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.

Undergraduate computational physics projects on quantum computing

NASA Astrophysics Data System (ADS)

Candela, D.

2015-08-01

Computational projects on quantum computing suitable for students in a junior-level quantum mechanics course are described. In these projects students write their own programs to simulate quantum computers. Knowledge is assumed of introductory quantum mechanics through the properties of spin 1/2. Initial, more easily programmed projects treat the basics of quantum computation, quantum gates, and Grover's quantum search algorithm. These are followed by more advanced projects to increase the number of qubits and implement Shor's quantum factoring algorithm. The projects can be run on a typical laptop or desktop computer, using most programming languages. Supplementing resources available elsewhere, the projects are presented here in a self-contained format especially suitable for a short computational module for physics students.

Research progress on quantum informatics and quantum computation

NASA Astrophysics Data System (ADS)

Zhao, Yusheng

2018-03-01

Quantum informatics is an emerging interdisciplinary subject developed by the combination of quantum mechanics, information science, and computer science in the 1980s. The birth and development of quantum information science has far-reaching significance in science and technology. At present, the application of quantum information technology has become the direction of people’s efforts. The preparation, storage, purification and regulation, transmission, quantum coding and decoding of quantum state have become the hotspot of scientists and technicians, which have a profound impact on the national economy and the people’s livelihood, technology and defense technology. This paper first summarizes the background of quantum information science and quantum computer and the current situation of domestic and foreign research, and then introduces the basic knowledge and basic concepts of quantum computing. Finally, several quantum algorithms are introduced in detail, including Quantum Fourier transform, Deutsch-Jozsa algorithm, Shor’s quantum algorithm, quantum phase estimation.

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

Single-server blind quantum computation with quantum circuit model

NASA Astrophysics Data System (ADS)

Zhang, Xiaoqian; Weng, Jian; Li, Xiaochun; Luo, Weiqi; Tan, Xiaoqing; Song, Tingting

2018-06-01

Blind quantum computation (BQC) enables the client, who has few quantum technologies, to delegate her quantum computation to a server, who has strong quantum computabilities and learns nothing about the client's quantum inputs, outputs and algorithms. In this article, we propose a single-server BQC protocol with quantum circuit model by replacing any quantum gate with the combination of rotation operators. The trap quantum circuits are introduced, together with the combination of rotation operators, such that the server is unknown about quantum algorithms. The client only needs to perform operations X and Z, while the server honestly performs rotation operators.

Quantum rendering

NASA Astrophysics Data System (ADS)

Lanzagorta, Marco O.; Gomez, Richard B.; Uhlmann, Jeffrey K.

2003-08-01

In recent years, computer graphics has emerged as a critical component of the scientific and engineering process, and it is recognized as an important computer science research area. Computer graphics are extensively used for a variety of aerospace and defense training systems and by Hollywood's special effects companies. All these applications require the computer graphics systems to produce high quality renderings of extremely large data sets in short periods of time. Much research has been done in "classical computing" toward the development of efficient methods and techniques to reduce the rendering time required for large datasets. Quantum Computing's unique algorithmic features offer the possibility of speeding up some of the known rendering algorithms currently used in computer graphics. In this paper we discuss possible implementations of quantum rendering algorithms. In particular, we concentrate on the implementation of Grover's quantum search algorithm for Z-buffering, ray-tracing, radiosity, and scene management techniques. We also compare the theoretical performance between the classical and quantum versions of the algorithms.

Arbitrated Quantum Signature with Hamiltonian Algorithm Based on Blind Quantum Computation

NASA Astrophysics Data System (ADS)

Shi, Ronghua; Ding, Wanting; Shi, Jinjing

2018-03-01

A novel arbitrated quantum signature (AQS) scheme is proposed motivated by the Hamiltonian algorithm (HA) and blind quantum computation (BQC). The generation and verification of signature algorithm is designed based on HA, which enables the scheme to rely less on computational complexity. It is unnecessary to recover original messages when verifying signatures since the blind quantum computation is applied, which can improve the simplicity and operability of our scheme. It is proved that the scheme can be deployed securely, and the extended AQS has some extensive applications in E-payment system, E-government, E-business, etc.

Arbitrated Quantum Signature with Hamiltonian Algorithm Based on Blind Quantum Computation

NASA Astrophysics Data System (ADS)

Shi, Ronghua; Ding, Wanting; Shi, Jinjing

2018-07-01

A novel arbitrated quantum signature (AQS) scheme is proposed motivated by the Hamiltonian algorithm (HA) and blind quantum computation (BQC). The generation and verification of signature algorithm is designed based on HA, which enables the scheme to rely less on computational complexity. It is unnecessary to recover original messages when verifying signatures since the blind quantum computation is applied, which can improve the simplicity and operability of our scheme. It is proved that the scheme can be deployed securely, and the extended AQS has some extensive applications in E-payment system, E-government, E-business, etc.

Experimental comparison of two quantum computing architectures.

PubMed

Linke, Norbert M; Maslov, Dmitri; Roetteler, Martin; Debnath, Shantanu; Figgatt, Caroline; Landsman, Kevin A; Wright, Kenneth; Monroe, Christopher

2017-03-28

We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device (www. ibm.com/ibm-q) with limited connectivity, and the other is a fully connected trapped-ion system. Even though the two systems have different native quantum interactions, both can be programed in a way that is blind to the underlying hardware, thus allowing a comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that use more connectivity clearly benefit from a better-connected system of qubits. Although the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that codesigning particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future.

Continuous-variable quantum Gaussian process regression and quantum singular value decomposition of nonsparse low-rank matrices

NASA Astrophysics Data System (ADS)

Das, Siddhartha; Siopsis, George; Weedbrook, Christian

2018-02-01

With the significant advancement in quantum computation during the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used technique in supervised classical machine learning. Here we introduce an algorithm for Gaussian process regression using continuous-variable quantum systems that can be realized with technology based on photonic quantum computers under certain assumptions regarding distribution of data and availability of efficient quantum access. Our algorithm shows that by using a continuous-variable quantum computer a dramatic speedup in computing Gaussian process regression can be achieved, i.e., the possibility of exponentially reducing the time to compute. Furthermore, our results also include a continuous-variable quantum-assisted singular value decomposition method of nonsparse low rank matrices and forms an important subroutine in our Gaussian process regression algorithm.

Shor's factoring algorithm and modern cryptography. An illustration of the capabilities inherent in quantum computers

NASA Astrophysics Data System (ADS)

Gerjuoy, Edward

2005-06-01

The security of messages encoded via the widely used RSA public key encryption system rests on the enormous computational effort required to find the prime factors of a large number N using classical (conventional) computers. In 1994 Peter Shor showed that for sufficiently large N, a quantum computer could perform the factoring with much less computational effort. This paper endeavors to explain, in a fashion comprehensible to the nonexpert, the RSA encryption protocol; the various quantum computer manipulations constituting the Shor algorithm; how the Shor algorithm performs the factoring; and the precise sense in which a quantum computer employing Shor's algorithm can be said to accomplish the factoring of very large numbers with less computational effort than a classical computer. It is made apparent that factoring N generally requires many successive runs of the algorithm. Our analysis reveals that the probability of achieving a successful factorization on a single run is about twice as large as commonly quoted in the literature.

Shor's quantum factoring algorithm on a photonic chip.

PubMed

Politi, Alberto; Matthews, Jonathan C F; O'Brien, Jeremy L

2009-09-04

Shor's quantum factoring algorithm finds the prime factors of a large number exponentially faster than any other known method, a task that lies at the heart of modern information security, particularly on the Internet. This algorithm requires a quantum computer, a device that harnesses the massive parallelism afforded by quantum superposition and entanglement of quantum bits (or qubits). We report the demonstration of a compiled version of Shor's algorithm on an integrated waveguide silica-on-silicon chip that guides four single-photon qubits through the computation to factor 15.

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.

Ramsey numbers and adiabatic quantum computing.

PubMed

Gaitan, Frank; Clark, Lane

2012-01-06

The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.

General Quantum Meet-in-the-Middle Search Algorithm Based on Target Solution of Fixed Weight

NASA Astrophysics Data System (ADS)

Fu, Xiang-Qun; Bao, Wan-Su; Wang, Xiang; Shi, Jian-Hong

2016-10-01

Similar to the classical meet-in-the-middle algorithm, the storage and computation complexity are the key factors that decide the efficiency of the quantum meet-in-the-middle algorithm. Aiming at the target vector of fixed weight, based on the quantum meet-in-the-middle algorithm, the algorithm for searching all n-product vectors with the same weight is presented, whose complexity is better than the exhaustive search algorithm. And the algorithm can reduce the storage complexity of the quantum meet-in-the-middle search algorithm. Then based on the algorithm and the knapsack vector of the Chor-Rivest public-key crypto of fixed weight d, we present a general quantum meet-in-the-middle search algorithm based on the target solution of fixed weight, whose computational complexity is \\sumj = 0d {(O(\\sqrt {Cn - k + 1d - j }) + O(C_kj log C_k^j))} with Σd i =0 Ck i memory cost. And the optimal value of k is given. Compared to the quantum meet-in-the-middle search algorithm for knapsack problem and the quantum algorithm for searching a target solution of fixed weight, the computational complexity of the algorithm is lower. And its storage complexity is smaller than the quantum meet-in-the-middle-algorithm. Supported by the National Basic Research Program of China under Grant No. 2013CB338002 and the National Natural Science Foundation of China under Grant No. 61502526

Simulated quantum computation of molecular energies.

