 193–216) no type of signal improves performance, in imperfect-recall trees quantum signals may bring an improvement. Isbell (Isbell 1957 In Contributions to the theory of games, vol. III (eds M Drescher, A Tucker, P Wolfe), pp. 79–96) proved that, in non-Kuhn trees, classical i.i.d. signals may improve performance. We show that further improvement may be possible by use of classical exchangeable or quantum signals. We include an example of the effect of quantum signals in the context of high-frequency trading. PMID:26621985

Team decision problems with classical and quantum signals.

PubMed

Brandenburger, Adam; La Mura, Pierfrancesco

2016-01-13

We study team decision problems where communication is not possible, but coordination among team members can be realized via signals in a shared environment. We consider a variety of decision problems that differ in what team members know about one another's actions and knowledge. For each type of decision problem, we investigate how different assumptions on the available signals affect team performance. Specifically, we consider the cases of perfectly correlated, i.i.d., and exchangeable classical signals, as well as the case of quantum signals. We find that, whereas in perfect-recall trees (Kuhn 1950 Proc. Natl Acad. Sci. USA 36, 570-576; Kuhn 1953 In Contributions to the theory of games, vol. II (eds H Kuhn, A Tucker), pp. 193-216) no type of signal improves performance, in imperfect-recall trees quantum signals may bring an improvement. Isbell (Isbell 1957 In Contributions to the theory of games, vol. III (eds M Drescher, A Tucker, P Wolfe), pp. 79-96) proved that, in non-Kuhn trees, classical i.i.d. signals may improve performance. We show that further improvement may be possible by use of classical exchangeable or quantum signals. We include an example of the effect of quantum signals in the context of high-frequency trading. © 2015 The Authors.

Decodoku: Quantum error rorrection as a simple puzzle game

NASA Astrophysics Data System (ADS)

Wootton, James

To build quantum computers, we need to detect and manage any noise that occurs. This will be done using quantum error correction. At the hardware level, QEC is a multipartite system that stores information non-locally. Certain measurements are made which do not disturb the stored information, but which do allow signatures of errors to be detected. Then there is a software problem. How to take these measurement outcomes and determine: a) The errors that caused them, and (b) how to remove their effects. For qubit error correction, the algorithms required to do this are well known. For qudits, however, current methods are far from optimal. We consider the error correction problem of qubit surface codes. At the most basic level, this is a problem that can be expressed in terms of a grid of numbers. Using this fact, we take the inherent problem at the heart of quantum error correction, remove it from its quantum context, and presented in terms of simple grid based puzzle games. We have developed three versions of these puzzle games, focussing on different aspects of the required algorithms. These have been presented and iOS and Android apps, allowing the public to try their hand at developing good algorithms to solve the puzzles. For more information, see www.decodoku.com. Funding from the NCCR QSIT.

BOOK REVIEW: The Quantum Mechanics Solver: How to Apply Quantum Theory to Modern Physics, 2nd edition

NASA Astrophysics Data System (ADS)

Robbin, J. M.

2007-07-01

he hallmark of a good book of problems is that it allows you to become acquainted with an unfamiliar topic quickly and efficiently. The Quantum Mechanics Solver fits this description admirably. The book contains 27 problems based mainly on recent experimental developments, including neutrino oscillations, tests of Bell's inequality, Bose Einstein condensates, and laser cooling and trapping of atoms, to name a few. Unlike many collections, in which problems are designed around a particular mathematical method, here each problem is devoted to a small group of phenomena or experiments. Most problems contain experimental data from the literature, and readers are asked to estimate parameters from the data, or compare theory to experiment, or both. Standard techniques (e.g., degenerate perturbation theory, addition of angular momentum, asymptotics of special functions) are introduced only as they are needed. The style is closer to a non-specialist seminar rather than an undergraduate lecture. The physical models are kept simple; the emphasis is on cultivating conceptual and qualitative understanding (although in many of the problems, the simple models fit the data quite well). Some less familiar theoretical techniques are introduced, e.g. a variational method for lower (not upper) bounds on ground-state energies for many-body systems with two-body interactions, which is then used to derive a surprisingly accurate relation between baryon and meson masses. The exposition is succinct but clear; the solutions can be read as worked examples if you don't want to do the problems yourself. Many problems have additional discussion on limitations and extensions of the theory, or further applications outside physics (e.g., the accuracy of GPS positioning in connection with atomic clocks; proton and ion tumor therapies in connection with the Bethe Bloch formula for charged particles in solids). The problems use mainly non-relativistic quantum mechanics and are organised into three sections: Elementary Particles, Nuclei and Atoms; Quantum Entanglement and Measurement; and Complex Systems. The coverage is not comprehensive; there is little on scattering theory, for example, and some areas of recent interest, such as topological aspects of quantum mechanics and semiclassics, are not included. The problems are based on examination questions given at the École Polytechnique in the last 15 years. The book is accessible to undergraduates, but working physicists should find it a delight.

Subspace projection method for unstructured searches with noisy quantum oracles using a signal-based quantum emulation device

NASA Astrophysics Data System (ADS)

La Cour, Brian R.; Ostrove, Corey I.

2017-01-01

This paper describes a novel approach to solving unstructured search problems using a classical, signal-based emulation of a quantum computer. The classical nature of the representation allows one to perform subspace projections in addition to the usual unitary gate operations. Although bandwidth requirements will limit the scale of problems that can be solved by this method, it can nevertheless provide a significant computational advantage for problems of limited size. In particular, we find that, for the same number of noisy oracle calls, the proposed subspace projection method provides a higher probability of success for finding a solution than does an single application of Grover's algorithm on the same device.

Fine Structure of Dark Energy and New Physics

DOE PAGES

Jejjala, Vishnu; Kavic, Michael; Minic, Djordje

2007-01-01

Following our recent work on the cosmological constant problem, in this letter we make a specific proposal regarding the fine structure (i.e., the spectrum) of dark energy. The proposal is motivated by a deep analogy between the blackbody radiation problem, which led to the development of quantum theory, and the cosmological constant problem, for which we have recently argued calls for a conceptual extension of the quantum theory. We argue that the fine structure of dark energy is governed by a Wien distribution, indicating its dual quantum and classical nature. We discuss observational consequences of such a picture of darkmore » energy and constrain the distribution function.« less

Computational studies of thermal and quantum phase transitions approached through non-equilibrium quenching

NASA Astrophysics Data System (ADS)

Liu, Cheng-Wei

Phase transitions and their associated critical phenomena are of fundamental importance and play a crucial role in the development of statistical physics for both classical and quantum systems. Phase transitions embody diverse aspects of physics and also have numerous applications outside physics, e.g., in chemistry, biology, and combinatorial optimization problems in computer science. Many problems can be reduced to a system consisting of a large number of interacting agents, which under some circumstances (e.g., changes of external parameters) exhibit collective behavior; this type of scenario also underlies phase transitions. The theoretical understanding of equilibrium phase transitions was put on a solid footing with the establishment of the renormalization group. In contrast, non-equilibrium phase transition are relatively less understood and currently a very active research topic. One important milestone here is the Kibble-Zurek (KZ) mechanism, which provides a useful framework for describing a system with a transition point approached through a non-equilibrium quench process. I developed two efficient Monte Carlo techniques for studying phase transitions, one is for classical phase transition and the other is for quantum phase transitions, both are under the framework of KZ scaling. For classical phase transition, I develop a non-equilibrium quench (NEQ) simulation that can completely avoid the critical slowing down problem. For quantum phase transitions, I develop a new algorithm, named quasi-adiabatic quantum Monte Carlo (QAQMC) algorithm for studying quantum quenches. I demonstrate the utility of QAQMC quantum Ising model and obtain high-precision results at the transition point, in particular showing generalized dynamic scaling in the quantum system. To further extend the methods, I study more complex systems such as spin-glasses and random graphs. The techniques allow us to investigate the problems efficiently. From the classical perspective, using the NEQ approach I verify the universality class of the 3D Ising spin-glasses. I also investigate the random 3-regular graphs in terms of both classical and quantum phase transitions. I demonstrate that under this simulation scheme, one can extract information associated with the classical and quantum spin-glass transitions without any knowledge prior to the simulation.

An Efficient Quantum Somewhat Homomorphic Symmetric Searchable Encryption

NASA Astrophysics Data System (ADS)

Sun, Xiaoqiang; Wang, Ting; Sun, Zhiwei; Wang, Ping; Yu, Jianping; Xie, Weixin

2017-04-01

In 2009, Gentry first introduced an ideal lattices fully homomorphic encryption (FHE) scheme. Later, based on the approximate greatest common divisor problem, learning with errors problem or learning with errors over rings problem, FHE has developed rapidly, along with the low efficiency and computational security. Combined with quantum mechanics, Liang proposed a symmetric quantum somewhat homomorphic encryption (QSHE) scheme based on quantum one-time pad, which is unconditional security. And it was converted to a quantum fully homomorphic encryption scheme, whose evaluation algorithm is based on the secret key. Compared with Liang's QSHE scheme, we propose a more efficient QSHE scheme for classical input states with perfect security, which is used to encrypt the classical message, and the secret key is not required in the evaluation algorithm. Furthermore, an efficient symmetric searchable encryption (SSE) scheme is constructed based on our QSHE scheme. SSE is important in the cloud storage, which allows users to offload search queries to the untrusted cloud. Then the cloud is responsible for returning encrypted files that match search queries (also encrypted), which protects users' privacy.

Necessary and sufficient optimality conditions for classical simulations of quantum communication processes

NASA Astrophysics Data System (ADS)

Montina, Alberto; Wolf, Stefan

2014-07-01

We consider the process consisting of preparation, transmission through a quantum channel, and subsequent measurement of quantum states. The communication complexity of the channel is the minimal amount of classical communication required for classically simulating it. Recently, we reduced the computation of this quantity to a convex minimization problem with linear constraints. Every solution of the constraints provides an upper bound on the communication complexity. In this paper, we derive the dual maximization problem of the original one. The feasible points of the dual constraints, which are inequalities, give lower bounds on the communication complexity, as illustrated with an example. The optimal values of the two problems turn out to be equal (zero duality gap). By this property, we provide necessary and sufficient conditions for optimality in terms of a set of equalities and inequalities. We use these conditions and two reasonable but unproven hypotheses to derive the lower bound n ×2n -1 for a noiseless quantum channel with capacity equal to n qubits. This lower bound can have interesting consequences in the context of the recent debate on the reality of the quantum state.

On the Possibility to Combine the Order Effect with Sequential Reproducibility for Quantum Measurements

NASA Astrophysics Data System (ADS)

Basieva, Irina; Khrennikov, Andrei

2015-10-01

In this paper we study the problem of a possibility to use quantum observables to describe a possible combination of the order effect with sequential reproducibility for quantum measurements. By the order effect we mean a dependence of probability distributions (of measurement results) on the order of measurements. We consider two types of the sequential reproducibility: adjacent reproducibility (A-A) (the standard perfect repeatability) and separated reproducibility(A-B-A). The first one is reproducibility with probability 1 of a result of measurement of some observable A measured twice, one A measurement after the other. The second one, A-B-A, is reproducibility with probability 1 of a result of A measurement when another quantum observable B is measured between two A's. Heuristically, it is clear that the second type of reproducibility is complementary to the order effect. We show that, surprisingly, this may not be the case. The order effect can coexist with a separated reproducibility as well as adjacent reproducibility for both observables A and B. However, the additional constraint in the form of separated reproducibility of the B-A-B type makes this coexistence impossible. The problem under consideration was motivated by attempts to apply the quantum formalism outside of physics, especially, in cognitive psychology and psychophysics. However, it is also important for foundations of quantum physics as a part of the problem about the structure of sequential quantum measurements.

Contrasting grading approaches in introductory physics and quantum mechanics: The case of graduate teaching assistants

NASA Astrophysics Data System (ADS)

Marshman, Emily; Sayer, Ryan; Henderson, Charles; Singh, Chandralekha

2017-06-01

At large research universities, physics graduate teaching assistants (TAs) are often responsible for grading in courses at all levels. However, few studies have focused on TAs' grading practices in introductory and advanced physics courses. This study was designed to investigate whether physics graduate TAs grade students in introductory physics and quantum mechanics using different criteria and if so, why they may be inclined to do so. To investigate possible discrepancies in TAs' grading approaches in courses at different levels, we implemented a sequence of instructional activities in a TA professional development course that asked TAs to grade student solutions of introductory physics and upper-level quantum mechanics problems and explain why, if at all, their grading approaches were different or similar in the two contexts. We analyzed the differences in TAs' grading approaches in the two contexts and discuss the reasons they provided for the differences in their grading approaches in introductory physics and quantum mechanics in individual interviews, class discussions, and written responses. We find that a majority of the TAs graded solutions to quantum mechanics problems differently than solutions to introductory physics problems. In quantum mechanics, the TAs focused more on physics concepts and reasoning and penalized students for not showing evidence of understanding. The findings of the study have implications for TA professional development programs, e.g., the importance of helping TAs think about the difficulty of a problem from an introductory students' perspective and reflecting on the benefits of formative assessment.

Applications and error correction for adiabatic quantum optimization

NASA Astrophysics Data System (ADS)

Pudenz, Kristen

Adiabatic quantum optimization (AQO) is a fast-developing subfield of quantum information processing which holds great promise in the relatively near future. Here we develop an application, quantum anomaly detection, and an error correction code, Quantum Annealing Correction (QAC), for use with AQO. The motivation for the anomaly detection algorithm is the problematic nature of classical software verification and validation (V&V). The number of lines of code written for safety-critical applications such as cars and aircraft increases each year, and with it the cost of finding errors grows exponentially (the cost of overlooking errors, which can be measured in human safety, is arguably even higher). We approach the V&V problem by using a quantum machine learning algorithm to identify charateristics of software operations that are implemented outside of specifications, then define an AQO to return these anomalous operations as its result. Our error correction work is the first large-scale experimental demonstration of quantum error correcting codes. We develop QAC and apply it to USC's equipment, the first and second generation of commercially available D-Wave AQO processors. We first show comprehensive experimental results for the code's performance on antiferromagnetic chains, scaling the problem size up to 86 logical qubits (344 physical qubits) and recovering significant encoded success rates even when the unencoded success rates drop to almost nothing. A broader set of randomized benchmarking problems is then introduced, for which we observe similar behavior to the antiferromagnetic chain, specifically that the use of QAC is almost always advantageous for problems of sufficient size and difficulty. Along the way, we develop problem-specific optimizations for the code and gain insight into the various on-chip error mechanisms (most prominently thermal noise, since the hardware operates at finite temperature) and the ways QAC counteracts them. We finish by showing that the scheme is robust to qubit loss on-chip, a significant benefit when considering an implemented system.