PubMed

Aspuru-Guzik, Alán; Dutoi, Anthony D; Love, Peter J; Head-Gordon, Martin

2005-09-09

The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical interest using modest numbers of quantum bits. Calculations of the water and lithium hydride molecular ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estimation algorithm. The recursive algorithm reduces the number of quantum bits required for the readout register from about 20 to 4. Mappings of the molecular wave function to the quantum bits are described. An adiabatic method for the preparation of a good approximate ground-state wave function is described and demonstrated for a stretched hydrogen molecule. The number of quantum bits required scales linearly with the number of basis functions, and the number of gates required grows polynomially with the number of quantum bits.

Programming languages and compiler design for realistic quantum hardware.

PubMed

Chong, Frederic T; Franklin, Diana; Martonosi, Margaret

2017-09-13

Quantum computing sits at an important inflection point. For years, high-level algorithms for quantum computers have shown considerable promise, and recent advances in quantum device fabrication offer hope of utility. A gap still exists, however, between the hardware size and reliability requirements of quantum computing algorithms and the physical machines foreseen within the next ten years. To bridge this gap, quantum computers require appropriate software to translate and optimize applications (toolflows) and abstraction layers. Given the stringent resource constraints in quantum computing, information passed between layers of software and implementations will differ markedly from in classical computing. Quantum toolflows must expose more physical details between layers, so the challenge is to find abstractions that expose key details while hiding enough complexity.

Programming languages and compiler design for realistic quantum hardware

NASA Astrophysics Data System (ADS)

Chong, Frederic T.; Franklin, Diana; Martonosi, Margaret

2017-09-01

Quantum computing sits at an important inflection point. For years, high-level algorithms for quantum computers have shown considerable promise, and recent advances in quantum device fabrication offer hope of utility. A gap still exists, however, between the hardware size and reliability requirements of quantum computing algorithms and the physical machines foreseen within the next ten years. To bridge this gap, quantum computers require appropriate software to translate and optimize applications (toolflows) and abstraction layers. Given the stringent resource constraints in quantum computing, information passed between layers of software and implementations will differ markedly from in classical computing. Quantum toolflows must expose more physical details between layers, so the challenge is to find abstractions that expose key details while hiding enough complexity.

Experimental comparison of two quantum computing architectures

PubMed Central

Linke, Norbert M.; Maslov, Dmitri; Roetteler, Martin; Debnath, Shantanu; Figgatt, Caroline; Landsman, Kevin A.; Wright, Kenneth; Monroe, Christopher

2017-01-01

We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device (www.research.ibm.com/ibm-q) with limited connectivity, and the other is a fully connected trapped-ion system. Even though the two systems have different native quantum interactions, both can be programed in a way that is blind to the underlying hardware, thus allowing a comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that use more connectivity clearly benefit from a better-connected system of qubits. Although the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that codesigning particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future. PMID:28325879

Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance.

PubMed

Vandersypen, L M; Steffen, M; Breyta, G; Yannoni, C S; Sherwood, M H; Chuang, I L

The number of steps any classical computer requires in order to find the prime factors of an l-digit integer N increases exponentially with l, at least using algorithms known at present. Factoring large integers is therefore conjectured to be intractable classically, an observation underlying the security of widely used cryptographic codes. Quantum computers, however, could factor integers in only polynomial time, using Shor's quantum factoring algorithm. Although important for the study of quantum computers, experimental demonstration of this algorithm has proved elusive. Here we report an implementation of the simplest instance of Shor's algorithm: factorization of N = 15 (whose prime factors are 3 and 5). We use seven spin-1/2 nuclei in a molecule as quantum bits, which can be manipulated with room temperature liquid-state nuclear magnetic resonance techniques. This method of using nuclei to store quantum information is in principle scalable to systems containing many quantum bits, but such scalability is not implied by the present work. The significance of our work lies in the demonstration of experimental and theoretical techniques for precise control and modelling of complex quantum computers. In particular, we present a simple, parameter-free but predictive model of decoherence effects in our system.

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.

Demonstration of a compiled version of Shor's quantum factoring algorithm using photonic qubits.

PubMed

Lu, Chao-Yang; Browne, Daniel E; Yang, Tao; Pan, Jian-Wei

2007-12-21

We report an experimental demonstration of a complied version of Shor's algorithm using four photonic qubits. We choose the simplest instance of this algorithm, that is, factorization of N=15 in the case that the period r=2 and exploit a simplified linear optical network to coherently implement the quantum circuits of the modular exponential execution and semiclassical quantum Fourier transformation. During this computation, genuine multiparticle entanglement is observed which well supports its quantum nature. This experiment represents an essential step toward full realization of Shor's algorithm and scalable linear optics quantum computation.

Quantum machine learning.

PubMed

Biamonte, Jacob; Wittek, Peter; Pancotti, Nicola; Rebentrost, Patrick; Wiebe, Nathan; Lloyd, Seth

2017-09-13

Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Quantum systems produce atypical patterns that classical systems are thought not to produce efficiently, so it is reasonable to postulate that quantum computers may outperform classical computers on machine learning tasks. The field of quantum machine learning explores how to devise and implement quantum software that could enable machine learning that is faster than that of classical computers. Recent work has produced quantum algorithms that could act as the building blocks of machine learning programs, but the hardware and software challenges are still considerable.

Quantum machine learning

NASA Astrophysics Data System (ADS)

Biamonte, Jacob; Wittek, Peter; Pancotti, Nicola; Rebentrost, Patrick; Wiebe, Nathan; Lloyd, Seth

2017-09-01

Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Quantum systems produce atypical patterns that classical systems are thought not to produce efficiently, so it is reasonable to postulate that quantum computers may outperform classical computers on machine learning tasks. The field of quantum machine learning explores how to devise and implement quantum software that could enable machine learning that is faster than that of classical computers. Recent work has produced quantum algorithms that could act as the building blocks of machine learning programs, but the hardware and software challenges are still considerable.

Quantum plug n’ play: modular computation in the quantum regime

NASA Astrophysics Data System (ADS)

Thompson, Jayne; Modi, Kavan; Vedral, Vlatko; Gu, Mile

2018-01-01

Classical computation is modular. It exploits plug n’ play architectures which allow us to use pre-fabricated circuits without knowing their construction. This bestows advantages such as allowing parts of the computational process to be outsourced, and permitting individual circuit components to be exchanged and upgraded. Here, we introduce a formal framework to describe modularity in the quantum regime. We demonstrate a ‘no-go’ theorem, stipulating that it is not always possible to make use of quantum circuits without knowing their construction. This has significant consequences for quantum algorithms, forcing the circuit implementation of certain quantum algorithms to be rebuilt almost entirely from scratch after incremental changes in the problem—such as changing the number being factored in Shor’s algorithm. We develop a workaround capable of restoring modularity, and apply it to design a modular version of Shor’s algorithm that exhibits increased versatility and reduced complexity. In doing so we pave the way to a realistic framework whereby ‘quantum chips’ and remote servers can be invoked (or assembled) to implement various parts of a more complex quantum computation.

Least significant qubit algorithm for quantum images

NASA Astrophysics Data System (ADS)

Sang, Jianzhi; Wang, Shen; Li, Qiong

2016-11-01

To study the feasibility of the classical image least significant bit (LSB) information hiding algorithm on quantum computer, a least significant qubit (LSQb) information hiding algorithm of quantum image is proposed. In this paper, we focus on a novel quantum representation for color digital images (NCQI). Firstly, by designing the three qubits comparator and unitary operators, the reasonability and feasibility of LSQb based on NCQI are presented. Then, the concrete LSQb information hiding algorithm is proposed, which can realize the aim of embedding the secret qubits into the least significant qubits of RGB channels of quantum cover image. Quantum circuit of the LSQb information hiding algorithm is also illustrated. Furthermore, the secrets extracting algorithm and circuit are illustrated through utilizing control-swap gates. The two merits of our algorithm are: (1) it is absolutely blind and (2) when extracting secret binary qubits, it does not need any quantum measurement operation or any other help from classical computer. Finally, simulation and comparative analysis show the performance of our algorithm.