Proposed Test of Relative Phase as Hidden Variable in Quantum Mechanics

DTIC Science & Technology

2012-01-01

implicitly due to its ubiquity in quantum theory , but searches for dependence of measurement outcome on other parameters have been lacking. For a two -state...implemen- tation for the specific case of an atomic two -state system with laser-induced fluores- cence for measurement. Keywords Quantum measurement...Measurement postulate · Born rule 1 Introduction 1.1 Problems with Quantum Measurement Quantum theory prescribes probabilities for outcomes of measurements

Quantum correlations in non-inertial cavity systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harsij, Zeynab, E-mail: z.harsij@ph.iut.ac.ir; Mirza, Behrouz, E-mail: b.mirza@cc.iut.ac.ir

2016-10-15

Non-inertial cavities are utilized to store and send Quantum Information between mode pairs. A two-cavity system is considered where one is inertial and the other accelerated in a finite time. Maclaurian series are applied to expand the related Bogoliubov coefficients and the problem is treated perturbatively. It is shown that Quantum Discord, which is a measure of quantumness of correlations, is degraded periodically. This is almost in agreement with previous results reached in accelerated systems where increment of acceleration decreases the degree of quantum correlations. As another finding of the study, it is explicitly shown that degradation of Quantum Discordmore » disappears when the state is in a single cavity which is accelerated for a finite time. This feature makes accelerating cavities useful instruments in Quantum Information Theory. - Highlights: • Non-inertial cavities are utilized to store and send information in Quantum Information Theory. • Cavities include boundary conditions which will protect the entanglement once it has been created. • The problem is treated perturbatively and the maclaurian series are applied to expand the related Bogoliubov coefficients. • When two cavities are considered degradation in the degree of quantum correlation happens and it appears periodically. • The interesting issue is when a single cavity is studied and the degradation in quantum correlations disappears.« less

Entanglement and Metrology with Singlet-Triplet Qubits

NASA Astrophysics Data System (ADS)

Shulman, Michael Dean

Electron spins confined in semiconductor quantum dots are emerging as a promising system to study quantum information science and to perform sensitive metrology. Their weak interaction with the environment leads to long coherence times and robust storage for quantum information, and the intrinsic tunability of semiconductors allows for controllable operations, initialization, and readout of their quantum state. These spin qubits are also promising candidates for the building block for a scalable quantum information processor due to their prospects for scalability and miniaturization. However, several obstacles limit the performance of quantum information experiments in these systems. For example, the weak coupling to the environment makes inter-qubit operations challenging, and a fluctuating nuclear magnetic field limits the performance of single-qubit operations. The focus of this thesis will be several experiments which address some of the outstanding problems in semiconductor spin qubits, in particular, singlet-triplet (S-T0) qubits. We use these qubits to probe both the electric field and magnetic field noise that limit the performance of these qubits. The magnetic noise bath is probed with high bandwidth and precision using novel techniques borrowed from the field of Hamiltonian learning, which are effective due to the rapid control and readout available in S-T 0 qubits. These findings allow us to effectively undo the undesired effects of the fluctuating nuclear magnetic field by tracking them in real-time, and we demonstrate a 30-fold improvement in the coherence time T2*. We probe the voltage noise environment of the qubit using coherent qubit oscillations, which is partially enabled by control of the nuclear magnetic field. We find that the voltage noise bath is frequency-dependent, even at frequencies as high as 1MHz, and it shows surprising and, as of yet, unexplained temperature dependence. We leverage this knowledge of the voltage noise environment, the nuclear magnetic field control, as well as new techniques for calibrated measurement of the density matrix in a singlet-triplet qubit to entangle two adjacent single-triplet qubits. We fully characterize the generated entangled states and prove that they are, indeed, entangled. This work opens new opportunities to use qubits as sensors for improved metrological capabilities, as well as for improved quantum information processing. The singlet-triplet qubit is unique in that it can be used to probe two fundamentally different noise baths, which are important for a large variety of solid state qubits. More specifically, this work establishes the singlet-triplet qubit as a viable candidate for the building block of a scalable quantum information processor.

Teaching Quantum Physics in Upper Secondary School in France:

ERIC Educational Resources Information Center

Lautesse, Philippe; Vila Valls, Adrien; Ferlin, Fabrice; Héraud, Jean-Loup; Chabot, Hugues

2015-01-01

One of the main problems in trying to understand quantum physics is the nature of the referent of quantum theory. This point is addressed in the official French curriculum in upper secondary school. Starting in 2012, after about 20 years of absence, quantum physics has returned to the national program. On the basis of the historical construction…

Hidden algebra method (quasi-exact-solvability in quantum mechanics)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Turbiner, Alexander; Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado, Postal 70-543, 04510 Mexico, D. F.

1996-02-20

A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland N-body problems ass ociated with an existence of the hidden algebra slN is discussed extensively.

Redesigning the Quantum Mechanics Curriculum to Incorporate Problem Solving Using a Computer Algebra System

NASA Astrophysics Data System (ADS)

Roussel, Marc R.

1999-10-01

One of the traditional obstacles to learning quantum mechanics is the relatively high level of mathematical proficiency required to solve even routine problems. Modern computer algebra systems are now sufficiently reliable that they can be used as mathematical assistants to alleviate this difficulty. In the quantum mechanics course at the University of Lethbridge, the traditional three lecture hours per week have been replaced by two lecture hours and a one-hour computer-aided problem solving session using a computer algebra system (Maple). While this somewhat reduces the number of topics that can be tackled during the term, students have a better opportunity to familiarize themselves with the underlying theory with this course design. Maple is also available to students during examinations. The use of a computer algebra system expands the class of feasible problems during a time-limited exercise such as a midterm or final examination. A modern computer algebra system is a complex piece of software, so some time needs to be devoted to teaching the students its proper use. However, the advantages to the teaching of quantum mechanics appear to outweigh the disadvantages.

On the emergence of the structure of physics

NASA Astrophysics Data System (ADS)

Majid, S.

2018-04-01

We consider Hilbert's problem of the axioms of physics at a qualitative or conceptual level. This is more pressing than ever as we seek to understand how both general relativity and quantum theory could emerge from some deeper theory of quantum gravity, and in this regard I have previously proposed a principle of self-duality or quantum Born reciprocity as a key structure. Here, I outline some of my recent work around the idea of quantum space-time as motivated by this non-standard philosophy, including a new toy model of gravity on a space-time consisting of four points forming a square. This article is part of the theme issue `Hilbert's sixth problem'.

Asymptotic quantum inelastic generalized Lorenz Mie theory

NASA Astrophysics Data System (ADS)

Gouesbet, G.

2007-10-01

The (electromagnetic) generalized Lorenz-Mie theory describes the interaction between an electromagnetic arbitrary shaped beam and a homogeneous sphere. It is a generalization of the Lorenz-Mie theory which deals with the simpler case of a plane wave illumination. In a recent paper, we consider (i) elastic cross-sections in electromagnetic generalized Lorenz-Mie theory and (ii) elastic cross-sections in an associated quantum generalized Lorenz-Mie theory. We demonstrated that the electromagnetic problem is equivalent to a superposition of two effective quantum problems. We now intend to generalize this result from elastic cross-sections to inelastic cross-sections. A prerequisite is to build an asymptotic quantum inelastic generalized Lorenz-Mie theory, which is presented in this paper.

Solving the Nonlocality Riddle by Conformal Quantum Geometrodynamics

NASA Astrophysics Data System (ADS)

Santamato, Enrico; de Martini, Francesco

2012-01-01

Since the 1935 proposal by Einstein, Podolsky and Rosen the riddle of nonlocality, today demonstrated by the violation of Bell's inequalities within innumerable experiments, has been a cause of concern and confusion within the debate over the foundations of quantum mechanics. The present paper tackles the problem by a nonrelativistic approach based on conformal differential geometry applied to the solution of the dynamical problem of two entangled spin 1/2 particles. It is found that the quantum nonlocality may be understood on the basis of a conformal quantum geometrodynamics acting necessarily on the full "configuration space" of the entangled particles. At the end, the violation of the Bell inequalities is demonstrated without making recourse to the common nonlocality paradigm.

On the emergence of the structure of physics.

PubMed

Majid, S

2018-04-28

We consider Hilbert's problem of the axioms of physics at a qualitative or conceptual level. This is more pressing than ever as we seek to understand how both general relativity and quantum theory could emerge from some deeper theory of quantum gravity, and in this regard I have previously proposed a principle of self-duality or quantum Born reciprocity as a key structure. Here, I outline some of my recent work around the idea of quantum space-time as motivated by this non-standard philosophy, including a new toy model of gravity on a space-time consisting of four points forming a square.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere

NASA Astrophysics Data System (ADS)

Okon, Elias; Sudarsky, Daniel

2016-07-01

In Crull (Found Phys 45:1019-1045, 2015) it is argued that, in order to confront outstanding problems in cosmology and quantum gravity, interpretational aspects of quantum theory can by bypassed because decoherence is able to resolve them. As a result, Crull (Found Phys 45:1019-1045, 2015) concludes that our focus on conceptual and interpretational issues, while dealing with such matters in Okon and Sudarsky (Found Phys 44:114-143, 2014), is avoidable and even pernicious. Here we will defend our position by showing in detail why decoherence does not help in the resolution of foundational questions in quantum mechanics, such as the measurement problem or the emergence of classicality.

Experimental demonstration of a BDCZ quantum repeater node.

PubMed

Yuan, Zhen-Sheng; Chen, Yu-Ao; Zhao, Bo; Chen, Shuai; Schmiedmayer, Jörg; Pan, Jian-Wei

2008-08-28

Quantum communication is a method that offers efficient and secure ways for the exchange of information in a network. Large-scale quantum communication (of the order of 100 km) has been achieved; however, serious problems occur beyond this distance scale, mainly due to inevitable photon loss in the transmission channel. Quantum communication eventually fails when the probability of a dark count in the photon detectors becomes comparable to the probability that a photon is correctly detected. To overcome this problem, Briegel, Dür, Cirac and Zoller (BDCZ) introduced the concept of quantum repeaters, combining entanglement swapping and quantum memory to efficiently extend the achievable distances. Although entanglement swapping has been experimentally demonstrated, the implementation of BDCZ quantum repeaters has proved challenging owing to the difficulty of integrating a quantum memory. Here we realize entanglement swapping with storage and retrieval of light, a building block of the BDCZ quantum repeater. We follow a scheme that incorporates the strategy of BDCZ with atomic quantum memories. Two atomic ensembles, each originally entangled with a single emitted photon, are projected into an entangled state by performing a joint Bell state measurement on the two single photons after they have passed through a 300-m fibre-based communication channel. The entanglement is stored in the atomic ensembles and later verified by converting the atomic excitations into photons. Our method is intrinsically phase insensitive and establishes the essential element needed to realize quantum repeaters with stationary atomic qubits as quantum memories and flying photonic qubits as quantum messengers.

Recent Developments in Quantum-Well Infrared Photodetectors

NASA Technical Reports Server (NTRS)

Gunapala, S. D.; Bandara, K. M. S. V.

1995-01-01

Intrinsic infrared (IR) detectors in the long wavelength range (8-20 Am) are based on an optically excited interband transition, which promotes an electron across the band gap (E(sub g)) from the valence band to the conduction band as shown. These photoelectrons can be collected efficiently, thereby producing a photocurrent in the external circuit. Since the incoming photon has to promote an electron from the valence band to the conduction band, the energy of the photon (h(sub upsilon)) must be higher than the E(sub g) of the photosensitive material. Therefore, the spectral response of the detectors can be controlled by controlling the E(sub g) of the photosensitive material. Examples for such materials are Hg(1-x), Cd(x), Te, and Pb(1-x), Sn(x), Te, in which the energy gap can be controlled by varying x. This means detection of very-long-wavelength IR radiation up to 20 microns requires small band gaps down to 62 meV. It is well known that these low band gap materials, characterized by weak bonding and low melting points, are more difficult to grow and process than large-band gap semiconductors such as GaAs. These difficulties motivate the exploration of utilizing the intersub-band transitions in multiquantum well (MQW) structures made of more refractory large-band gap semiconductors. The idea of using MQW structures to detect IR radiation can be explained by using the basic principles of quantum mechanics. The quantum well is equivalent to the well-known particle in a box problem in quantum mechanics, which can be solved by the time independent Schroudiner equation.

Harnessing quantum transport by transient chaos.

PubMed

Yang, Rui; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso; Pecora, Louis M

2013-03-01

Chaos has long been recognized to be generally advantageous from the perspective of control. In particular, the infinite number of unstable periodic orbits embedded in a chaotic set and the intrinsically sensitive dependence on initial conditions imply that a chaotic system can be controlled to a desirable state by using small perturbations. Investigation of chaos control, however, was largely limited to nonlinear dynamical systems in the classical realm. In this paper, we show that chaos may be used to modulate or harness quantum mechanical systems. To be concrete, we focus on quantum transport through nanostructures, a problem of considerable interest in nanoscience, where a key feature is conductance fluctuations. We articulate and demonstrate that chaos, more specifically transient chaos, can be effective in modulating the conductance-fluctuation patterns. Experimentally, this can be achieved by applying an external gate voltage in a device of suitable geometry to generate classically inaccessible potential barriers. Adjusting the gate voltage allows the characteristics of the dynamical invariant set responsible for transient chaos to be varied in a desirable manner which, in turn, can induce continuous changes in the statistical characteristics of the quantum conductance-fluctuation pattern. To understand the physical mechanism of our scheme, we develop a theory based on analyzing the spectrum of the generalized non-Hermitian Hamiltonian that includes the effect of leads, or electronic waveguides, as self-energy terms. As the escape rate of the underlying non-attracting chaotic set is increased, the imaginary part of the complex eigenenergy becomes increasingly large so that pointer states are more difficult to form, making smoother the conductance-fluctuation pattern.

Impurity-generated non-Abelions

NASA Astrophysics Data System (ADS)

Simion, G.; Kazakov, A.; Rokhinson, L. P.; Wojtowicz, T.; Lyanda-Geller, Y. B.

2018-06-01

Two classes of topological superconductors and Majorana modes in condensed matter systems are known to date: one in which disorder induced by impurities strongly suppresses topological superconducting gap and is detrimental to Majorana modes, and another where Majorana fermions are protected by a disorder-robust topological superconductor gap. Observation and control of Majorana fermions and other non-Abelions often requires a symmetry of an underlying system leading to a gap in the single-particle or quasiparticle spectra. In semiconductor structures, impurities that provide charge carriers introduce states into the gap and enable conductance and proximity-induced superconductivity via the in-gap states. Thus a third class of topological superconductivity and Majorana modes emerges, in which topological superconductivity and Majorana fermions appear exclusively when impurities generate in-gap states. We show that impurity-enabled topological superconductivity is realized in a quantum Hall ferromagnet, when a helical domain wall is coupled to an s -wave superconductor. As an example of emergence of topological superconductivity in quantum Hall ferromagnets, we consider the integer quantum Hall effect in Mn-doped CdTe quantum wells. Recent experiments on transport through the quantum Hall ferromagnet domain wall in this system indicated a vital role of impurities in the conductance, but left unresolved the question whether impurities preclude generation of Majorana fermions and other non-Abelions in such systems in general. Here, solving a general quantum-mechanical problem of impurity bound states in a system of spin-orbit coupled Landau levels, we demonstrate that impurity-induced Majorana modes emerge at boundaries between topological and conventional superconducting states generated in a domain wall due to proximity to an s superconductor. We consider both short-range disorder and a smooth random potential. The phase diagram of the system is defined by characteristic disorder, gate voltage induced angular momentum splitting of impurity levels, and by a proximity superconducting gap. The phase diagram exhibits two ranges of gate voltage with conventional superconducting order separated by a gate voltage range with topological superconductivity. We show that electrostatic control of domain walls in an integer quantum Hall ferromagnet allows manipulation of Majorana fermions. Ferromagnetic transitions in the fractional quantum Hall regime may lead to the formation and electrostatic control of higher order non-Abelian excitations.

Sampled-data design for sliding mode control based on various robust specifications in open quantum system

NASA Astrophysics Data System (ADS)

Ji, Yinghua; Ju-Ju, Hu; Jian-Hua, Huang; Qiang, Ke

Due to the influence of decoherence, the quantum state probably evolves from the initial pure state to the mixed state, resulting in loss of fidelity, coherence and purity, which is deteriorating for quantum information transmission. Thus, in quantum engineering, quantum control should not only realize the transfer and track of quantum states through manipulation of the external electromagnetic field but also enhance the robustness against decoherence. In this paper, we aim to design a control law to steer the system into the sliding mode domain and maintain it in that domain when bounded uncertainties exist in the system Hamiltonian. We first define the required control performance by fidelity, degree of coherence and purity in terms of the uncertainty of the Hamiltonian in Markovian open quantum system. By characterizing the required robustness using a sliding mode domain, a sampled-data design method is introduced for decoherence control in the quantum system. Furthermore, utilizing the sampled data, a control scheme has been designed on the basis of sliding mode control, and the choice of sampling operator and driving of quantum state during the sampling by the Lyapunov control method are discussed.

Quantum factorization of 143 on a dipolar-coupling nuclear magnetic resonance system.

PubMed

Xu, Nanyang; Zhu, Jing; Lu, Dawei; Zhou, Xianyi; Peng, Xinhua; Du, Jiangfeng

2012-03-30

Quantum algorithms could be much faster than classical ones in solving the factoring problem. Adiabatic quantum computation for this is an alternative approach other than Shor's algorithm. Here we report an improved adiabatic factoring algorithm and its experimental realization to factor the number 143 on a liquid-crystal NMR quantum processor with dipole-dipole couplings. We believe this to be the largest number factored in quantum-computation realizations, which shows the practical importance of adiabatic quantum algorithms.

Adiabatic quantum computing with spin qubits hosted by molecules.

PubMed

Yamamoto, Satoru; Nakazawa, Shigeaki; Sugisaki, Kenji; Sato, Kazunobu; Toyota, Kazuo; Shiomi, Daisuke; Takui, Takeji

2015-01-28

A molecular spin quantum computer (MSQC) requires electron spin qubits, which pulse-based electron spin/magnetic resonance (ESR/MR) techniques can afford to manipulate for implementing quantum gate operations in open shell molecular entities. Importantly, nuclear spins, which are topologically connected, particularly in organic molecular spin systems, are client qubits, while electron spins play a role of bus qubits. Here, we introduce the implementation for an adiabatic quantum algorithm, suggesting the possible utilization of molecular spins with optimized spin structures for MSQCs. We exemplify the utilization of an adiabatic factorization problem of 21, compared with the corresponding nuclear magnetic resonance (NMR) case. Two molecular spins are selected: one is a molecular spin composed of three exchange-coupled electrons as electron-only qubits and the other an electron-bus qubit with two client nuclear spin qubits. Their electronic spin structures are well characterized in terms of the quantum mechanical behaviour in the spin Hamiltonian. The implementation of adiabatic quantum computing/computation (AQC) has, for the first time, been achieved by establishing ESR/MR pulse sequences for effective spin Hamiltonians in a fully controlled manner of spin manipulation. The conquered pulse sequences have been compared with the NMR experiments and shown much faster CPU times corresponding to the interaction strength between the spins. Significant differences are shown in rotational operations and pulse intervals for ESR/MR operations. As a result, we suggest the advantages and possible utilization of the time-evolution based AQC approach for molecular spin quantum computers and molecular spin quantum simulators underlain by sophisticated ESR/MR pulsed spin technology.

CUGatesDensity—Quantum circuit analyser extended to density matrices

NASA Astrophysics Data System (ADS)

Loke, T.; Wang, J. B.

2013-12-01

CUGatesDensity is an extension of the original quantum circuit analyser CUGates (Loke and Wang, 2011) [7] to provide explicit support for the use of density matrices. The new package enables simulation of quantum circuits involving statistical ensemble of mixed quantum states. Such analysis is of vital importance in dealing with quantum decoherence, measurements, noise and error correction, and fault tolerant computation. Several examples involving mixed state quantum computation are presented to illustrate the use of this package. Catalogue identifier: AEPY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPY_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5368 No. of bytes in distributed program, including test data, etc.: 143994 Distribution format: tar.gz Programming language: Mathematica. Computer: Any computer installed with a copy of Mathematica 6.0 or higher. Operating system: Any system with a copy of Mathematica 6.0 or higher installed. Classification: 4.15. Nature of problem: To simulate arbitrarily complex quantum circuits comprised of single/multiple qubit and qudit quantum gates with mixed state registers. Solution method: A density matrix representation for mixed states and a state vector representation for pure states are used. The construct is based on an irreducible form of matrix decomposition, which allows a highly efficient implementation of general controlled gates with multiple conditionals. Running time: The examples provided in the notebook CUGatesDensity.nb take approximately 30 s to run on a laptop PC.

A quantum-like model of homeopathy clinical trials: importance of in situ randomization and unblinding.

PubMed

Beauvais, Francis

2013-04-01

The randomized controlled trial (RCT) is the 'gold standard' of modern clinical pharmacology. However, for many practitioners of homeopathy, blind RCTs are an inadequate research tool for testing complex therapies such as homeopathy. Classical probabilities used in biological sciences and in medicine are only a special case of the generalized theory of probability used in quantum physics. I describe homeopathy trials using a quantum-like statistical model, a model inspired by quantum physics and taking into consideration superposition of states, non-commuting observables, probability interferences, contextuality, etc. The negative effect of blinding on success of homeopathy trials and the 'smearing effect' ('specific' effects of homeopathy medicine occurring in the placebo group) are described by quantum-like probabilities without supplementary ad hoc hypotheses. The difference of positive outcome rates between placebo and homeopathy groups frequently vanish in centralized blind trials. The model proposed here suggests a way to circumvent such problems in masked homeopathy trials by incorporating in situ randomization/unblinding. In this quantum-like model of homeopathy clinical trials, success in open-label setting and failure with centralized blind RCTs emerge logically from the formalism. This model suggests that significant differences between placebo and homeopathy in blind RCTs would be found more frequently if in situ randomization/unblinding was used. Copyright © 2013. Published by Elsevier Ltd.

Quantum Change Point

NASA Astrophysics Data System (ADS)

Sentís, Gael; Bagan, Emilio; Calsamiglia, John; Chiribella, Giulio; Muñoz-Tapia, Ramon

2016-10-01

Sudden changes are ubiquitous in nature. Identifying them is crucial for a number of applications in biology, medicine, and social sciences. Here we take the problem of detecting sudden changes to the quantum domain. We consider a source that emits quantum particles in a default state, until a point where a mutation occurs that causes the source to switch to another state. The problem is then to find out where the change occurred. We determine the maximum probability of correctly identifying the change point, allowing for collective measurements on the whole sequence of particles emitted by the source. Then, we devise online strategies where the particles are measured individually and an answer is provided as soon as a new particle is received. We show that these online strategies substantially underperform the optimal quantum measurement, indicating that quantum sudden changes, although happening locally, are better detected globally.

Supersymmetric symplectic quantum mechanics

NASA Astrophysics Data System (ADS)

de Menezes, Miralvo B.; Fernandes, M. C. B.; Martins, Maria das Graças R.; Santana, A. E.; Vianna, J. D. M.

2018-02-01

Symplectic Quantum Mechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article we extend the methods of supersymmetric quantum mechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantum mechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function.

Performance Models for Split-execution Computing Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Humble, Travis S; McCaskey, Alex; Schrock, Jonathan

Split-execution computing leverages the capabilities of multiple computational models to solve problems, but splitting program execution across different computational models incurs costs associated with the translation between domains. We analyze the performance of a split-execution computing system developed from conventional and quantum processing units (QPUs) by using behavioral models that track resource usage. We focus on asymmetric processing models built using conventional CPUs and a family of special-purpose QPUs that employ quantum computing principles. Our performance models account for the translation of a classical optimization problem into the physical representation required by the quantum processor while also accounting for hardwaremore » limitations and conventional processor speed and memory. We conclude that the bottleneck in this split-execution computing system lies at the quantum-classical interface and that the primary time cost is independent of quantum processor behavior.« less

Quantum Barro-Gordon game in monetary economics

NASA Astrophysics Data System (ADS)

Samadi, Ali Hussein; Montakhab, Afshin; Marzban, Hussein; Owjimehr, Sakine

2018-01-01

Classical game theory addresses decision problems in multi-agent environment where one rational agent's decision affects other agents' payoffs. Game theory has widespread application in economic, social and biological sciences. In recent years quantum versions of classical games have been proposed and studied. In this paper, we consider a quantum version of the classical Barro-Gordon game which captures the problem of time inconsistency in monetary economics. Such time inconsistency refers to the temptation of weak policy maker to implement high inflation when the public expects low inflation. The inconsistency arises when the public punishes the weak policy maker in the next cycle. We first present a quantum version of the Barro-Gordon game. Next, we show that in a particular case of the quantum game, time-consistent Nash equilibrium could be achieved when public expects low inflation, thus resolving the game.

Modern Quantum Field Theory II - Proceeeings of the International Colloquium

NASA Astrophysics Data System (ADS)

Das, S. R.; Mandal, G.; Mukhi, S.; Wadia, S. R.

1995-08-01

The Table of Contents for the book is as follows: * Foreword * 1. Black Holes and Quantum Gravity * Quantum Black Holes and the Problem of Time * Black Hole Entropy and the Semiclassical Approximation * Entropy and Information Loss in Two Dimensions * Strings on a Cone and Black Hole Entropy (Abstract) * Boundary Dynamics, Black Holes and Spacetime Fluctuations in Dilation Gravity (Abstract) * Pair Creation of Black Holes (Abstract) * A Brief View of 2-Dim. String Theory and Black Holes (Abstract) * 2. String Theory * Non-Abelian Duality in WZW Models * Operators and Correlation Functions in c ≤ 1 String Theory * New Symmetries in String Theory * A Look at the Discretized Superstring Using Random Matrices * The Nested BRST Structure of Wn-Symmetries * Landau-Ginzburg Model for a Critical Topological String (Abstract) * On the Geometry of Wn Gravity (Abstract) * O(d, d) Tranformations, Marginal Deformations and the Coset Construction in WZNW Models (Abstract) * Nonperturbative Effects and Multicritical Behaviour of c = 1 Matrix Model (Abstract) * Singular Limits and String Solutions (Abstract) * BV Algebra on the Moduli Spaces of Riemann Surfaces and String Field Theory (Abstract) * 3. Condensed Matter and Statistical Mechanics * Stochastic Dynamics in a Deposition-Evaporation Model on a Line * Models with Inverse-Square Interactions: Conjectured Dynamical Correlation Functions of the Calogero-Sutherland Model at Rational Couplings * Turbulence and Generic Scale Invariance * Singular Perturbation Approach to Phase Ordering Dynamics * Kinetics of Diffusion-Controlled and Ballistically-Controlled Reactions * Field Theory of a Frustrated Heisenberg Spin Chain * FQHE Physics in Relativistic Field Theories * Importance of Initial Conditions in Determining the Dynamical Class of Cellular Automata (Abstract) * Do Hard-Core Bosons Exhibit Quantum Hall Effect? (Abstract) * Hysteresis in Ferromagnets * 4. Fundamental Aspects of Quantum Mechanics and Quantum Field Theory * Finite Quantum Physics and Noncommutative Geometry * Higgs as Gauge Field and the Standard Model * Canonical Quantisation of an Off-Conformal Theory * Deterministic Quantum Mechanics in One Dimension * Spin-Statistics Relations for Topological Geons in 2+1 Quantum Gravity * Generalized Fock Spaces * Geometrical Expression for Short Distance Singularities in Field Theory * 5. Mathematics and Quantum Field Theory * Knot Invariants from Quantum Field Theories * Infinite Grassmannians and Moduli Spaces of G-Bundles * A Review of an Algebraic Geometry Approach to a Model Quantum Field Theory on a Curve (Abstract) * 6. Integrable Models * Spectral Representation of Correlation Functions in Two-Dimensional Quantum Field Theories * On Various Avatars of the Pasquier Algebra * Supersymmetric Integrable Field Theories and Eight Vertex Free Fermion Models (Abstract) * 7. Lattice Field Theory * From Kondo Model and Strong Coupling Lattice QCD to the Isgur-Wise Function * Effective Confinement from a Logarithmically Running Coupling (Abstract)

Experimental benchmarking of quantum control in zero-field nuclear magnetic resonance.