Quantum Computation

NASA Astrophysics Data System (ADS)

Aharonov, Dorit

In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically powerful computational tool, capable of performing tasks which seem intractable for classical computers. This review is about to tell the story of theoretical quantum computation. I l out the developing topic of experimental realizations of the model, and neglected other closely related topics which are quantum information and quantum communication. As a result of narrowing the scope of this paper, I hope it has gained the benefit of being an almost self contained introduction to the exciting field of quantum computation. The review begins with background on theoretical computer science, Turing machines and Boolean circuits. In light of these models, I define quantum computers, and discuss the issue of universal quantum gates. Quantum algorithms, including Shor's factorization algorithm and Grover's algorithm for searching databases, are explained. I will devote much attention to understanding what the origins of the quantum computational power are, and what the limits of this power are. Finally, I describe the recent theoretical results which show that quantum computers maintain their complexity power even in the presence of noise, inaccuracies and finite precision. This question cannot be separated from that of quantum complexity because any realistic model will inevitably be subjected to such inaccuracies. I tried to put all results in their context, asking what the implications to other issues in computer science and physics are. In the end of this review, I make these connections explicit by discussing the possible implications of quantum computation on fundamental physical questions such as the transition from quantum to classical physics.

A quantum–quantum Metropolis algorithm

PubMed Central

Yung, Man-Hong; Aspuru-Guzik, Alán

2012-01-01

The classical Metropolis sampling method is a cornerstone of many statistical modeling applications that range from physics, chemistry, and biology to economics. This method is particularly suitable for sampling the thermal distributions of classical systems. The challenge of extending this method to the simulation of arbitrary quantum systems is that, in general, eigenstates of quantum Hamiltonians cannot be obtained efficiently with a classical computer. However, this challenge can be overcome by quantum computers. Here, we present a quantum algorithm which fully generalizes the classical Metropolis algorithm to the quantum domain. The meaning of quantum generalization is twofold: The proposed algorithm is not only applicable to both classical and quantum systems, but also offers a quantum speedup relative to the classical counterpart. Furthermore, unlike the classical method of quantum Monte Carlo, this quantum algorithm does not suffer from the negative-sign problem associated with fermionic systems. Applications of this algorithm include the study of low-temperature properties of quantum systems, such as the Hubbard model, and preparing the thermal states of sizable molecules to simulate, for example, chemical reactions at an arbitrary temperature. PMID:22215584

A software methodology for compiling quantum programs

NASA Astrophysics Data System (ADS)

Häner, Thomas; Steiger, Damian S.; Svore, Krysta; Troyer, Matthias

2018-04-01

Quantum computers promise to transform our notions of computation by offering a completely new paradigm. To achieve scalable quantum computation, optimizing compilers and a corresponding software design flow will be essential. We present a software architecture for compiling quantum programs from a high-level language program to hardware-specific instructions. We describe the necessary layers of abstraction and their differences and similarities to classical layers of a computer-aided design flow. For each layer of the stack, we discuss the underlying methods for compilation and optimization. Our software methodology facilitates more rapid innovation among quantum algorithm designers, quantum hardware engineers, and experimentalists. It enables scalable compilation of complex quantum algorithms and can be targeted to any specific quantum hardware implementation.

Quantum walk computation

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

Kendon, Viv

2014-12-04

Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. Recent results showing quantum walks are “universal for quantum computation” relate to algorithms, to be run on quantum computers. We consider whether an experimental implementation of a quantum walk could provide useful computation before we have a universal quantum computer.

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.

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.

An introduction to quantum machine learning

NASA Astrophysics Data System (ADS)

Schuld, Maria; Sinayskiy, Ilya; Petruccione, Francesco

2015-04-01

Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT industry. In the last couple of years, researchers investigated if quantum computing can help to improve classical machine learning algorithms. Ideas range from running computationally costly algorithms or their subroutines efficiently on a quantum computer to the translation of stochastic methods into the language of quantum theory. This contribution gives a systematic overview of the emerging field of quantum machine learning. It presents the approaches as well as technical details in an accessible way, and discusses the potential of a future theory of quantum learning.

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.

Quantum adiabatic computation and adiabatic conditions

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

Wei Zhaohui; Ying Mingsheng

2007-08-15

Recently, quantum adiabatic computation has attracted more and more attention in the literature. It is a novel quantum computation model based on adiabatic approximation, and the analysis of a quantum adiabatic algorithm depends highly on the adiabatic conditions. However, it has been pointed out that the traditional adiabatic conditions are problematic. Thus, results obtained previously should be checked and sufficient adiabatic conditions applicable to adiabatic computation should be proposed. Based on a result of Tong et al. [Phys. Rev. Lett. 98, 150402 (2007)], we propose a modified adiabatic criterion which is more applicable to the analysis of adiabatic algorithms. Asmore » an example, we prove the validity of the local adiabatic search algorithm by employing our criterion.« less

A Programmable Five Qubit Quantum Computer Using Trapped Atomic Ions

NASA Astrophysics Data System (ADS)

Debnath, Shantanu

Quantum computers can solve certain problems more efficiently compared to conventional classical methods. In the endeavor to build a quantum computer, several competing platforms have emerged that can implement certain quantum algorithms using a few qubits. However, the demonstrations so far have been done usually by tailoring the hardware to meet the requirements of a particular algorithm implemented for a limited number of instances. Although such proof of principal implementations are important to verify the working of algorithms on a physical system, they further need to have the potential to serve as a general purpose quantum computer allowing the flexibility required for running multiple algorithms and be scaled up to host more qubits. Here we demonstrate a small programmable quantum computer based on five trapped atomic ions each of which serves as a qubit. By optically resolving each ion we can individually address them in order to perform a complete set of single-qubit and fully connected two-qubit quantum gates and alsoperform efficient individual qubit measurements. We implement a computation architecture that accepts an algorithm from a user interface in the form of a standard logic gate sequence and decomposes it into fundamental quantum operations that are native to the hardware using a set of compilation instructions that are defined within the software. These operations are then effected through a pattern of laser pulses that perform coherent rotations on targeted qubits in the chain. The architecture implemented in the experiment therefore gives us unprecedented flexibility in the programming of any quantum algorithm while staying blind to the underlying hardware. As a demonstration we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms on the five-qubit processor and achieve average success rates of 95 and 90 percent, respectively. We also implement a five-qubit coherent quantum Fourier transform and examine its performance in the period finding and phase estimation protocol. We find fidelities of 84 and 62 percent, respectively. While maintaining the same computation architecture the system can be scaled to more ions using resources that scale favorably (O(N. 2)) with the numberof qubits N.

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.

Quantum Simulation of Tunneling in Small Systems

PubMed Central

Sornborger, Andrew T.

2012-01-01

A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator. Here, we show that a set of tunneling problems may be investigated with no ancillary qubits and a cost of one single-qubit operator per time step for the potential evolution, eliminating at least half of the quantum gates required for the algorithm and more than that in the general case. Such simulations are within reach of current quantum computer architectures. PMID:22916333

Numerical characteristics of quantum computer simulation

NASA Astrophysics Data System (ADS)

Chernyavskiy, A.; Khamitov, K.; Teplov, A.; Voevodin, V.; Voevodin, Vl.

2016-12-01

The simulation of quantum circuits is significantly important for the implementation of quantum information technologies. The main difficulty of such modeling is the exponential growth of dimensionality, thus the usage of modern high-performance parallel computations is relevant. As it is well known, arbitrary quantum computation in circuit model can be done by only single- and two-qubit gates, and we analyze the computational structure and properties of the simulation of such gates. We investigate the fact that the unique properties of quantum nature lead to the computational properties of the considered algorithms: the quantum parallelism make the simulation of quantum gates highly parallel, and on the other hand, quantum entanglement leads to the problem of computational locality during simulation. We use the methodology of the AlgoWiki project (algowiki-project.org) to analyze the algorithm. This methodology consists of theoretical (sequential and parallel complexity, macro structure, and visual informational graph) and experimental (locality and memory access, scalability and more specific dynamic characteristics) parts. Experimental part was made by using the petascale Lomonosov supercomputer (Moscow State University, Russia). We show that the simulation of quantum gates is a good base for the research and testing of the development methods for data intense parallel software, and considered methodology of the analysis can be successfully used for the improvement of the algorithms in quantum information science.

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.

ProjectQ Software Framework

NASA Astrophysics Data System (ADS)

Steiger, Damian S.; Haener, Thomas; Troyer, Matthias

Quantum computers promise to transform our notions of computation by offering a completely new paradigm. A high level quantum programming language and optimizing compilers are essential components to achieve scalable quantum computation. In order to address this, we introduce the ProjectQ software framework - an open source effort to support both theorists and experimentalists by providing intuitive tools to implement and run quantum algorithms. Here, we present our ProjectQ quantum compiler, which compiles a quantum algorithm from our high-level Python-embedded language down to low-level quantum gates available on the target system. We demonstrate how this compiler can be used to control actual hardware and to run high-performance simulations.