PubMed

Jiang, Min; Wu, Teng; Blanchard, John W; Feng, Guanru; Peng, Xinhua; Budker, Dmitry

2018-06-01

Demonstration of coherent control and characterization of the control fidelity is important for the development of quantum architectures such as nuclear magnetic resonance (NMR). We introduce an experimental approach to realize universal quantum control, and benchmarking thereof, in zero-field NMR, an analog of conventional high-field NMR that features less-constrained spin dynamics. We design a composite pulse technique for both arbitrary one-spin rotations and a two-spin controlled-not (CNOT) gate in a heteronuclear two-spin system at zero field, which experimentally demonstrates universal quantum control in such a system. Moreover, using quantum information-inspired randomized benchmarking and partial quantum process tomography, we evaluate the quality of the control, achieving single-spin control for 13 C with an average fidelity of 0.9960(2) and two-spin control via a CNOT gate with a fidelity of 0.9877(2). Our method can also be extended to more general multispin heteronuclear systems at zero field. The realization of universal quantum control in zero-field NMR is important for quantum state/coherence preparation, pulse sequence design, and is an essential step toward applications to materials science, chemical analysis, and fundamental physics.

Experimental benchmarking of quantum control in zero-field nuclear magnetic resonance

PubMed Central

Feng, Guanru

2018-01-01

Demonstration of coherent control and characterization of the control fidelity is important for the development of quantum architectures such as nuclear magnetic resonance (NMR). We introduce an experimental approach to realize universal quantum control, and benchmarking thereof, in zero-field NMR, an analog of conventional high-field NMR that features less-constrained spin dynamics. We design a composite pulse technique for both arbitrary one-spin rotations and a two-spin controlled-not (CNOT) gate in a heteronuclear two-spin system at zero field, which experimentally demonstrates universal quantum control in such a system. Moreover, using quantum information–inspired randomized benchmarking and partial quantum process tomography, we evaluate the quality of the control, achieving single-spin control for 13C with an average fidelity of 0.9960(2) and two-spin control via a CNOT gate with a fidelity of 0.9877(2). Our method can also be extended to more general multispin heteronuclear systems at zero field. The realization of universal quantum control in zero-field NMR is important for quantum state/coherence preparation, pulse sequence design, and is an essential step toward applications to materials science, chemical analysis, and fundamental physics. PMID:29922714

Continuous-time quantum random walks require discrete space

NASA Astrophysics Data System (ADS)

Manouchehri, K.; Wang, J. B.

2007-11-01

Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the case of continuous-time quantum random walks, such peculiar dynamics can arise from simple evolution operators closely resembling the quantum free-wave propagator. We investigate the divergence of quantum walk dynamics from the free-wave evolution and show that, in order for continuous-time quantum walks to display their characteristic propagation, the state space must be discrete. This behavior rules out many continuous quantum systems as possible candidates for implementing continuous-time quantum random walks.

Quantum annealing with parametrically driven nonlinear oscillators

NASA Astrophysics Data System (ADS)

Puri, Shruti

While progress has been made towards building Ising machines to solve hard combinatorial optimization problems, quantum speedups have so far been elusive. Furthermore, protecting annealers against decoherence and achieving long-range connectivity remain important outstanding challenges. With the hope of overcoming these challenges, I introduce a new paradigm for quantum annealing that relies on continuous variable states. Unlike the more conventional approach based on two-level systems, in this approach, quantum information is encoded in two coherent states that are stabilized by parametrically driving a nonlinear resonator. I will show that a fully connected Ising problem can be mapped onto a network of such resonators, and outline an annealing protocol based on adiabatic quantum computing. During the protocol, the resonators in the network evolve from vacuum to coherent states representing the ground state configuration of the encoded problem. In short, the system evolves between two classical states following non-classical dynamics. As will be supported by numerical results, this new annealing paradigm leads to superior noise resilience. Finally, I will discuss a realistic circuit QED realization of an all-to-all connected network of parametrically driven nonlinear resonators. The continuous variable nature of the states in the large Hilbert space of the resonator provides new opportunities for exploring quantum phase transitions and non-stoquastic dynamics during the annealing schedule.

Hidden Statistics Approach to Quantum Simulations

NASA Technical Reports Server (NTRS)

Zak, Michail

2010-01-01

Recent advances in quantum information theory have inspired an explosion of interest in new quantum algorithms for solving hard computational (quantum and non-quantum) problems. The basic principle of quantum computation is that the quantum properties can be used to represent structure data, and that quantum mechanisms can be devised and built to perform operations with this data. Three basic non-classical properties of quantum mechanics superposition, entanglement, and direct-product decomposability were main reasons for optimism about capabilities of quantum computers that promised simultaneous processing of large massifs of highly correlated data. Unfortunately, these advantages of quantum mechanics came with a high price. One major problem is keeping the components of the computer in a coherent state, as the slightest interaction with the external world would cause the system to decohere. That is why the hardware implementation of a quantum computer is still unsolved. The basic idea of this work is to create a new kind of dynamical system that would preserve the main three properties of quantum physics superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. In other words, such a system would reinforce the advantages and minimize limitations of both quantum and classical aspects. Based upon a concept of hidden statistics, a new kind of dynamical system for simulation of Schroedinger equation is proposed. The system represents a modified Madelung version of Schroedinger equation. It preserves superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. Such an optimal combination of characteristics is a perfect match for simulating quantum systems. The model includes a transitional component of quantum potential (that has been overlooked in previous treatment of the Madelung equation). The role of the transitional potential is to provide a jump from a deterministic state to a random state with prescribed probability density. This jump is triggered by blowup instability due to violation of Lipschitz condition generated by the quantum potential. As a result, the dynamics attains quantum properties on a classical scale. The model can be implemented physically as an analog VLSI-based (very-large-scale integration-based) computer, or numerically on a digital computer. This work opens a way of developing fundamentally new algorithms for quantum simulations of exponentially complex problems that expand NASA capabilities in conducting space activities. It has been illustrated that the complexity of simulations of particle interaction can be reduced from an exponential one to a polynomial one.

ON THE DYNAMICAL DERIVATION OF EQUILIBRIUM STATISTICAL MECHANICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prigogine, I.; Balescu, R.; Henin, F.

1960-12-01

Work on nonequilibrium statistical mechanics, which allows an extension of the kinetic proof to all results of equilibrium statistical mechanics involving a finite number of degrees of freedom, is summarized. As an introduction to the general N-body problem, the scattering theory in classical mechanics is considered. The general N-body problem is considered for the case of classical mechanics, quantum mechanics with Boltzmann statistics, and quantum mechanics including quantum statistics. Six basic diagrams, which describe the elementary processes of the dynamics of correlations, were obtained. (M.C.G.)

Temperature Scaling Law for Quantum Annealing Optimizers.

PubMed

Albash, Tameem; Martin-Mayor, Victor; Hen, Itay

2017-09-15

Physical implementations of quantum annealing unavoidably operate at finite temperatures. We point to a fundamental limitation of fixed finite temperature quantum annealers that prevents them from functioning as competitive scalable optimizers and show that to serve as optimizers annealer temperatures must be appropriately scaled down with problem size. We derive a temperature scaling law dictating that temperature must drop at the very least in a logarithmic manner but also possibly as a power law with problem size. We corroborate our results by experiment and simulations and discuss the implications of these to practical annealers.

Benefits of Objective Collapse Models for Cosmology and Quantum Gravity

NASA Astrophysics Data System (ADS)

Okon, Elias; Sudarsky, Daniel

2014-02-01

We display a number of advantages of objective collapse theories for the resolution of long-standing problems in cosmology and quantum gravity. In particular, we examine applications of objective reduction models to three important issues: the origin of the seeds of cosmic structure, the problem of time in quantum gravity and the information loss paradox; we show how reduction models contain the necessary tools to provide solutions for these issues. We wrap up with an adventurous proposal, which relates the spontaneous collapse events of objective collapse models to microscopic virtual black holes.

A quantum heuristic algorithm for the traveling salesman problem

NASA Astrophysics Data System (ADS)

Bang, Jeongho; Ryu, Junghee; Lee, Changhyoup; Yoo, Seokwon; Lim, James; Lee, Jinhyoung

2012-12-01

We propose a quantum heuristic algorithm to solve the traveling salesman problem by generalizing the Grover search. Sufficient conditions are derived to greatly enhance the probability of finding the tours with the cheapest costs reaching almost to unity. These conditions are characterized by the statistical properties of tour costs and are shown to be automatically satisfied in the large-number limit of cities. In particular for a continuous distribution of the tours along the cost, we show that the quantum heuristic algorithm exhibits a quadratic speedup compared to its classical heuristic algorithm.

Book Review:

NASA Astrophysics Data System (ADS)

Giannetto, E.

2005-08-01

This book is a sort of tribute to Rob Clifton (1964 2002), Associate Professor of Philosophy and Associate Director of the Center for Philosophy of Science at the University of Pittsburgh, philosopher of physics and editor of the journal Studies in the History and Philosophy of Modern Physics, who tragically died of cancer. It contains fourteen papers by Clifton, for the most part written in collaboration with other authors (Jeffrey Bub (2), Sheldon Goldstein, Michael Dickson, Hans Halvorson (6), Adrian Kent (2)), published between 1995 and 2002. The choice of papers made by the editors is very impressive. They concern the foundations of quantum mechanics and quantum field theory. Among the issues discussed are the modal interpretations of quantum mechanics, the problems of hidden variables theories, non-locality, Bell's inequality, the Einstein Podolsky Rosen paradox, Lorentz invariance, de-coherence, non-contextuality, complementarity, entanglement and quantum information. A consequence of such investigations is that non-separability is a more complex issue than violation of Bell's inequality. Apart from the perspective one can follow—whether one agrees or not with Clifton—these papers are effective contributions to an understanding of the problems involved in the foundations of quantum mechanics. The most interesting parts, in my opinion, are related to the extension of the discussion of foundational problems to quantum field theory: on the algebraic approach, and on the twin concepts of particle and vacuum. Non-locality appears to be `worse' in relativistic quantum field theory than in non-relativistic quantum mechanics. All the papers deal with relevant epistemological and even historical aspects of quantum mechanics interpretations, but all the issues are discussed from a technical, logical and mathematical approach. A complete bibliography of Clifton's papers is given at the end of the volume.

Secure Communication via Key Generation with Quantum Measurement Advantage in the Telecom Band

DTIC Science & Technology

2013-10-30

II: Summary of Project In this basic research program we proposed to investigate the use of keyed communication in quantum noise as a key generation...implement quantum limited detection in our running-code OCDMA experiment to demonstrate (a) quantum measurement advantage creation between two users, (b...neither is adequate against known-plaintext attacks. This is a serious security problem facing the whole field of quantum cryptography in regard to both

Control of noisy quantum systems: Field-theory approach to error mitigation

NASA Astrophysics Data System (ADS)

Hipolito, Rafael; Goldbart, Paul M.

2016-04-01

We consider the basic quantum-control task of obtaining a target unitary operation (i.e., a quantum gate) via control fields that couple to the quantum system and are chosen to best mitigate errors resulting from time-dependent noise, which frustrate this task. We allow for two sources of noise: fluctuations in the control fields and fluctuations arising from the environment. We address the issue of control-error mitigation by means of a formulation rooted in the Martin-Siggia-Rose (MSR) approach to noisy, classical statistical-mechanical systems. To do this, we express the noisy control problem in terms of a path integral, and integrate out the noise to arrive at an effective, noise-free description. We characterize the degree of success in error mitigation via a fidelity metric, which characterizes the proximity of the sought-after evolution to ones that are achievable in the presence of noise. Error mitigation is then best accomplished by applying the optimal control fields, i.e., those that maximize the fidelity subject to any constraints obeyed by the control fields. To make connection with MSR, we reformulate the fidelity in terms of a Schwinger-Keldysh (SK) path integral, with the added twist that the "forward" and "backward" branches of the time contour are inequivalent with respect to the noise. The present approach naturally and readily allows the incorporation of constraints on the control fields—a useful feature in practice, given that constraints feature in all real experiments. In addition to addressing the noise average of the fidelity, we consider its full probability distribution. The information content present in this distribution allows one to address more complex questions regarding error mitigation, including, in principle, questions of extreme value statistics, i.e., the likelihood and impact of rare instances of the fidelity and how to harness or cope with their influence. We illustrate this MSR-SK reformulation by considering a model system consisting of a single spin-s freedom (with s arbitrary), focusing on the case of 1 /f noise in the weak-noise limit. We discover that optimal error mitigation is accomplished via a universal control field protocol that is valid for all s , from the qubit (i.e., s =1 /2 ) case to the classical (i.e., s →∞ ) limit. In principle, this MSR-SK approach provides a transparent framework for addressing quantum control in the presence of noise for systems of arbitrary complexity.

A pedestrian approach to the measurement problem in quantum mechanics

NASA Astrophysics Data System (ADS)

Boughn, Stephen; Reginatto, Marcel

2013-09-01

The quantum theory of measurement has been a matter of debate for over eighty years. Most of the discussion has focused on theoretical issues with the consequence that other aspects (such as the operational prescriptions that are an integral part of experimental physics) have been largely ignored. This has undoubtedly exacerbated attempts to find a solution to the "measurement problem". How the measurement problem is defined depends to some extent on how the theoretical concepts introduced by the theory are interpreted. In this paper, we fully embrace the minimalist statistical (ensemble) interpretation of quantum mechanics espoused by Einstein, Ballentine, and others. According to this interpretation, the quantum state description applies only to a statistical ensemble of similarly prepared systems rather than representing an individual system. Thus, the statistical interpretation obviates the need to entertain reduction of the state vector, one of the primary dilemmas of the measurement problem. The other major aspect of the measurement problem, the necessity of describing measurements in terms of classical concepts that lay outside of quantum theory, remains. A consistent formalism for interacting quantum and classical systems, like the one based on ensembles on configuration space that we refer to in this paper, might seem to eliminate this facet of the measurement problem; however, we argue that the ultimate interface with experiments is described by operational prescriptions and not in terms of the concepts of classical theory. There is no doubt that attempts to address the measurement problem have yielded important advances in fundamental physics; however, it is also very clear that the measurement problem is still far from being resolved. The pedestrian approach presented here suggests that this state of affairs is in part the result of searching for a theoretical/mathematical solution to what is fundamentally an experimental/observational question. It suggests also that the measurement problem is, in some sense, ill-posed and might never be resolved. This point of view is tenable so long as one is willing to view physical theories as providing models of nature rather than complete descriptions of reality. Among other things, these considerations lead us to suggest that the Copenhagen interpretation's insistence on the classicality of the measurement apparatus should be replaced by the requirement that a measurement, which is specified operationally, should simply be of sufficient precision.

Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states

DOE Office of Scientific and Technical Information (OSTI.GOV)

McClean, Jarrod R.; Kimchi-Schwartz, Mollie E.; Carter, Jonathan

Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One powerful example of such a hybrid quantum-classical approach optimized for classically intractable eigenvalue problems is the variational quantum eigensolver, built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed as leaders among the candidates for the first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even nonsystematic decoherence errors by introducing an exactly solvable channelmore » model of variational state preparation. Moreover, we develop a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions by leveraging additional measurements and classical resources. In conclusion, we demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal error-correction codes.« less

Quantum mechanics over sets

NASA Astrophysics Data System (ADS)

Ellerman, David

2014-03-01

In models of QM over finite fields (e.g., Schumacher's ``modal quantum theory'' MQT), one finite field stands out, Z2, since Z2 vectors represent sets. QM (finite-dimensional) mathematics can be transported to sets resulting in quantum mechanics over sets or QM/sets. This gives a full probability calculus (unlike MQT with only zero-one modalities) that leads to a fulsome theory of QM/sets including ``logical'' models of the double-slit experiment, Bell's Theorem, QIT, and QC. In QC over Z2 (where gates are non-singular matrices as in MQT), a simple quantum algorithm (one gate plus one function evaluation) solves the Parity SAT problem (finding the parity of the sum of all values of an n-ary Boolean function). Classically, the Parity SAT problem requires 2n function evaluations in contrast to the one function evaluation required in the quantum algorithm. This is quantum speedup but with all the calculations over Z2 just like classical computing. This shows definitively that the source of quantum speedup is not in the greater power of computing over the complex numbers, and confirms the idea that the source is in superposition.

Connes' embedding problem and Tsirelson's problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Junge, M.; Palazuelos, C.; Navascues, M.

2011-01-15

We show that Tsirelson's problem concerning the set of quantum correlations and Connes' embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchberg's QWEP conjecture) are essentially equivalent. Specifically, Tsirelson's problem asks whether the set of bipartite quantum correlations generated between tensor product separated systems is the same as the set of correlations between commuting C{sup *}-algebras. Connes' embedding problem asks whether any separable II{sub 1} factor is a subfactor of the ultrapower of the hyperfinite II{sub 1} factor. We show that an affirmative answer to Connes' question implies a positive answer to Tsirelson's. Conversely,more » a positive answer to a matrix valued version of Tsirelson's problem implies a positive one to Connes' problem.« less

Automatic spin-chain learning to explore the quantum speed limit

NASA Astrophysics Data System (ADS)

Zhang, Xiao-Ming; Cui, Zi-Wei; Wang, Xin; Yung, Man-Hong

2018-05-01

One of the ambitious goals of artificial intelligence is to build a machine that outperforms human intelligence, even if limited knowledge and data are provided. Reinforcement learning (RL) provides one such possibility to reach this goal. In this work, we consider a specific task from quantum physics, i.e., quantum state transfer in a one-dimensional spin chain. The mission for the machine is to find transfer schemes with the fastest speeds while maintaining high transfer fidelities. The first scenario we consider is when the Hamiltonian is time independent. We update the coupling strength by minimizing a loss function dependent on both the fidelity and the speed. Compared with a scheme proven to be at the quantum speed limit for the perfect state transfer, the scheme provided by RL is faster while maintaining the infidelity below 5 ×10-4 . In the second scenario where a time-dependent external field is introduced, we convert the state transfer process into a Markov decision process that can be understood by the machine. We solve it with the deep Q-learning algorithm. After training, the machine successfully finds transfer schemes with high fidelities and speeds, which are faster than previously known ones. These results show that reinforcement learning can be a powerful tool for quantum control problems.

Non-stationary and relaxation phenomena in cavity-assisted quantum memories

NASA Astrophysics Data System (ADS)

Veselkova, N. G.; Sokolov, I. V.

2017-12-01

We investigate the non-stationary and relaxation phenomena in cavity-assisted quantum memories for light. As a storage medium we consider an ensemble of cold atoms with standard Lambda-scheme of working levels. Some theoretical aspects of the problem were treated previously by many authors, and recent experiments stimulate more deep insight into the ultimate ability and limitations of the device. Since quantum memories can be used not only for the storage of quantum information, but also for a substantial manipulation of ensembles of quantum states, the speed of such manipulation and hence the ability to write and retrieve the signals of relatively short duration becomes important. In our research we do not apply the so-called bad cavity limit, and consider the memory operation of the signals whose duration is not much larger than the cavity field lifetime, accounting also for the finite lifetime of atomic coherence. In our paper we present an effective approach that makes it possible to find the non-stationary amplitude and phase behavior of strong classical control field, that matches the desirable time profile of both the envelope and the phase of the retrieved quantized signal. The phase properties of the retrieved quantized signals are of importance for the detection and manipulation of squeezing, entanglement, etc by means of optical mixing and homodyning.

Superadiabatic holonomic quantum computation in cavity QED

NASA Astrophysics Data System (ADS)

Liu, Bao-Jie; Huang, Zhen-Hua; Xue, Zheng-Yuan; Zhang, Xin-Ding

2017-06-01

Adiabatic quantum control is a powerful tool for quantum engineering and a key component in some quantum computation models, where accurate control over the timing of the involved pulses is not needed. However, the adiabatic condition requires that the process be very slow and thus limits its application in quantum computation, where quantum gates are preferred to be fast due to the limited coherent times of the quantum systems. Here, we propose a feasible scheme to implement universal holonomic quantum computation based on non-Abelian geometric phases with superadiabatic quantum control, where the adiabatic manipulation is sped up while retaining its robustness against errors in the timing control. Consolidating the advantages of both strategies, our proposal is thus both robust and fast. The cavity QED system is adopted as a typical example to illustrate the merits where the proposed scheme can be realized in a tripod configuration by appropriately controlling the pulse shapes and their relative strength. To demonstrate the distinct performance of our proposal, we also compare our scheme with the conventional adiabatic strategy.

Training Schrödinger's cat: quantum optimal control. Strategic report on current status, visions and goals for research in Europe

NASA Astrophysics Data System (ADS)

Glaser, Steffen J.; Boscain, Ugo; Calarco, Tommaso; Koch, Christiane P.; Köckenberger, Walter; Kosloff, Ronnie; Kuprov, Ilya; Luy, Burkhard; Schirmer, Sophie; Schulte-Herbrüggen, Thomas; Sugny, Dominique; Wilhelm, Frank K.

2015-12-01

It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a dynamical system from a given initial state into a desired target state with minimized expenditure of energy and resources. As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantum-enhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation. In this communication, state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium of experts in optimal control theory and applications to spectroscopy, imaging, as well as quantum dynamics of closed and open systems. We address key challenges and sketch a roadmap for future developments.

Computationally Efficient Nonlinear Bell Inequalities for Quantum Networks

NASA Astrophysics Data System (ADS)

Luo, Ming-Xing

2018-04-01

The correlations in quantum networks have attracted strong interest with new types of violations of the locality. The standard Bell inequalities cannot characterize the multipartite correlations that are generated by multiple sources. The main problem is that no computationally efficient method is available for constructing useful Bell inequalities for general quantum networks. In this work, we show a significant improvement by presenting new, explicit Bell-type inequalities for general networks including cyclic networks. These nonlinear inequalities are related to the matching problem of an equivalent unweighted bipartite graph that allows constructing a polynomial-time algorithm. For the quantum resources consisting of bipartite entangled pure states and generalized Greenberger-Horne-Zeilinger (GHZ) states, we prove the generic nonmultilocality of quantum networks with multiple independent observers using new Bell inequalities. The violations are maximal with respect to the presented Tsirelson's bound for Einstein-Podolsky-Rosen states and GHZ states. Moreover, these violations hold for Werner states or some general noisy states. Our results suggest that the presented Bell inequalities can be used to characterize experimental quantum networks.

Quantum annealing versus classical machine learning applied to a simplified computational biology problem

NASA Astrophysics Data System (ADS)

Li, Richard Y.; Di Felice, Rosa; Rohs, Remo; Lidar, Daniel A.

2018-03-01

Transcription factors regulate gene expression, but how these proteins recognize and specifically bind to their DNA targets is still debated. Machine learning models are effective means to reveal interaction mechanisms. Here we studied the ability of a quantum machine learning approach to classify and rank binding affinities. Using simplified data sets of a small number of DNA sequences derived from actual binding affinity experiments, we trained a commercially available quantum annealer to classify and rank transcription factor binding. The results were compared to state-of-the-art classical approaches for the same simplified data sets, including simulated annealing, simulated quantum annealing, multiple linear regression, LASSO, and extreme gradient boosting. Despite technological limitations, we find a slight advantage in classification performance and nearly equal ranking performance using the quantum annealer for these fairly small training data sets. Thus, we propose that quantum annealing might be an effective method to implement machine learning for certain computational biology problems.

An Efficient and Secure Arbitrary N-Party Quantum Key Agreement Protocol Using Bell States

NASA Astrophysics Data System (ADS)

Liu, Wen-Jie; Xu, Yong; Yang, Ching-Nung; Gao, Pei-Pei; Yu, Wen-Bin

2018-01-01

Two quantum key agreement protocols using Bell states and Bell measurement were recently proposed by Shukla et al. (Quantum Inf. Process. 13(11), 2391-2405, 2014). However, Zhu et al. pointed out that there are some security flaws and proposed an improved version (Quantum Inf. Process. 14(11), 4245-4254, 2015). In this study, we will show Zhu et al.'s improvement still exists some security problems, and its efficiency is not high enough. For solving these problems, we utilize four Pauli operations { I, Z, X, Y} to encode two bits instead of the original two operations { I, X} to encode one bit, and then propose an efficient and secure arbitrary N-party quantum key agreement protocol. In the protocol, the channel checking with decoy single photons is introduced to avoid the eavesdropper's flip attack, and a post-measurement mechanism is used to prevent against the collusion attack. The security analysis shows the present protocol can guarantee the correctness, security, privacy and fairness of quantum key agreement.

Quantum demolition filtering and optimal control of unstable systems.

PubMed

Belavkin, V P

2012-11-28

A brief account of the quantum information dynamics and dynamical programming methods for optimal control of quantum unstable systems is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme, we exploit the separation theorem of filtering and control aspects as in the usual case of quantum stable systems with non-demolition observation. This allows us to start with the Belavkin quantum filtering equation generalized to demolition observations and derive the generalized Hamilton-Jacobi-Bellman equation using standard arguments of classical control theory. This is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term if the control is restricted to Hamiltonian terms in the filtering equation. An unstable controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure quantum qubit state from a mixed one.

FIBER AND INTEGRATED OPTICS: Problems involved in the profiling of quantum wells and barriers for optoelectronic applications

NASA Astrophysics Data System (ADS)

Eliseev, P. G.; Zakhar'ev, B. N.

1992-10-01

Some important problems concerning the profiling of the potential energy in quantum-well lasers are discussed. The goals being sought are to introduce a relative shift of the levels of localized states, to introduce an energy gap, and to reduce the transmission of barriers without increasing their height.

Adaptive hybrid optimal quantum control for imprecisely characterized systems.

PubMed

Egger, D J; Wilhelm, F K

2014-06-20

Optimal quantum control theory carries a huge promise for quantum technology. Its experimental application, however, is often hindered by imprecise knowledge of the input variables, the quantum system's parameters. We show how to overcome this by adaptive hybrid optimal control, using a protocol named Ad-HOC. This protocol combines open- and closed-loop optimal control by first performing a gradient search towards a near-optimal control pulse and then an experimental fidelity estimation with a gradient-free method. For typical settings in solid-state quantum information processing, adaptive hybrid optimal control enhances gate fidelities by an order of magnitude, making optimal control theory applicable and useful.

Demonstration of entanglement of electrostatically coupled singlet-triplet qubits.

PubMed

Shulman, M D; Dial, O E; Harvey, S P; Bluhm, H; Umansky, V; Yacoby, A

2012-04-13

Quantum computers have the potential to solve certain problems faster than classical computers. To exploit their power, it is necessary to perform interqubit operations and generate entangled states. Spin qubits are a promising candidate for implementing a quantum processor because of their potential for scalability and miniaturization. However, their weak interactions with the environment, which lead to their long coherence times, make interqubit operations challenging. We performed a controlled two-qubit operation between singlet-triplet qubits using a dynamically decoupled sequence that maintains the two-qubit coupling while decoupling each qubit from its fluctuating environment. Using state tomography, we measured the full density matrix of the system and determined the concurrence and the fidelity of the generated state, providing proof of entanglement.