Quantum computation in the analysis of hyperspectral data

NASA Astrophysics Data System (ADS)

Gomez, Richard B.; Ghoshal, Debabrata; Jayanna, Anil

2004-08-01

Recent research on the topic of quantum computation provides us with some quantum algorithms with higher efficiency and speedup compared to their classical counterparts. In this paper, it is our intent to provide the results of our investigation of several applications of such quantum algorithms - especially the Grover's Search algorithm - in the analysis of Hyperspectral Data. We found many parallels with Grover's method in existing data processing work that make use of classical spectral matching algorithms. Our efforts also included the study of several methods dealing with hyperspectral image analysis work where classical computation methods involving large data sets could be replaced with quantum computation methods. The crux of the problem in computation involving a hyperspectral image data cube is to convert the large amount of data in high dimensional space to real information. Currently, using the classical model, different time consuming methods and steps are necessary to analyze these data including: Animation, Minimum Noise Fraction Transform, Pixel Purity Index algorithm, N-dimensional scatter plot, Identification of Endmember spectra - are such steps. If a quantum model of computation involving hyperspectral image data can be developed and formalized - it is highly likely that information retrieval from hyperspectral image data cubes would be a much easier process and the final information content would be much more meaningful and timely. In this case, dimensionality would not be a curse, but a blessing.

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.

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.

A programmable five qubit quantum computer using trapped atomic ions

NASA Astrophysics Data System (ADS)

Debnath, Shantanu

2017-04-01

In order to harness the power of quantum information processing, several candidate systems have been investigated, and tailored to demonstrate only specific computations. In my thesis work, we construct a general-purpose multi-qubit device using a linear chain of trapped ion qubits, which in principle can be programmed to run any quantum algorithm. To achieve such flexibility, we develop a pulse shaping technique to realize a set of fully connected two-qubit rotations that entangle arbitrary pairs of qubits using multiple motional modes of the chain. Following a computation architecture, such highly expressive two-qubit gates along with arbitrary single-qubit rotations can be used to compile modular universal logic gates that are effected by targeted optical fields and hence can be reconfigured according to any algorithm circuit programmed in the software. As a demonstration, we run the Deutsch-Jozsa and Bernstein-Vazirani algorithm, and a fully coherent quantum Fourier transform, that we use to solve the `period finding' and `quantum phase estimation' problem. Combining these results with recent demonstrations of quantum fault-tolerance, Grover's search algorithm, and simulation of boson hopping establishes the versatility of such a computation module that can potentially be connected to other modules for future large-scale computations.

Quantum Chemistry on Quantum Computers: A Polynomial-Time Quantum Algorithm for Constructing the Wave Functions of Open-Shell Molecules.

PubMed

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

2016-08-18

Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum. The proposed quantum algorithm enables us to prepare the wave function consisting of an exponential number of Slater determinants only by a polynomial number of quantum operations.

Architectures and Applications for Scalable Quantum Information Systems

DTIC Science & Technology

2007-01-01

quantum computation models, such as adiabatic quantum computing , can be converted to quantum circuits. Therefore, in our design flow’s first phase...vol. 26, no. 5, pp. 1484–1509, 1997. [19] A. Childs, E. Farhi, and J. Preskill, “Robustness of adiabatic quantum computation ,” Phys. Rev. A, vol. 65...magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic

Lower bound on the time complexity of local adiabatic evolution

NASA Astrophysics Data System (ADS)

Chen, Zhenghao; Koh, Pang Wei; Zhao, Yan

2006-11-01

The adiabatic theorem of quantum physics has been, in recent times, utilized in the design of local search quantum algorithms, and has been proven to be equivalent to standard quantum computation, that is, the use of unitary operators [D. Aharonov in Proceedings of the 45th Annual Symposium on the Foundations of Computer Science, 2004, Rome, Italy (IEEE Computer Society Press, New York, 2004), pp. 42-51]. Hence, the study of the time complexity of adiabatic evolution algorithms gives insight into the computational power of quantum algorithms. In this paper, we present two different approaches of evaluating the time complexity for local adiabatic evolution using time-independent parameters, thus providing effective tests (not requiring the evaluation of the entire time-dependent gap function) for the time complexity of newly developed algorithms. We further illustrate our tests by displaying results from the numerical simulation of some problems, viz. specially modified instances of the Hamming weight problem.

Classical boson sampling algorithms with superior performance to near-term experiments

NASA Astrophysics Data System (ADS)

Neville, Alex; Sparrow, Chris; Clifford, Raphaël; Johnston, Eric; Birchall, Patrick M.; Montanaro, Ashley; Laing, Anthony

2017-12-01

It is predicted that quantum computers will dramatically outperform their conventional counterparts. However, large-scale universal quantum computers are yet to be built. Boson sampling is a rudimentary quantum algorithm tailored to the platform of linear optics, which has sparked interest as a rapid way to demonstrate such quantum supremacy. Photon statistics are governed by intractable matrix functions, which suggests that sampling from the distribution obtained by injecting photons into a linear optical network could be solved more quickly by a photonic experiment than by a classical computer. The apparently low resource requirements for large boson sampling experiments have raised expectations of a near-term demonstration of quantum supremacy by boson sampling. Here we present classical boson sampling algorithms and theoretical analyses of prospects for scaling boson sampling experiments, showing that near-term quantum supremacy via boson sampling is unlikely. Our classical algorithm, based on Metropolised independence sampling, allowed the boson sampling problem to be solved for 30 photons with standard computing hardware. Compared to current experiments, a demonstration of quantum supremacy over a successful implementation of these classical methods on a supercomputer would require the number of photons and experimental components to increase by orders of magnitude, while tackling exponentially scaling photon loss.

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.

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.

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.

Quantum algorithms for quantum field theories.

PubMed

Jordan, Stephen P; Lee, Keith S M; Preskill, John

2012-06-01

Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.

Quantum Algorithms and Protocols

NASA Astrophysics Data System (ADS)

Divincenzo, David

2001-06-01

Quantum Computing is better than classical computing, but not just because it speeds up some computations. Some of the best known quantum algorithms, like Grover's, may well have their most interesting applications in settings that involve the combination of computation and communication. Thus, Grover speeds up the appointment scheduling problem by reducing the amount of communication needed between two parties who want to find a common free slot on their calendars. I will review various other applications of this sort that are being explored. Other distributed computing protocols are required to have other attributes like obliviousness and privacy; I will discuss our recent applications involving quantum data hiding.

Quantum computation and analysis of Wigner and Husimi functions: toward a quantum image treatment.

PubMed

Terraneo, M; Georgeot, B; Shepelyansky, D L

2005-06-01

We study the efficiency of quantum algorithms which aim at obtaining phase-space distribution functions of quantum systems. Wigner and Husimi functions are considered. Different quantum algorithms are envisioned to build these functions, and compared with the classical computation. Different procedures to extract more efficiently information from the final wave function of these algorithms are studied, including coarse-grained measurements, amplitude amplification, and measure of wavelet-transformed wave function. The algorithms are analyzed and numerically tested on a complex quantum system showing different behavior depending on parameters: namely, the kicked rotator. The results for the Wigner function show in particular that the use of the quantum wavelet transform gives a polynomial gain over classical computation. For the Husimi distribution, the gain is much larger than for the Wigner function and is larger with the help of amplitude amplification and wavelet transforms. We discuss the generalization of these results to the simulation of other quantum systems. We also apply the same set of techniques to the analysis of real images. The results show that the use of the quantum wavelet transform allows one to lower dramatically the number of measurements needed, but at the cost of a large loss of information.

Procedural Quantum Programming

NASA Astrophysics Data System (ADS)

Ömer, Bernhard

2002-09-01

While classical computing science has developed a variety of methods and programming languages around the concept of the universal computer, the typical description of quantum algorithms still uses a purely mathematical, non-constructive formalism which makes no difference between a hydrogen atom and a quantum computer. This paper investigates, how the concept of procedural programming languages, the most widely used classical formalism for describing and implementing algorithms, can be adopted to the field of quantum computing, and how non-classical features like the reversibility of unitary transformations, the non-observability of quantum states or the lack of copy and erase operations can be reflected semantically. It introduces the key concepts of procedural quantum programming (hybrid target architecture, operator hierarchy, quantum data types, memory management, etc.) and presents the experimental language QCL, which implements these principles.

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.

Decoherence in adiabatic quantum computation

NASA Astrophysics Data System (ADS)

Albash, Tameem; Lidar, Daniel A.