Pulse propagation and optically controllable switch in coupled semiconductor-double-quantum-dot nanostructures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hamedi, H. R., E-mail: hamid.r.hamedi@gmail.com, E-mail: hamid.hamedi@tfai.vu.lt

The problem of pulse propagation is theoretically investigated through a coupled semiconductor-double-quantum-dot (SDQD) nanostructure. Solving the coupled Maxwell–Bloch equations for the SDQD and field simultaneously, the dynamic control of pulse propagation through the medium is numerically explored. It is found that when all the control fields are in exact resonance with their corresponding transitions, a weak Gaussian-shaped probe pulse is transmitted through the medium nearly without any significant absorption and losses so that it can preserve its shape for quite a long propagation distance. In contrast, when one of the control fields is not in resonance with its corresponding transition,more » the probe pulse will be absorbed by the QD medium after a short distance. Then we consider the probe pulses with higher intensities. It is realized that an intense probe pulse experiences remarkable absorption and broadening during propagation. Finally, we demonstrate that this SDQD system can be employed as an optically controllable switch for the wave propagation to transit from an absorbing phase to a perfect transparency for the probe field. The required time for such switch is also estimated through realistic values.« less

Control of spin defects in wide-bandgap semiconductors for quantum technologies

DOE PAGES

Heremans, F. Joseph; Yale, Christopher G.; Awschalom, David D.

2016-05-24

Deep-level defects are usually considered undesirable in semiconductors as they typically interfere with the performance of present-day electronic and optoelectronic devices. However, the electronic spin states of certain atomic-scale defects have recently been shown to be promising quantum bits for quantum information processing as well as exquisite nanoscale sensors due to their local environmental sensitivity. In this review, we will discuss recent advances in quantum control protocols of several of these spin defects, the negatively charged nitrogen-vacancy (NV -) center in diamond and a variety of forms of the neutral divacancy (VV 0) complex in silicon carbide (SiC). These defectsmore » exhibit a spin-triplet ground state that can be controlled through a variety of techniques, several of which allow for room temperature operation. Microwave control has enabled sophisticated decoupling schemes to extend coherence times as well as nanoscale sensing of temperature along with magnetic and electric fields. On the other hand, photonic control of these spin states has provided initial steps toward integration into quantum networks, including entanglement, quantum state teleportation, and all-optical control. Electrical and mechanical control also suggest pathways to develop quantum transducers and quantum hybrid systems. In conclusion, the versatility of the control mechanisms demonstrated should facilitate the development of quantum technologies based on these spin defects.« less

Scalable quantum computer architecture with coupled donor-quantum dot qubits

DOEpatents

Schenkel, Thomas; Lo, Cheuk Chi; Weis, Christoph; Lyon, Stephen; Tyryshkin, Alexei; Bokor, Jeffrey

2014-08-26

A quantum bit computing architecture includes a plurality of single spin memory donor atoms embedded in a semiconductor layer, a plurality of quantum dots arranged with the semiconductor layer and aligned with the donor atoms, wherein a first voltage applied across at least one pair of the aligned quantum dot and donor atom controls a donor-quantum dot coupling. A method of performing quantum computing in a scalable architecture quantum computing apparatus includes arranging a pattern of single spin memory donor atoms in a semiconductor layer, forming a plurality of quantum dots arranged with the semiconductor layer and aligned with the donor atoms, applying a first voltage across at least one aligned pair of a quantum dot and donor atom to control a donor-quantum dot coupling, and applying a second voltage between one or more quantum dots to control a Heisenberg exchange J coupling between quantum dots and to cause transport of a single spin polarized electron between quantum dots.

Implementation of quantum game theory simulations using Python

NASA Astrophysics Data System (ADS)

Madrid S., A.

2013-05-01

This paper provides some examples about quantum games simulated in Python's programming language. The quantum games have been developed with the Sympy Python library, which permits solving quantum problems in a symbolic form. The application of these methods of quantum mechanics to game theory gives us more possibility to achieve results not possible before. To illustrate the results of these methods, in particular, there have been simulated the quantum battle of the sexes, the prisoner's dilemma and card games. These solutions are able to exceed the classic bottle neck and obtain optimal quantum strategies. In this form, python demonstrated that is possible to do more advanced and complicated quantum games algorithms.

Analysis of limiting information characteristics of quantum-cryptography protocols

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sych, D V; Grishanin, Boris A; Zadkov, Viktor N

2005-01-31

The problem of increasing the critical error rate of quantum-cryptography protocols by varying a set of letters in a quantum alphabet for space of a fixed dimensionality is studied. Quantum alphabets forming regular polyhedra on the Bloch sphere and the continual alphabet equally including all the quantum states are considered. It is shown that, in the absence of basis reconciliation, a protocol with the tetrahedral alphabet has the highest critical error rate among the protocols considered, while after the basis reconciliation, a protocol with the continual alphabet possesses the highest critical error rate. (quantum optics and quantum computation)

Quantum-classical correspondence in the vicinity of periodic orbits

NASA Astrophysics Data System (ADS)

Kumari, Meenu; Ghose, Shohini

2018-05-01

Quantum-classical correspondence in chaotic systems is a long-standing problem. We describe a method to quantify Bohr's correspondence principle and calculate the size of quantum numbers for which we can expect to observe quantum-classical correspondence near periodic orbits of Floquet systems. Our method shows how the stability of classical periodic orbits affects quantum dynamics. We demonstrate our method by analyzing quantum-classical correspondence in the quantum kicked top (QKT), which exhibits both regular and chaotic behavior. We use our correspondence conditions to identify signatures of classical bifurcations even in a deep quantum regime. Our method can be used to explain the breakdown of quantum-classical correspondence in chaotic systems.

Analysis and Improvement of Large Payload Bidirectional Quantum Secure Direct Communication Without Information Leakage

NASA Astrophysics Data System (ADS)

Liu, Zhi-Hao; Chen, Han-Wu

2018-02-01

As we know, the information leakage problem should be avoided in a secure quantum communication protocol. Unfortunately, it is found that this problem does exist in the large payload bidirectional quantum secure direct communication (BQSDC) protocol (Ye Int. J. Quantum. Inf. 11(5), 1350051 2013) which is based on entanglement swapping between any two Greenberger-Horne-Zeilinger (GHZ) states. To be specific, one half of the information interchanged in this protocol is leaked out unconsciously without any active attack from an eavesdropper. Afterward, this BQSDC protocol is revised to the one without information leakage. It is shown that the improved BQSDC protocol is secure against the general individual attack and has some obvious features compared with the original one.

Solving the quantum many-body problem with artificial neural networks

NASA Astrophysics Data System (ADS)

Carleo, Giuseppe; Troyer, Matthias

2017-02-01

The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the nontrivial correlations encoded in the exponential complexity of the many-body wave function. Here we demonstrate that systematic machine learning of the wave function can reduce this complexity to a tractable computational form for some notable cases of physical interest. We introduce a variational representation of quantum states based on artificial neural networks with a variable number of hidden neurons. A reinforcement-learning scheme we demonstrate is capable of both finding the ground state and describing the unitary time evolution of complex interacting quantum systems. Our approach achieves high accuracy in describing prototypical interacting spins models in one and two dimensions.

Three-player quantum Kolkata restaurant problem under decoherence

NASA Astrophysics Data System (ADS)

Ramzan, M.

2013-01-01

Effect of quantum decoherence in a three-player quantum Kolkata restaurant problem is investigated using tripartite entangled qutrit states. Different qutrit channels such as, amplitude damping, depolarizing, phase damping, trit-phase flip and phase flip channels are considered to analyze the behaviour of players payoffs. It is seen that Alice's payoff is heavily influenced by the amplitude damping channel as compared to the depolarizing and flipping channels. However, for higher level of decoherence, Alice's payoff is strongly affected by depolarizing noise. Whereas the behaviour of phase damping channel is symmetrical around 50% decoherence. It is also seen that for maximum decoherence ( p = 1), the influence of amplitude damping channel dominates over depolarizing and flipping channels. Whereas, phase damping channel has no effect on the Alice's payoff. Therefore, the problem becomes noiseless at maximum decoherence in case of phase damping channel. Furthermore, the Nash equilibrium of the problem does not change under decoherence.

Quantum computing and probability.

PubMed

Ferry, David K

2009-11-25

Over the past two decades, quantum computing has become a popular and promising approach to trying to solve computationally difficult problems. Missing in many descriptions of quantum computing is just how probability enters into the process. Here, we discuss some simple examples of how uncertainty and probability enter, and how this and the ideas of quantum computing challenge our interpretations of quantum mechanics. It is found that this uncertainty can lead to intrinsic decoherence, and this raises challenges for error correction.

From Dualism to Unity in Quantum Physics

NASA Astrophysics Data System (ADS)

Landé, Alfred

2016-02-01

Preface; Introduction; 1. Causality, chance, continuity; 2. States, observables, probabilities; 3. The metric law of probabilities; 4. Quantum dynamics; 5. Quantum fact and fiction; Retrospect. From dualism to unity, from positivism to realism; Appendix 1. Survey of elementary postulates; Appendix 2. Two problems of uniqueness; References; Index.

Higher-dimensional communication complexity problems: Classical protocols versus quantum ones based on Bell's theorem or prepare-transmit-measure schemes

NASA Astrophysics Data System (ADS)

Tavakoli, Armin; Żukowski, Marek

2017-04-01

Communication complexity problems (CCPs) are tasks in which separated parties attempt to compute a function whose inputs are distributed among the parties. Their communication is limited so that not all inputs can be sent. We show that broad classes of Bell inequalities can be mapped to CCPs and that a quantum violation of a Bell inequality is a necessary and sufficient condition for an enhancement of the related CCP beyond its classical limitation. However, one can implement CCPs by transmitting a quantum system, encoding no more information than is allowed in the CCP, and extracting information by performing measurements. We show that for a large class of Bell inequalities, the improvement of the CCP associated with a quantum violation of a Bell inequality can be no greater than the improvement obtained from quantum prepare-transmit-measure strategies.

Student understanding of time dependence in quantum mechanics

NASA Astrophysics Data System (ADS)

Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.

2015-12-01

[This paper is part of the Focused Collection on Upper Division Physics Courses.] The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing the key role of the energy eigenbasis in determining the time dependence of wave functions. Through analysis of student responses to a set of four interrelated tasks, we categorize some of the difficulties that underlie common errors. The conceptual and reasoning difficulties that have been identified are illustrated through student responses to four sets of questions administered at different points in a junior-level course on quantum mechanics. Evidence is also given that the problems persist throughout undergraduate instruction and into the graduate level.

The quantum Zeno effect in double well tunnelling

NASA Astrophysics Data System (ADS)

Lerner, L.

2018-05-01

Measurement lies at the heart of quantum theory, and introductory textbooks in quantum mechanics cover the measurement problem in topics such as the Schrödinger’s cat thought experiment, the EPR problem, and the quantum Zeno effect (QZE). In this article we present a new treatment of the QZE suitable for undergraduate students, for the case of a particle tunnelling between two wells while being observed in one of the wells. The analysis shows that as the observation rate increases, the tunnelling rate tends towards zero, in accordance with Zeno’s maxim ‘a watched pot never boils’. The method relies on decoherence theory, which replaces aspects of quantum collapse by the Schrödinger evolution of an open system, and its recently simplified treatment for undergraduates. Our presentation uses concepts familiar to undergraduate students, so that calculations involving many-body theory and the formal properties of the density matrix are avoided.

Measurement-device-independent quantum key distribution.

PubMed

Lo, Hoi-Kwong; Curty, Marcos; Qi, Bing

2012-03-30

How to remove detector side channel attacks has been a notoriously hard problem in quantum cryptography. Here, we propose a simple solution to this problem--measurement-device-independent quantum key distribution (QKD). It not only removes all detector side channels, but also doubles the secure distance with conventional lasers. Our proposal can be implemented with standard optical components with low detection efficiency and highly lossy channels. In contrast to the previous solution of full device independent QKD, the realization of our idea does not require detectors of near unity detection efficiency in combination with a qubit amplifier (based on teleportation) or a quantum nondemolition measurement of the number of photons in a pulse. Furthermore, its key generation rate is many orders of magnitude higher than that based on full device independent QKD. The results show that long-distance quantum cryptography over say 200 km will remain secure even with seriously flawed detectors.

QSPIN: A High Level Java API for Quantum Computing Experimentation

NASA Technical Reports Server (NTRS)

Barth, Tim

2017-01-01

QSPIN is a high level Java language API for experimentation in QC models used in the calculation of Ising spin glass ground states and related quadratic unconstrained binary optimization (QUBO) problems. The Java API is intended to facilitate research in advanced QC algorithms such as hybrid quantum-classical solvers, automatic selection of constraint and optimization parameters, and techniques for the correction and mitigation of model and solution errors. QSPIN includes high level solver objects tailored to the D-Wave quantum annealing architecture that implement hybrid quantum-classical algorithms [Booth et al.] for solving large problems on small quantum devices, elimination of variables via roof duality, and classical computing optimization methods such as GPU accelerated simulated annealing and tabu search for comparison. A test suite of documented NP-complete applications ranging from graph coloring, covering, and partitioning to integer programming and scheduling are provided to demonstrate current capabilities.

More on Weinberg's no-go theorem in quantum gravity

NASA Astrophysics Data System (ADS)

Nagahama, Munehiro; Oda, Ichiro

2018-05-01

We complement Weinberg's no-go theorem on the cosmological constant problem in quantum gravity by generalizing it to the case of a scale-invariant theory. Our analysis makes use of the effective action and the BRST symmetry in a manifestly covariant quantum gravity instead of the classical Lagrangian density and the G L (4 ) symmetry in classical gravity. In this sense, our proof is very general since it does not depend on details of quantum gravity and holds true for general gravitational theories which are invariant under diffeomorphisms. As an application of our theorem, we comment on an idea that in the asymptotic safety scenario the functional renormalization flow drives a cosmological constant to zero, solving the cosmological constant problem without reference to fine tuning of parameters. Finally, we also comment on the possibility of extending the Weinberg theorem in quantum gravity to the case where the translational invariance is spontaneously broken.

A modified Lax-Phillips scattering theory for quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Strauss, Y., E-mail: ystrauss@cs.bgu.ac.il

The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for themore » quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.« less

Relativistic quantum cryptography

NASA Astrophysics Data System (ADS)

Molotkov, S. N.; Nazin, S. S.