2015-06-01

Recent experiments with increasingly larger numbers of qubits have sparked renewed interest in adiabatic quantum computation, and in particular quantum annealing. A central question that is repeatedly asked is whether quantum features of the evolution can survive over the long time scales used for quantum annealing relative to standard measures of the decoherence time. We reconsider the role of decoherence in adiabatic quantum computation and quantum annealing using the adiabatic quantum master-equation formalism. We restrict ourselves to the weak-coupling and singular-coupling limits, which correspond to decoherence in the energy eigenbasis and in the computational basis, respectively. We demonstrate that decoherence in the instantaneous energy eigenbasis does not necessarily detrimentally affect adiabatic quantum computation, and in particular that a short single-qubit T2 time need not imply adverse consequences for the success of the quantum adiabatic algorithm. We further demonstrate that boundary cancellation methods, designed to improve the fidelity of adiabatic quantum computing in the closed-system setting, remain beneficial in the open-system setting. To address the high computational cost of master-equation simulations, we also demonstrate that a quantum Monte Carlo algorithm that explicitly accounts for a thermal bosonic bath can be used to interpolate between classical and quantum annealing. Our study highlights and clarifies the significantly different role played by decoherence in the adiabatic and circuit models of quantum computing.

Scheme for Entering Binary Data Into a Quantum Computer

NASA Technical Reports Server (NTRS)

Williams, Colin

2005-01-01

A quantum algorithm provides for the encoding of an exponentially large number of classical data bits by use of a smaller (polynomially large) number of quantum bits (qubits). The development of this algorithm was prompted by the need, heretofore not satisfied, for a means of entering real-world binary data into a quantum computer. The data format provided by this algorithm is suitable for subsequent ultrafast quantum processing of the entered data. Potential applications lie in disciplines (e.g., genomics) in which one needs to search for matches between parts of very long sequences of data. For example, the algorithm could be used to encode the N-bit-long human genome in only log2N qubits. The resulting log2N-qubit state could then be used for subsequent quantum data processing - for example, to perform rapid comparisons of sequences.

Estimating the Resources for Quantum Computation with the QuRE Toolbox

DTIC Science & Technology

2013-05-31

quantum computing. Quantum Info. Comput., 9(7):666–682, July 2009. [13] M. Saffman, T. G. Walker, and K. Mølmer. Quantum information with rydberg atoms...109(5):735–750, 2011. [24] Aram Harrow , Avinatan Hassidim, and Seth Lloyd. Quantum algorithm for solving linear systems of equations. Phys. Rev

Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor.

PubMed

Mitra, Avik; Ghosh, Arindam; Das, Ranabir; Patel, Apoorva; Kumar, Anil

2005-12-01

Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required output state. In some cases, such as the adiabatic versions of Grover's search algorithm and Deutsch-Jozsa algorithm, applying the global adiabatic evolution yields a complexity similar to their classical algorithms. However, using the local adiabatic evolution, the algorithms given by J. Roland and N.J. Cerf for Grover's search [J. Roland, N.J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65 (2002) 042308] and by Saurya Das, Randy Kobes, and Gabor Kunstatter for the Deutsch-Jozsa algorithm [S. Das, R. Kobes, G. Kunstatter, Adiabatic quantum computation and Deutsh's algorithm, Phys. Rev. A 65 (2002) 062301], yield a complexity of order N (where N=2(n) and n is the number of qubits). In this paper, we report the experimental implementation of these local adiabatic evolution algorithms on a 2-qubit quantum information processor, by Nuclear Magnetic Resonance.

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.

Adiabatic Quantum Anomaly Detection and Machine Learning

NASA Astrophysics Data System (ADS)

Pudenz, Kristen; Lidar, Daniel

2012-02-01

We present methods of anomaly detection and machine learning using adiabatic quantum computing. The machine learning algorithm is a boosting approach which seeks to optimally combine somewhat accurate classification functions to create a unified classifier which is much more accurate than its components. This algorithm then becomes the first part of the larger anomaly detection algorithm. In the anomaly detection routine, we first use adiabatic quantum computing to train two classifiers which detect two sets, the overlap of which forms the anomaly class. We call this the learning phase. Then, in the testing phase, the two learned classification functions are combined to form the final Hamiltonian for an adiabatic quantum computation, the low energy states of which represent the anomalies in a binary vector space.

Quantum algorithm for support matrix machines

NASA Astrophysics Data System (ADS)

Duan, Bojia; Yuan, Jiabin; Liu, Ying; Li, Dan

2017-09-01

We propose a quantum algorithm for support matrix machines (SMMs) that efficiently addresses an image classification problem by introducing a least-squares reformulation. This algorithm consists of two core subroutines: a quantum matrix inversion (Harrow-Hassidim-Lloyd, HHL) algorithm and a quantum singular value thresholding (QSVT) algorithm. The two algorithms can be implemented on a universal quantum computer with complexity O[log(npq) ] and O[log(pq)], respectively, where n is the number of the training data and p q is the size of the feature space. By iterating the algorithms, we can find the parameters for the SMM classfication model. Our analysis shows that both HHL and QSVT algorithms achieve an exponential increase of speed over their classical counterparts.

Irreconcilable difference between quantum walks and adiabatic quantum computing

NASA Astrophysics Data System (ADS)

Wong, Thomas G.; Meyer, David A.

2016-06-01

Continuous-time quantum walks and adiabatic quantum evolution are two general techniques for quantum computing, both of which are described by Hamiltonians that govern their evolutions by Schrödinger's equation. In the former, the Hamiltonian is fixed, while in the latter, the Hamiltonian varies with time. As a result, their formulations of Grover's algorithm evolve differently through Hilbert space. We show that this difference is fundamental; they cannot be made to evolve along each other's path without introducing structure more powerful than the standard oracle for unstructured search. For an adiabatic quantum evolution to evolve like the quantum walk search algorithm, it must interpolate between three fixed Hamiltonians, one of which is complex and introduces structure that is stronger than the oracle for unstructured search. Conversely, for a quantum walk to evolve along the path of the adiabatic search algorithm, it must be a chiral quantum walk on a weighted, directed star graph with structure that is also stronger than the oracle for unstructured search. Thus, the two techniques, although similar in being described by Hamiltonians that govern their evolution, compute by fundamentally irreconcilable means.

Adiabatic Quantum Search in Open Systems.

PubMed

Wild, Dominik S; Gopalakrishnan, Sarang; Knap, Michael; Yao, Norman Y; Lukin, Mikhail D

2016-10-07

Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.

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.

Nontrivial Quantum Effects in Biology: A Skeptical Physicists' View

NASA Astrophysics Data System (ADS)

Wiseman, Howard; Eisert, Jens

The following sections are included: * Introduction * A Quantum Life Principle * A quantum chemistry principle? * The anthropic principle * Quantum Computing in the Brain * Nature did everything first? * Decoherence as the make or break issue * Quantum error correction * Uselessness of quantum algorithms for organisms * Quantum Computing in Genetics * Quantum search * Teleological aspects and the fast-track to life * Quantum Consciousness * Computability and free will * Time scales * Quantum Free Will * Predictability and free will * Determinism and free will * Acknowledgements * References

Improving Quantum Gate Simulation using a GPU

NASA Astrophysics Data System (ADS)

Gutierrez, Eladio; Romero, Sergio; Trenas, Maria A.; Zapata, Emilio L.

2008-11-01

Due to the increasing computing power of the graphics processing units (GPU), they are becoming more and more popular when solving general purpose algorithms. As the simulation of quantum computers results on a problem with exponential complexity, it is advisable to perform a parallel computation, such as the one provided by the SIMD multiprocessors present in recent GPUs. In this paper, we focus on an important quantum algorithm, the quantum Fourier transform (QTF), in order to evaluate different parallelization strategies on a novel GPU architecture. Our implementation makes use of the new CUDA software/hardware architecture developed recently by NVIDIA.

Exponential vanishing of the ground-state gap of the quantum random energy model via adiabatic quantum computing

NASA Astrophysics Data System (ADS)

Adame, J.; Warzel, S.

2015-11-01

In this note, we use ideas of Farhi et al. [Int. J. Quantum. Inf. 6, 503 (2008) and Quantum Inf. Comput. 11, 840 (2011)] who link a lower bound on the run time of their quantum adiabatic search algorithm to an upper bound on the energy gap above the ground-state of the generators of this algorithm. We apply these ideas to the quantum random energy model (QREM). Our main result is a simple proof of the conjectured exponential vanishing of the energy gap of the QREM.

Exponential vanishing of the ground-state gap of the quantum random energy model via adiabatic quantum computing

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

Adame, J.; Warzel, S., E-mail: warzel@ma.tum.de

In this note, we use ideas of Farhi et al. [Int. J. Quantum. Inf. 6, 503 (2008) and Quantum Inf. Comput. 11, 840 (2011)] who link a lower bound on the run time of their quantum adiabatic search algorithm to an upper bound on the energy gap above the ground-state of the generators of this algorithm. We apply these ideas to the quantum random energy model (QREM). Our main result is a simple proof of the conjectured exponential vanishing of the energy gap of the QREM.

Triple-server blind quantum computation using entanglement swapping

NASA Astrophysics Data System (ADS)

Li, Qin; Chan, Wai Hong; Wu, Chunhui; Wen, Zhonghua

2014-04-01

Blind quantum computation allows a client who does not have enough quantum resources or technologies to achieve quantum computation on a remote quantum server such that the client's input, output, and algorithm remain unknown to the server. Up to now, single- and double-server blind quantum computation have been considered. In this work, we propose a triple-server blind computation protocol where the client can delegate quantum computation to three quantum servers by the use of entanglement swapping. Furthermore, the three quantum servers can communicate with each other and the client is almost classical since one does not require any quantum computational power, quantum memory, and the ability to prepare any quantum states and only needs to be capable of getting access to quantum channels.

Majorana-Based Fermionic Quantum Computation.

PubMed

O'Brien, T E; Rożek, P; Akhmerov, A R

2018-06-01

Because Majorana zero modes store quantum information nonlocally, they are protected from noise, and have been proposed as a building block for a quantum computer. We show how to use the same protection from noise to implement universal fermionic quantum computation. Our architecture requires only two Majorana modes to encode a fermionic quantum degree of freedom, compared to alternative implementations which require a minimum of four Majorana modes for a spin quantum degree of freedom. The fermionic degrees of freedom support both unitary coupled cluster variational quantum eigensolver and quantum phase estimation algorithms, proposed for quantum chemistry simulations. Because we avoid the Jordan-Wigner transformation, our scheme has a lower overhead for implementing both of these algorithms, allowing for simulation of the Trotterized Hubbard Hamiltonian in O(1) time per unitary step. We finally demonstrate magic state distillation in our fermionic architecture, giving a universal set of topologically protected fermionic quantum gates.

Majorana-Based Fermionic Quantum Computation

NASA Astrophysics Data System (ADS)

O'Brien, T. E.; RoŻek, P.; Akhmerov, A. R.

2018-06-01

Because Majorana zero modes store quantum information nonlocally, they are protected from noise, and have been proposed as a building block for a quantum computer. We show how to use the same protection from noise to implement universal fermionic quantum computation. Our architecture requires only two Majorana modes to encode a fermionic quantum degree of freedom, compared to alternative implementations which require a minimum of four Majorana modes for a spin quantum degree of freedom. The fermionic degrees of freedom support both unitary coupled cluster variational quantum eigensolver and quantum phase estimation algorithms, proposed for quantum chemistry simulations. Because we avoid the Jordan-Wigner transformation, our scheme has a lower overhead for implementing both of these algorithms, allowing for simulation of the Trotterized Hubbard Hamiltonian in O (1 ) time per unitary step. We finally demonstrate magic state distillation in our fermionic architecture, giving a universal set of topologically protected fermionic quantum gates.

Quantum computing applied to calculations of molecular energies: CH2 benchmark.

PubMed

Veis, Libor; Pittner, Jiří

2010-11-21

Quantum computers are appealing for their ability to solve some tasks much faster than their classical counterparts. It was shown in [Aspuru-Guzik et al., Science 309, 1704 (2005)] that they, if available, would be able to perform the full configuration interaction (FCI) energy calculations with a polynomial scaling. This is in contrast to conventional computers where FCI scales exponentially. We have developed a code for simulation of quantum computers and implemented our version of the quantum FCI algorithm. We provide a detailed description of this algorithm and the results of the assessment of its performance on the four lowest lying electronic states of CH(2) molecule. This molecule was chosen as a benchmark, since its two lowest lying (1)A(1) states exhibit a multireference character at the equilibrium geometry. It has been shown that with a suitably chosen initial state of the quantum register, one is able to achieve the probability amplification regime of the iterative phase estimation algorithm even in this case.

Towards topological quantum computer

NASA Astrophysics Data System (ADS)

Melnikov, D.; Mironov, A.; Mironov, S.; Morozov, A.; Morozov, An.

2018-01-01

Quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates) for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.

Demonstration of blind quantum computing.

PubMed

Barz, Stefanie; Kashefi, Elham; Broadbent, Anne; Fitzsimons, Joseph F; Zeilinger, Anton; Walther, Philip

2012-01-20

Quantum computers, besides offering substantial computational speedups, are also expected to preserve the privacy of a computation. We present an experimental demonstration of blind quantum computing in which the input, computation, and output all remain unknown to the computer. We exploit the conceptual framework of measurement-based quantum computation that enables a client to delegate a computation to a quantum server. Various blind delegated computations, including one- and two-qubit gates and the Deutsch and Grover quantum algorithms, are demonstrated. The client only needs to be able to prepare and transmit individual photonic qubits. Our demonstration is crucial for unconditionally secure quantum cloud computing and might become a key ingredient for real-life applications, especially when considering the challenges of making powerful quantum computers widely available.

Blind Quantum Signature with Blind Quantum Computation

NASA Astrophysics Data System (ADS)

Li, Wei; Shi, Ronghua; Guo, Ying

2017-04-01

Blind quantum computation allows a client without quantum abilities to interact with a quantum server to perform a unconditional secure computing protocol, while protecting client's privacy. Motivated by confidentiality of blind quantum computation, a blind quantum signature scheme is designed with laconic structure. Different from the traditional signature schemes, the signing and verifying operations are performed through measurement-based quantum computation. Inputs of blind quantum computation are securely controlled with multi-qubit entangled states. The unique signature of the transmitted message is generated by the signer without leaking information in imperfect channels. Whereas, the receiver can verify the validity of the signature using the quantum matching algorithm. The security is guaranteed by entanglement of quantum system for blind quantum computation. It provides a potential practical application for e-commerce in the cloud computing and first-generation quantum computation.

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.

Simulation of quantum dynamics based on the quantum stochastic differential equation.

PubMed

Li, Ming

2013-01-01

The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm.

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

Baart, T. A.; Vandersypen, L. M. K.; Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft

We report the computer-automated tuning of gate-defined semiconductor double quantum dots in GaAs heterostructures. We benchmark the algorithm by creating three double quantum dots inside a linear array of four quantum dots. The algorithm sets the correct gate voltages for all the gates to tune the double quantum dots into the single-electron regime. The algorithm only requires (1) prior knowledge of the gate design and (2) the pinch-off value of the single gate T that is shared by all the quantum dots. This work significantly alleviates the user effort required to tune multiple quantum dot devices.

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

Operating Quantum States in Single Magnetic Molecules: Implementation of Grover's Quantum Algorithm.

PubMed

Godfrin, C; Ferhat, A; Ballou, R; Klyatskaya, S; Ruben, M; Wernsdorfer, W; Balestro, F

2017-11-03

Quantum algorithms use the principles of quantum mechanics, such as, for example, quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimization, simulation, and solving large systems of linear equations. Here, we implement Grover's quantum algorithm, proposed to find an element in an unsorted list, using a single nuclear 3/2 spin carried by a Tb ion sitting in a single molecular magnet transistor. The coherent manipulation of this multilevel quantum system (qudit) is achieved by means of electric fields only. Grover's search algorithm is implemented by constructing a quantum database via a multilevel Hadamard gate. The Grover sequence then allows us to select each state. The presented method is of universal character and can be implemented in any multilevel quantum system with nonequal spaced energy levels, opening the way to novel quantum search algorithms.

Operating Quantum States in Single Magnetic Molecules: Implementation of Grover's Quantum Algorithm

NASA Astrophysics Data System (ADS)

Godfrin, C.; Ferhat, A.; Ballou, R.; Klyatskaya, S.; Ruben, M.; Wernsdorfer, W.; Balestro, F.

2017-11-01

Quantum algorithms use the principles of quantum mechanics, such as, for example, quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimization, simulation, and solving large systems of linear equations. Here, we implement Grover's quantum algorithm, proposed to find an element in an unsorted list, using a single nuclear 3 /2 spin carried by a Tb ion sitting in a single molecular magnet transistor. The coherent manipulation of this multilevel quantum system (qudit) is achieved by means of electric fields only. Grover's search algorithm is implemented by constructing a quantum database via a multilevel Hadamard gate. The Grover sequence then allows us to select each state. The presented method is of universal character and can be implemented in any multilevel quantum system with nonequal spaced energy levels, opening the way to novel quantum search algorithms.