2003-07-01

The problem of unconditional security of quantum cryptography (i.e. the security which is guaranteed by the fundamental laws of nature rather than by technical limitations) is one of the central points in quantum information theory. We propose a relativistic quantum cryptosystem and prove its unconditional security against any eavesdropping attempts. Relativistitic causality arguments allow to demonstrate the security of the system in a simple way. Since the proposed protocol does not empoly collective measurements and quantum codes, the cryptosystem can be experimentally realized with the present state-of-art in fiber optics technologies. The proposed cryptosystem employs only the individual measurements and classical codes and, in addition, the key distribution problem allows to postpone the choice of the state encoding scheme until after the states are already received instead of choosing it before sending the states into the communication channel (i.e. to employ a sort of "antedate" coding).

Controlling the Transport of an Ion: Classical and Quantum Mechanical Solutions

DTIC Science & Technology

2014-07-09

quantum systems: tools, achievements, and limitations Christiane P Koch Shortcuts to adiabaticity for an ion in a rotating radially- tight trap M Palmero...Keywords: coherent control, ion traps, quantum information, optimal control theory 1. Introduction Control methods are key enabling techniques in many...figure 6. 3.4. Feasibility analysis of quantum optimal control Numerical optimization of the wavepacket motion is expected to become necessary once

Compressed Sensing Quantum Process Tomography for Superconducting Quantum Gates

NASA Astrophysics Data System (ADS)

Rodionov, Andrey

An important challenge in quantum information science and quantum computing is the experimental realization of high-fidelity quantum operations on multi-qubit systems. Quantum process tomography (QPT) is a procedure devised to fully characterize a quantum operation. We first present the results of the estimation of the process matrix for superconducting multi-qubit quantum gates using the full data set employing various methods: linear inversion, maximum likelihood, and least-squares. To alleviate the problem of exponential resource scaling needed to characterize a multi-qubit system, we next investigate a compressed sensing (CS) method for QPT of two-qubit and three-qubit quantum gates. Using experimental data for two-qubit controlled-Z gates, taken with both Xmon and superconducting phase qubits, we obtain estimates for the process matrices with reasonably high fidelities compared to full QPT, despite using significantly reduced sets of initial states and measurement configurations. We show that the CS method still works when the amount of data is so small that the standard QPT would have an underdetermined system of equations. We also apply the CS method to the analysis of the three-qubit Toffoli gate with simulated noise, and similarly show that the method works well for a substantially reduced set of data. For the CS calculations we use two different bases in which the process matrix is approximately sparse (the Pauli-error basis and the singular value decomposition basis), and show that the resulting estimates of the process matrices match with reasonably high fidelity. For both two-qubit and three-qubit gates, we characterize the quantum process by its process matrix and average state fidelity, as well as by the corresponding standard deviation defined via the variation of the state fidelity for different initial states. We calculate the standard deviation of the average state fidelity both analytically and numerically, using a Monte Carlo method. Overall, we show that CS QPT offers a significant reduction in the needed amount of experimental data for two-qubit and three-qubit quantum gates.

Number Partitioning via Quantum Adiabatic Computation

NASA Technical Reports Server (NTRS)

Smelyanskiy, Vadim N.; Toussaint, Udo

2002-01-01

We study both analytically and numerically the complexity of the adiabatic quantum evolution algorithm applied to random instances of combinatorial optimization problems. We use as an example the NP-complete set partition problem and obtain an asymptotic expression for the minimal gap separating the ground and exited states of a system during the execution of the algorithm. We show that for computationally hard problem instances the size of the minimal gap scales exponentially with the problem size. This result is in qualitative agreement with the direct numerical simulation of the algorithm for small instances of the set partition problem. We describe the statistical properties of the optimization problem that are responsible for the exponential behavior of the algorithm.

How to Build a Quantum Computer

NASA Astrophysics Data System (ADS)

Sanders, Barry C.

2017-11-01

Quantum computer technology is progressing rapidly with dozens of qubits and hundreds of quantum logic gates now possible. Although current quantum computer technology is distant from being able to solve computational problems beyond the reach of non-quantum computers, experiments have progressed well beyond simply demonstrating the requisite components. We can now operate small quantum logic processors with connected networks of qubits and quantum logic gates, which is a great stride towards functioning quantum computers. This book aims to be accessible to a broad audience with basic knowledge of computers, electronics and physics. The goal is to convey key notions relevant to building quantum computers and to present state-of-the-art quantum-computer research in various media such as trapped ions, superconducting circuits, photonics and beyond.

BOOK REVIEW: Quantum Gravity: third edition Quantum Gravity: third edition

NASA Astrophysics Data System (ADS)

Rovelli, Carlo

2012-09-01

The request by Classical and Quantum Gravity to review the third edition of Claus Kiefer's 'Quantum Gravity' puts me in a slightly awkward position. This is a remarkably good book, which every person working in quantum gravity should have on the shelf. But in my opinion quantum gravity has undergone some dramatic advances in the last few years, of which the book makes no mention. Perhaps the omission only attests to the current vitality of the field, where progress is happening fast, but it is strange for me to review a thoughtful, knowledgeable and comprehensive book on my own field of research, which ignores what I myself consider the most interesting results to date. Kiefer's book is unique as a broad introduction and a reliable overview of quantum gravity. There are numerous books in the field which (often notwithstanding titles) focus on a single approach. There are also countless conference proceedings and article collections aiming to be encyclopaedic, but offering disorganized patchworks. Kiefer's book is a careful and thoughtful presentation of all aspects of the immense problem of quantum gravity. Kiefer is very learned, and brings together three rare qualities: he is pedagogical, he is capable of simplifying matter to the bones and capturing the essential, and he offers a serious and balanced evaluation of views and ideas. In a fractured field based on a major problem that does not yet have a solution, these qualities are precious. I recommend Kiefer's book to my students entering the field: to work in quantum gravity one needs a vast amount of technical knowledge as well as a grasp of different ideas, and Kiefer's book offers this with remarkable clarity. This novel third edition simplifies and improves the presentation of several topics, but also adds very valuable new material on quantum gravity phenomenology, loop quantum cosmology, asymptotic safety, Horava-Lifshitz gravity, analogue gravity, the holographic principle, and more. This is a testament to the wide-angle attention of Claus Kiefer to the recent evolution of the field. It is also because of this attention that the neglect of a thriving research direction on which a large number of research groups are currently engaged jumps to the eye. The book provides a nice introduction to loop quantum gravity. The main kinematical results of the loop approach are carefully explained. At the point of discussing dynamics, however, it focuses only on the canonical formulation, mentioning the covariant loop theory only en passant. Given Kiefer's open-mindness, I imagine that the shortfall is due to the novelty of the major results of the covariant theory (or spinfoam formalism). The theorem proving the finiteness of the transition amplitudes to all orders, due to Han, Fairbairn and Meusburger, for instance, dates only from 2010. But the various theorems on the asymptotic of the vertex amplitude, by Barrett-Pereira-Dowdall-Fairbairn-Hellmann, Friedel-Conrady and others, which have sparked interest in the spinfoam approach by indicating that the theory may have the correct classical limit, are from 2009. The fact that they are not even mentioned in Kiefer's book is strident for me. The covariant loop amplitudes may not be the final solution to the problem of quantum gravity, but the existence of a family of Lorentz covariant amplitudes with indications of the correct classical limit, which are finite at each order of the expansion, is a result that cannot be ignored in a broad book that aims at being comprehensive in quantum gravity. There are other pages of the book where I was not very happy. For instance, the discussion of the so-called 'problem of time'. But surely a broad book in a recalcitrant field like quantum gravity will never make everybody entirely happy: at least as long as the problem is not solved. Which, we all hope, might not be too far into the future. Few fundamental problems have resisted the investigation of theoretical physics for so long, and today advances are fast. So, here is my recommendation: study this book, complement it with what is missing, and help us in finally solving the extraordinarily beautiful problem of understanding quantum spacetime.

Systematic Dimensionality Reduction for Quantum Walks: Optimal Spatial Search and Transport on Non-Regular Graphs

PubMed Central

Novo, Leonardo; Chakraborty, Shantanav; Mohseni, Masoud; Neven, Hartmut; Omar, Yasser

2015-01-01

Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that confine the dynamics to a smaller subspace of the full Hilbert space. In this work, we use invariant subspace methods, that can be computed systematically using the Lanczos algorithm, to obtain the reduced set of states that encompass the dynamics of the problem at hand without the specific knowledge of underlying symmetries. First, we apply this method to obtain new instances of graphs where the spatial quantum search algorithm is optimal: complete graphs with broken links and complete bipartite graphs, in particular, the star graph. These examples show that regularity and high-connectivity are not needed to achieve optimal spatial search. We also show that this method considerably simplifies the calculation of quantum transport efficiencies. Furthermore, we observe improved efficiencies by removing a few links from highly symmetric graphs. Finally, we show that this reduction method also allows us to obtain an upper bound for the fidelity of a single qubit transfer on an XY spin network. PMID:26330082

Adiabatic two-qubit state preparation in a superconducting qubit system

NASA Astrophysics Data System (ADS)

Filipp, Stefan; Ganzhorn, Marc; Egger, Daniel; Fuhrer, Andreas; Moll, Nikolaj; Mueller, Peter; Roth, Marco; Schmidt, Sebastian

The adiabatic transport of a quantum system from an initial eigenstate to its final state while remaining in the instantaneous eigenstate of the driving Hamiltonian can be used for robust state preparation. With control over both qubit frequencies and qubit-qubit couplings this method can be used to drive the system from initially trivial eigenstates of the uncoupled qubits to complex entangled multi-qubit states. In the context of quantum simulation, the final state may encode a non-trivial ground-state of a complex molecule or, in the context of adiabatic quantum computing, the solution to an optimization problem. Here, we present experimental results on a system comprising fixed-frequency superconducting transmon qubits and a tunable coupler to adjust the qubit-qubit coupling via parametric frequency modulation. We realize different types of interaction by adjusting the frequency of the modulation. A slow variation of drive amplitude and phase leads to an adiabatic steering of the system to its final state showing entanglement between the qubits.

General theory of feedback control of a nuclear spin ensemble in quantum dots

NASA Astrophysics Data System (ADS)

Yang, Wen; Sham, L. J.

2013-12-01

We present a microscopic theory of the nonequilibrium nuclear spin dynamics driven by the electron and/or hole under continuous-wave pumping in a quantum dot. We show the correlated dynamics of the nuclear spin ensemble and the electron and/or hole under optical excitation as a quantum feedback loop and investigate the dynamics of the many nuclear spins as a nonlinear collective motion. This gives rise to three observable effects: (i) hysteresis, (ii) locking (avoidance) of the pump absorption strength to (from) the natural resonance, and (iii) suppression (amplification) of the fluctuation of weakly polarized nuclear spins, leading to prolonged (shortened) electron-spin coherence time. A single nonlinear feedback function is constructed which determines the different outcomes of the three effects listed above depending on the feedback being negative or positive. The general theory also helps to put in perspective the wide range of existing theories on the problem of a single electron spin in a nuclear spin bath.

Superadiabatic Controlled Evolutions and Universal Quantum Computation.

PubMed

Santos, Alan C; Sarandy, Marcelo S

2015-10-29

Adiabatic state engineering is a powerful technique in quantum information and quantum control. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided by the superadiabatic theory, constitute a valuable tool to speed up the adiabatic quantum behavior. Here, we propose a superadiabatic route to implement universal quantum computation. Our method is based on the realization of piecewise controlled superadiabatic evolutions. Remarkably, they can be obtained by simple time-independent counter-diabatic Hamiltonians. In particular, we discuss the implementation of fast rotation gates and arbitrary n-qubit controlled gates, which can be used to design different sets of universal quantum gates. Concerning the energy cost of the superadiabatic implementation, we show that it is dictated by the quantum speed limit, providing an upper bound for the corresponding adiabatic counterparts.

Superadiabatic Controlled Evolutions and Universal Quantum Computation

PubMed Central

Santos, Alan C.; Sarandy, Marcelo S.

2015-01-01

Adiabatic state engineering is a powerful technique in quantum information and quantum control. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided by the superadiabatic theory, constitute a valuable tool to speed up the adiabatic quantum behavior. Here, we propose a superadiabatic route to implement universal quantum computation. Our method is based on the realization of piecewise controlled superadiabatic evolutions. Remarkably, they can be obtained by simple time-independent counter-diabatic Hamiltonians. In particular, we discuss the implementation of fast rotation gates and arbitrary n-qubit controlled gates, which can be used to design different sets of universal quantum gates. Concerning the energy cost of the superadiabatic implementation, we show that it is dictated by the quantum speed limit, providing an upper bound for the corresponding adiabatic counterparts. PMID:26511064

Measurement and quantum indeterminateness

NASA Astrophysics Data System (ADS)

Healey, Richard

1993-08-01

Albert and Loewer[1] have recently clarified their earlier objection to the interactive interpretation presented in Healey[2]. They now charge that this interpretation fails to solve a problem of which the measurement problem is but a special case. The general problem is to reconcile quantum mechanics with the prima facie determinateness of such dynamical properties as the positions of macroscopic objects. In response I defend both the preeminent significance of determinate measurement outcomes and the claim that the models of Healey[3] go a long way toward securing their determinateness.

Controlling the Shannon Entropy of Quantum Systems

PubMed Central

Xing, Yifan; Wu, Jun

2013-01-01

This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking. PMID:23818819

Controlling the shannon entropy of quantum systems.

PubMed

Xing, Yifan; Wu, Jun

2013-01-01

This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.

PubMed

Goto, Hayato

2016-02-22

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

NASA Astrophysics Data System (ADS)

Goto, Hayato

2016-02-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

Optimal Control for Quantum Driving of Two-Level Systems

NASA Astrophysics Data System (ADS)

Qi, Xiao-Qiu

2018-01-01

In this paper, the optimal quantum control of two-level systems is studied by the decompositions of SU(2). Using the Pontryagin maximum principle, the minimum time of quantum control is analyzed in detail. The solution scheme of the optimal control function is given in the general case. Finally, two specific cases, which can be applied in many quantum systems, are used to illustrate the scheme, while the corresponding optimal control functions are obtained.

Hidden algebra method (quasi-exact-solvability in quantum mechanics)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Turbiner, A.

1996-02-01

A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland {ital N}-body problems ass ociated with an existence of the hidden algebra {ital sl}{sub {ital N}} is discussed extensively. {copyright} {ital 1996 American Institute of Physics.}

Topics in quantum cryptography, quantum error correction, and channel simulation

NASA Astrophysics Data System (ADS)

Luo, Zhicheng

In this thesis, we mainly investigate four different topics: efficiently implementable codes for quantum key expansion [51], quantum error-correcting codes based on privacy amplification [48], private classical capacity of quantum channels [44], and classical channel simulation with quantum side information [49, 50]. For the first topic, we propose an efficiently implementable quantum key expansion protocol, capable of increasing the size of a pre-shared secret key by a constant factor. Previously, the Shor-Preskill proof [64] of the security of the Bennett-Brassard 1984 (BB84) [6] quantum key distribution protocol relied on the theoretical existence of good classical error-correcting codes with the "dual-containing" property. But the explicit and efficiently decodable construction of such codes is unknown. We show that we can lift the dual-containing constraint by employing the non-dual-containing codes with excellent performance and efficient decoding algorithms. For the second topic, we propose a construction of Calderbank-Shor-Steane (CSS) [19, 68] quantum error-correcting codes, which are originally based on pairs of mutually dual-containing classical codes, by combining a classical code with a two-universal hash function. We show, using the results of Renner and Koenig [57], that the communication rates of such codes approach the hashing bound on tensor powers of Pauli channels in the limit of large block-length. For the third topic, we prove a regularized formula for the secret key assisted capacity region of a quantum channel for transmitting private classical information. This result parallels the work of Devetak on entanglement assisted quantum communication capacity. This formula provides a new family protocol, the private father protocol, under the resource inequality framework that includes the private classical communication without the assisted secret keys as a child protocol. For the fourth topic, we study and solve the problem of classical channel simulation with quantum side information at the receiver. Our main theorem has two important corollaries: rate-distortion theory with quantum side information and common randomness distillation. Simple proofs of achievability of classical multi-terminal source coding problems can be made via a unified approach using the channel simulation theorem as building blocks. The fully quantum generalization of the problem is also conjectured with outer and inner bounds on the achievable rate pairs.

Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator

NASA Astrophysics Data System (ADS)

Karthiga, S.; Chithiika Ruby, V.; Senthilvelan, M.; Lakshmanan, M.

2017-10-01

In position dependent mass (PDM) problems, the quantum dynamics of the associated systems have been understood well in the literature for particular orderings. However, no efforts seem to have been made to solve such PDM problems for general orderings to obtain a global picture. In this connection, we here consider the general ordered quantum Hamiltonian of an interesting position dependent mass problem, namely, the Mathews-Lakshmanan oscillator, and try to solve the quantum problem for all possible orderings including Hermitian and non-Hermitian ones. The other interesting point in our study is that for all possible orderings, although the Schrödinger equation of this Mathews-Lakshmanan oscillator is uniquely reduced to the associated Legendre differential equation, their eigenfunctions cannot be represented in terms of the associated Legendre polynomials with integral degree and order. Rather the eigenfunctions are represented in terms of associated Legendre polynomials with non-integral degree and order. We here explore such polynomials and represent the discrete and continuum states of the system. We also exploit the connection between associated Legendre polynomials with non-integral degree with other orthogonal polynomials such as Jacobi and Gegenbauer polynomials.

Preparation of freezing quantum state for quantum coherence

NASA Astrophysics Data System (ADS)

Yang, Lian-Wu; Man, Zhong-Xiao; Zhang, Ying-Jie; Han, Feng; Du, Shao-jiang; Xia, Yun-Jie

2018-06-01

We provide a method to prepare the freezing quantum state for quantum coherence via unitary operations. The initial product state consists of the control qubit and target qubit; when it satisfies certain conditions, the initial product state converts into the particular Bell diagonal state under the unitary operations, which have the property of freezing of quantum coherence under quantum channels. We calculate the frozen quantum coherence and corresponding quantum correlations, and find that the quantities are determined by the control qubit only when the freezing phenomena occur.

Statistical mechanics based on fractional classical and quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Korichi, Z.; Meftah, M. T., E-mail: mewalid@yahoo.com

2014-03-15

The purpose of this work is to study some problems in statistical mechanics based on the fractional classical and quantum mechanics. At first stage we have presented the thermodynamical properties of the classical ideal gas and the system of N classical oscillators. In both cases, the Hamiltonian contains fractional exponents of the phase space (position and momentum). At the second stage, in the context of the fractional quantum mechanics, we have calculated the thermodynamical properties for the black body radiation, studied the Bose-Einstein statistics with the related problem of the condensation and the Fermi-Dirac statistics.

The quantum limit for gravitational-wave detectors and methods of circumventing it

NASA Technical Reports Server (NTRS)

Thorne, K. S.; Caves, C. M.; Sandberg, V. D.; Zimmermann, M.; Drever, R. W. P.

1979-01-01

The Heisenberg uncertainty principle prevents the monitoring of the complex amplitude of a mechanical oscillator more accurately than a certain limit value. This 'quantum limit' is a serious obstacle to the achievement of a 10 to the -21st gravitational-wave detection sensitivity. This paper examines the principles of the back-action evasion technique and finds that this technique may be able to overcome the problem of the quantum limit. Back-action evasion does not solve, however, other problems of detection, such as weak coupling, large amplifier noise, and large Nyquist noise.

Abstract quantum computing machines and quantum computational logics

NASA Astrophysics Data System (ADS)

Chiara, Maria Luisa Dalla; Giuntini, Roberto; Sergioli, Giuseppe; Leporini, Roberto

2016-06-01

Classical and quantum parallelism are deeply different, although it is sometimes claimed that quantum Turing machines are nothing but special examples of classical probabilistic machines. We introduce the concepts of deterministic state machine, classical probabilistic state machine and quantum state machine. On this basis, we discuss the question: To what extent can quantum state machines be simulated by classical probabilistic state machines? Each state machine is devoted to a single task determined by its program. Real computers, however, behave differently, being able to solve different kinds of problems. This capacity can be modeled, in the quantum case, by the mathematical notion of abstract quantum computing machine, whose different programs determine different quantum state machines. The computations of abstract quantum computing machines can be linguistically described by the formulas of a particular form of quantum logic, termed quantum computational logic.

RESEARCH AREA 7.1: Exploring the Systematics of Controlling Quantum Phenomena

DTIC Science & Technology

2016-10-05

the bottom to the top of the landscape. Computational analyses for simple model quantum systems are performed to ascertain the relative abundance of...SECURITY CLASSIFICATION OF: This research is concerned with the theoretical and experimental control quantum dynamics phenomena. Advances include new...algorithms to accelerate quantum control as well as provide physical insights into the controlled dynamics. The latter research includes the

A short walk in quantum probability

NASA Astrophysics Data System (ADS)

Hudson, Robin

2018-04-01

This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas. This article is part of the themed issue `Hilbert's sixth problem'.

Temporal Planning for Compilation of Quantum Approximate Optimization Algorithm Circuits

NASA Technical Reports Server (NTRS)

Venturelli, Davide; Do, Minh Binh; Rieffel, Eleanor Gilbert; Frank, Jeremy David

2017-01-01

We investigate the application of temporal planners to the problem of compiling quantum circuits to newly emerging quantum hardware. While our approach is general, we focus our initial experiments on Quantum Approximate Optimization Algorithm (QAOA) circuits that have few ordering constraints and allow highly parallel plans. We report on experiments using several temporal planners to compile circuits of various sizes to a realistic hardware. This early empirical evaluation suggests that temporal planning is a viable approach to quantum circuit compilation.

Quantum attack-resistent certificateless multi-receiver signcryption scheme.

PubMed

Li, Huixian; Chen, Xubao; Pang, Liaojun; Shi, Weisong

2013-01-01

The existing certificateless signcryption schemes were designed mainly based on the traditional public key cryptography, in which the security relies on the hard problems, such as factor decomposition and discrete logarithm. However, these problems will be easily solved by the quantum computing. So the existing certificateless signcryption schemes are vulnerable to the quantum attack. Multivariate public key cryptography (MPKC), which can resist the quantum attack, is one of the alternative solutions to guarantee the security of communications in the post-quantum age. Motivated by these concerns, we proposed a new construction of the certificateless multi-receiver signcryption scheme (CLMSC) based on MPKC. The new scheme inherits the security of MPKC, which can withstand the quantum attack. Multivariate quadratic polynomial operations, which have lower computation complexity than bilinear pairing operations, are employed in signcrypting a message for a certain number of receivers in our scheme. Security analysis shows that our scheme is a secure MPKC-based scheme. We proved its security under the hardness of the Multivariate Quadratic (MQ) problem and its unforgeability under the Isomorphism of Polynomials (IP) assumption in the random oracle model. The analysis results show that our scheme also has the security properties of non-repudiation, perfect forward secrecy, perfect backward secrecy and public verifiability. Compared with the existing schemes in terms of computation complexity and ciphertext length, our scheme is more efficient, which makes it suitable for terminals with low computation capacity like smart cards.

Chaos Quantum-Behaved Cat Swarm Optimization Algorithm and Its Application in the PV MPPT

PubMed Central

2017-01-01

Cat Swarm Optimization (CSO) algorithm was put forward in 2006. Despite a faster convergence speed compared with Particle Swarm Optimization (PSO) algorithm, the application of CSO is greatly limited by the drawback of “premature convergence,” that is, the possibility of trapping in local optimum when dealing with nonlinear optimization problem with a large number of local extreme values. In order to surmount the shortcomings of CSO, Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed in this paper. Firstly, Quantum-behaved Cat Swarm Optimization (QCSO) algorithm improves the accuracy of the CSO algorithm, because it is easy to fall into the local optimum in the later stage. Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed by introducing tent map for jumping out of local optimum in this paper. Secondly, CQCSO has been applied in the simulation of five different test functions, showing higher accuracy and less time consumption than CSO and QCSO. Finally, photovoltaic MPPT model and experimental platform are established and global maximum power point tracking control strategy is achieved by CQCSO algorithm, the effectiveness and efficiency of which have been verified by both simulation and experiment. PMID:29181020

Chaos Quantum-Behaved Cat Swarm Optimization Algorithm and Its Application in the PV MPPT.

PubMed

Nie, Xiaohua; Wang, Wei; Nie, Haoyao

2017-01-01

Cat Swarm Optimization (CSO) algorithm was put forward in 2006. Despite a faster convergence speed compared with Particle Swarm Optimization (PSO) algorithm, the application of CSO is greatly limited by the drawback of "premature convergence," that is, the possibility of trapping in local optimum when dealing with nonlinear optimization problem with a large number of local extreme values. In order to surmount the shortcomings of CSO, Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed in this paper. Firstly, Quantum-behaved Cat Swarm Optimization (QCSO) algorithm improves the accuracy of the CSO algorithm, because it is easy to fall into the local optimum in the later stage. Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed by introducing tent map for jumping out of local optimum in this paper. Secondly, CQCSO has been applied in the simulation of five different test functions, showing higher accuracy and less time consumption than CSO and QCSO. Finally, photovoltaic MPPT model and experimental platform are established and global maximum power point tracking control strategy is achieved by CQCSO algorithm, the effectiveness and efficiency of which have been verified by both simulation and experiment.

Frequency-tuned microwave photon counter based on a superconductive quantum interferometer

NASA Astrophysics Data System (ADS)

Shnyrkov, V. I.; Yangcao, Wu; Soroka, A. A.; Turutanov, O. G.; Lyakhno, V. Yu.

2018-03-01

Various types of single-photon counters operating in infrared, ultraviolet, and optical wavelength ranges are successfully used to study electromagnetic fields, analyze radiation sources, and solve problems in quantum informatics. However, their operating principles become ineffective at millimeter band, S-band, and ultra-high frequency bands of wavelengths due to the decrease in quantum energy by 4-5 orders of magnitude. Josephson circuits with discrete Hamiltonians and qubits are a good foundation for the construction of single-photon counters at these frequencies. This paper presents a frequency-tuned microwave photon counter based on a single-junction superconducting quantum interferometer and flux qutrit. The control pulse converts the interferometer into a two-level system for resonance absorption of photons. Decay of the photon-induced excited state changes the magnetic flux in the interferometer, which is measured by a SQUID magnetometer. Schemes for recording the magnetic flux using a DC SQUID or ideal parametric detector, based on a qutrit with high-frequency excitation, are discussed. It is shown that the counter consisting of an interferometer with a Josephson junction and a parametric detector demonstrates high performance and is capable of detecting single photons in a microwave band.

Simultaneous deterministic control of distant qubits in two semiconductor quantum dots.

PubMed

Gamouras, A; Mathew, R; Freisem, S; Deppe, D G; Hall, K C

2013-10-09

In optimal quantum control (OQC), a target quantum state of matter is achieved by tailoring the phase and amplitude of the control Hamiltonian through femtosecond pulse-shaping techniques and powerful adaptive feedback algorithms. Motivated by recent applications of OQC in quantum information science as an approach to optimizing quantum gates in atomic and molecular systems, here we report the experimental implementation of OQC in a solid-state system consisting of distinguishable semiconductor quantum dots. We demonstrate simultaneous high-fidelity π and 2π single qubit gates in two different quantum dots using a single engineered infrared femtosecond pulse. These experiments enhance the scalability of semiconductor-based quantum hardware and lay the foundation for applications of pulse shaping to optimize quantum gates in other solid-state systems.

Dynamical generation of noiseless quantum subsystems

PubMed

Viola; Knill; Lloyd

2000-10-16

We combine dynamical decoupling and universal control methods for open quantum systems with coding procedures. By exploiting a general algebraic approach, we show how appropriate encodings of quantum states result in obtaining universal control over dynamically generated noise-protected subsystems with limited control resources. In particular, we provide a constructive scheme based on two-body Hamiltonians for performing universal quantum computation over large noiseless spaces which can be engineered in the presence of arbitrary linear quantum noise.