Efficient Online Optimized Quantum Control for Adiabatic Quantum Computation

NASA Astrophysics Data System (ADS)

Quiroz, Gregory

Adiabatic quantum computation (AQC) relies on controlled adiabatic evolution to implement a quantum algorithm. While control evolution can take many forms, properly designed time-optimal control has been shown to be particularly advantageous for AQC. Grover's search algorithm is one such example where analytically-derived time-optimal control leads to improved scaling of the minimum energy gap between the ground state and first excited state and thus, the well-known quadratic quantum speedup. Analytical extensions beyond Grover's search algorithm present a daunting task that requires potentially intractable calculations of energy gaps and a significant degree of model certainty. Here, an in situ quantum control protocol is developed for AQC. The approach is shown to yield controls that approach the analytically-derived time-optimal controls for Grover's search algorithm. In addition, the protocol's convergence rate as a function of iteration number is shown to be essentially independent of system size. Thus, the approach is potentially scalable to many-qubit systems.

Private quantum computation: an introduction to blind quantum computing and related protocols

NASA Astrophysics Data System (ADS)

Fitzsimons, Joseph F.

2017-06-01

Quantum technologies hold the promise of not only faster algorithmic processing of data, via quantum computation, but also of more secure communications, in the form of quantum cryptography. In recent years, a number of protocols have emerged which seek to marry these concepts for the purpose of securing computation rather than communication. These protocols address the task of securely delegating quantum computation to an untrusted device while maintaining the privacy, and in some instances the integrity, of the computation. We present a review of the progress to date in this emerging area.

GPU-accelerated algorithms for many-particle continuous-time quantum walks

NASA Astrophysics Data System (ADS)

Piccinini, Enrico; Benedetti, Claudia; Siloi, Ilaria; Paris, Matteo G. A.; Bordone, Paolo

2017-06-01

Many-particle continuous-time quantum walks (CTQWs) represent a resource for several tasks in quantum technology, including quantum search algorithms and universal quantum computation. In order to design and implement CTQWs in a realistic scenario, one needs effective simulation tools for Hamiltonians that take into account static noise and fluctuations in the lattice, i.e. Hamiltonians containing stochastic terms. To this aim, we suggest a parallel algorithm based on the Taylor series expansion of the evolution operator, and compare its performances with those of algorithms based on the exact diagonalization of the Hamiltonian or a 4th order Runge-Kutta integration. We prove that both Taylor-series expansion and Runge-Kutta algorithms are reliable and have a low computational cost, the Taylor-series expansion showing the additional advantage of a memory allocation not depending on the precision of calculation. Both algorithms are also highly parallelizable within the SIMT paradigm, and are thus suitable for GPGPU computing. In turn, we have benchmarked 4 NVIDIA GPUs and 3 quad-core Intel CPUs for a 2-particle system over lattices of increasing dimension, showing that the speedup provided by GPU computing, with respect to the OPENMP parallelization, lies in the range between 8x and (more than) 20x, depending on the frequency of post-processing. GPU-accelerated codes thus allow one to overcome concerns about the execution time, and make it possible simulations with many interacting particles on large lattices, with the only limit of the memory available on the device.

Concrete resource analysis of the quantum linear-system algorithm used to compute the electromagnetic scattering cross section of a 2D target

NASA Astrophysics Data System (ADS)

Scherer, Artur; Valiron, Benoît; Mau, Siun-Chuon; Alexander, Scott; van den Berg, Eric; Chapuran, Thomas E.

2017-03-01

We provide a detailed estimate for the logical resource requirements of the quantum linear-system algorithm (Harrow et al. in Phys Rev Lett 103:150502, 2009) including the recently described elaborations and application to computing the electromagnetic scattering cross section of a metallic target (Clader et al. in Phys Rev Lett 110:250504, 2013). Our resource estimates are based on the standard quantum-circuit model of quantum computation; they comprise circuit width (related to parallelism), circuit depth (total number of steps), the number of qubits and ancilla qubits employed, and the overall number of elementary quantum gate operations as well as more specific gate counts for each elementary fault-tolerant gate from the standard set { X, Y, Z, H, S, T, { CNOT } }. In order to perform these estimates, we used an approach that combines manual analysis with automated estimates generated via the Quipper quantum programming language and compiler. Our estimates pertain to the explicit example problem size N=332{,}020{,}680 beyond which, according to a crude big-O complexity comparison, the quantum linear-system algorithm is expected to run faster than the best known classical linear-system solving algorithm. For this problem size, a desired calculation accuracy ɛ =0.01 requires an approximate circuit width 340 and circuit depth of order 10^{25} if oracle costs are excluded, and a circuit width and circuit depth of order 10^8 and 10^{29}, respectively, if the resource requirements of oracles are included, indicating that the commonly ignored oracle resources are considerable. In addition to providing detailed logical resource estimates, it is also the purpose of this paper to demonstrate explicitly (using a fine-grained approach rather than relying on coarse big-O asymptotic approximations) how these impressively large numbers arise with an actual circuit implementation of a quantum algorithm. While our estimates may prove to be conservative as more efficient advanced quantum-computation techniques are developed, they nevertheless provide a valid baseline for research targeting a reduction of the algorithmic-level resource requirements, implying that a reduction by many orders of magnitude is necessary for the algorithm to become practical.

Exploiting Locality in Quantum Computation for Quantum Chemistry.

PubMed

McClean, Jarrod R; Babbush, Ryan; Love, Peter J; Aspuru-Guzik, Alán

2014-12-18

Accurate prediction of chemical and material properties from first-principles quantum chemistry is a challenging task on traditional computers. Recent developments in quantum computation offer a route toward highly accurate solutions with polynomial cost; however, this solution still carries a large overhead. In this Perspective, we aim to bring together known results about the locality of physical interactions from quantum chemistry with ideas from quantum computation. We show that the utilization of spatial locality combined with the Bravyi-Kitaev transformation offers an improvement in the scaling of known quantum algorithms for quantum chemistry and provides numerical examples to help illustrate this point. We combine these developments to improve the outlook for the future of quantum chemistry on quantum computers.

Blind topological measurement-based quantum computation.

PubMed

Morimae, Tomoyuki; Fujii, Keisuke

2012-01-01

Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantum computation in realistic noisy conditions. Here we show that fault-tolerant blind quantum computation is possible in a topologically protected manner using the Raussendorf-Harrington-Goyal scheme. The error threshold of our scheme is 4.3 × 10(-3), which is comparable to that (7.5 × 10(-3)) of non-blind topological quantum computation. As the error per gate of the order 10(-3) was already achieved in some experimental systems, our result implies that secure cloud quantum computation is within reach.

Blind topological measurement-based quantum computation

NASA Astrophysics Data System (ADS)

Morimae, Tomoyuki; Fujii, Keisuke

2012-09-01

Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantum computation in realistic noisy conditions. Here we show that fault-tolerant blind quantum computation is possible in a topologically protected manner using the Raussendorf-Harrington-Goyal scheme. The error threshold of our scheme is 4.3×10-3, which is comparable to that (7.5×10-3) of non-blind topological quantum computation. As the error per gate of the order 10-3 was already achieved in some experimental systems, our result implies that secure cloud quantum computation is within reach.

Low-cost autonomous perceptron neural network inspired by quantum computation

NASA Astrophysics Data System (ADS)

Zidan, Mohammed; Abdel-Aty, Abdel-Haleem; El-Sadek, Alaa; Zanaty, E. A.; Abdel-Aty, Mahmoud

2017-11-01

Achieving low cost learning with reliable accuracy is one of the important goals to achieve intelligent machines to save time, energy and perform learning process over limited computational resources machines. In this paper, we propose an efficient algorithm for a perceptron neural network inspired by quantum computing composite from a single neuron to classify inspirable linear applications after a single training iteration O(1). The algorithm is applied over a real world data set and the results are outer performs the other state-of-the art algorithms.

Quantum Algorithms to Simulate Many-Body Physics of Correlated Fermions

NASA Astrophysics Data System (ADS)

Jiang, Zhang; Sung, Kevin J.; Kechedzhi, Kostyantyn; Smelyanskiy, Vadim N.; Boixo, Sergio

2018-04-01

Simulating strongly correlated fermionic systems is notoriously hard on classical computers. An alternative approach, as proposed by Feynman, is to use a quantum computer. We discuss simulating strongly correlated fermionic systems using near-term quantum devices. We focus specifically on two-dimensional (2D) or linear geometry with nearest-neighbor qubit-qubit couplings, typical for superconducting transmon qubit arrays. We improve an existing algorithm to prepare an arbitrary Slater determinant by exploiting a unitary symmetry. We also present a quantum algorithm to prepare an arbitrary fermionic Gaussian state with O (N2) gates and O (N ) circuit depth. Both algorithms are optimal in the sense that the numbers of parameters in the quantum circuits are equal to those describing the quantum states. Furthermore, we propose an algorithm to implement the 2D fermionic Fourier transformation on a 2D qubit array with only O (N1.5) gates and O (√{N }) circuit depth, which is the minimum depth required for quantum information to travel across the qubit array. We also present methods to simulate each time step in the evolution of the 2D Fermi-Hubbard model—again on a 2D qubit array—with O (N ) gates and O (√{N }) circuit depth. Finally, we discuss how these algorithms can be used to determine the ground-state properties and phase diagrams of strongly correlated quantum systems using the Hubbard model as an example.

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.

Improved Quantum Artificial Fish Algorithm Application to Distributed Network Considering Distributed Generation.

PubMed

Du, Tingsong; Hu, Yang; Ke, Xianting

2015-01-01

An improved quantum artificial fish swarm algorithm (IQAFSA) for solving distributed network programming considering distributed generation is proposed in this work. The IQAFSA based on quantum computing which has exponential acceleration for heuristic algorithm uses quantum bits to code artificial fish and quantum revolving gate, preying behavior, and following behavior and variation of quantum artificial fish to update the artificial fish for searching for optimal value. Then, we apply the proposed new algorithm, the quantum artificial fish swarm algorithm (QAFSA), the basic artificial fish swarm algorithm (BAFSA), and the global edition artificial fish swarm algorithm (GAFSA) to the simulation experiments for some typical test functions, respectively. The simulation results demonstrate that the proposed algorithm can escape from the local extremum effectively and has higher convergence speed and better accuracy. Finally, applying IQAFSA to distributed network problems and the simulation results for 33-bus radial distribution network system show that IQAFSA can get the minimum power loss after comparing with BAFSA, GAFSA, and QAFSA.

Improved Quantum Artificial Fish Algorithm Application to Distributed Network Considering Distributed Generation

PubMed Central

Hu, Yang; Ke, Xianting

2015-01-01

An improved quantum artificial fish swarm algorithm (IQAFSA) for solving distributed network programming considering distributed generation is proposed in this work. The IQAFSA based on quantum computing which has exponential acceleration for heuristic algorithm uses quantum bits to code artificial fish and quantum revolving gate, preying behavior, and following behavior and variation of quantum artificial fish to update the artificial fish for searching for optimal value. Then, we apply the proposed new algorithm, the quantum artificial fish swarm algorithm (QAFSA), the basic artificial fish swarm algorithm (BAFSA), and the global edition artificial fish swarm algorithm (GAFSA) to the simulation experiments for some typical test functions, respectively. The simulation results demonstrate that the proposed algorithm can escape from the local extremum effectively and has higher convergence speed and better accuracy. Finally, applying IQAFSA to distributed network problems and the simulation results for 33-bus radial distribution network system show that IQAFSA can get the minimum power loss after comparing with BAFSA, GAFSA, and QAFSA. PMID:26447713

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

Cloud Quantum Computing of an Atomic Nucleus

NASA Astrophysics Data System (ADS)

Dumitrescu, E. F.; McCaskey, A. J.; Hagen, G.; Jansen, G. R.; Morris, T. D.; Papenbrock, T.; Pooser, R. C.; Dean, D. J.; Lougovski, P.

2018-05-01

We report a quantum simulation of the deuteron binding energy on quantum processors accessed via cloud servers. We use a Hamiltonian from pionless effective field theory at leading order. We design a low-depth version of the unitary coupled-cluster ansatz, use the variational quantum eigensolver algorithm, and compute the binding energy to within a few percent. Our work is the first step towards scalable nuclear structure computations on a quantum processor via the cloud, and it sheds light on how to map scientific computing applications onto nascent quantum devices.

Cloud Quantum Computing of an Atomic Nucleus

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

Dumitrescu, Eugene F.; McCaskey, Alex J.; Hagen, Gaute

Here, we report a quantum simulation of the deuteron binding energy on quantum processors accessed via cloud servers. We use a Hamiltonian from pionless effective field theory at leading order. We design a low-depth version of the unitary coupled-cluster ansatz, use the variational quantum eigensolver algorithm, and compute the binding energy to within a few percent. Our work is the first step towards scalable nuclear structure computations on a quantum processor via the cloud, and it sheds light on how to map scientific computing applications onto nascent quantum devices.

Cloud Quantum Computing of an Atomic Nucleus.

PubMed

Dumitrescu, E F; McCaskey, A J; Hagen, G; Jansen, G R; Morris, T D; Papenbrock, T; Pooser, R C; Dean, D J; Lougovski, P

2018-05-25

We report a quantum simulation of the deuteron binding energy on quantum processors accessed via cloud servers. We use a Hamiltonian from pionless effective field theory at leading order. We design a low-depth version of the unitary coupled-cluster ansatz, use the variational quantum eigensolver algorithm, and compute the binding energy to within a few percent. Our work is the first step towards scalable nuclear structure computations on a quantum processor via the cloud, and it sheds light on how to map scientific computing applications onto nascent quantum devices.

Cloud Quantum Computing of an Atomic Nucleus

DOE PAGES

Dumitrescu, Eugene F.; McCaskey, Alex J.; Hagen, Gaute; ...

2018-05-23

Here, we report a quantum simulation of the deuteron binding energy on quantum processors accessed via cloud servers. We use a Hamiltonian from pionless effective field theory at leading order. We design a low-depth version of the unitary coupled-cluster ansatz, use the variational quantum eigensolver algorithm, and compute the binding energy to within a few percent. Our work is the first step towards scalable nuclear structure computations on a quantum processor via the cloud, and it sheds light on how to map scientific computing applications onto nascent quantum devices.

Optimization and experimental realization of the quantum permutation algorithm

NASA Astrophysics Data System (ADS)

Yalçınkaya, I.; Gedik, Z.

2017-12-01

The quantum permutation algorithm provides computational speed-up over classical algorithms for determining the parity of a given cyclic permutation. For its n -qubit implementations, the number of required quantum gates scales quadratically with n due to the quantum Fourier transforms included. We show here for the n -qubit case that the algorithm can be simplified so that it requires only O (n ) quantum gates, which theoretically reduces the complexity of the implementation. To test our results experimentally, we utilize IBM's 5-qubit quantum processor to realize the algorithm by using the original and simplified recipes for the 2-qubit case. It turns out that the latter results in a significantly higher success probability which allows us to verify the algorithm more precisely than the previous experimental realizations. We also verify the algorithm for the first time for the 3-qubit case with a considerable success probability by taking the advantage of our simplified scheme.

Workflow of the Grover algorithm simulation incorporating CUDA and GPGPU

NASA Astrophysics Data System (ADS)

Lu, Xiangwen; Yuan, Jiabin; Zhang, Weiwei

2013-09-01

The Grover quantum search algorithm, one of only a few representative quantum algorithms, can speed up many classical algorithms that use search heuristics. No true quantum computer has yet been developed. For the present, simulation is one effective means of verifying the search algorithm. In this work, we focus on the simulation workflow using a compute unified device architecture (CUDA). Two simulation workflow schemes are proposed. These schemes combine the characteristics of the Grover algorithm and the parallelism of general-purpose computing on graphics processing units (GPGPU). We also analyzed the optimization of memory space and memory access from this perspective. We implemented four programs on CUDA to evaluate the performance of schemes and optimization. Through experimentation, we analyzed the organization of threads suited to Grover algorithm simulations, compared the storage costs of the four programs, and validated the effectiveness of optimization. Experimental results also showed that the distinguished program on CUDA outperformed the serial program of libquantum on a CPU with a speedup of up to 23 times (12 times on average), depending on the scale of the simulation.

Basis for a neuronal version of Grover's quantum algorithm

PubMed Central

Clark, Kevin B.

2014-01-01

Grover's quantum (search) algorithm exploits principles of quantum information theory and computation to surpass the strong Church–Turing limit governing classical computers. The algorithm initializes a search field into superposed N (eigen)states to later execute nonclassical “subroutines” involving unitary phase shifts of measured states and to produce root-rate or quadratic gain in the algorithmic time (O(N1/2)) needed to find some “target” solution m. Akin to this fast technological search algorithm, single eukaryotic cells, such as differentiated neurons, perform natural quadratic speed-up in the search for appropriate store-operated Ca2+ response regulation of, among other processes, protein and lipid biosynthesis, cell energetics, stress responses, cell fate and death, synaptic plasticity, and immunoprotection. Such speed-up in cellular decision making results from spatiotemporal dynamics of networked intracellular Ca2+-induced Ca2+ release and the search (or signaling) velocity of Ca2+ wave propagation. As chemical processes, such as the duration of Ca2+ mobilization, become rate-limiting over interstore distances, Ca2+ waves quadratically decrease interstore-travel time from slow saltatory to fast continuous gradients proportional to the square-root of the classical Ca2+ diffusion coefficient, D1/2, matching the computing efficiency of Grover's quantum algorithm. In this Hypothesis and Theory article, I elaborate on these traits using a fire-diffuse-fire model of store-operated cytosolic Ca2+ signaling valid for glutamatergic neurons. Salient model features corresponding to Grover's quantum algorithm are parameterized to meet requirements for the Oracle Hadamard transform and Grover's iteration. A neuronal version of Grover's quantum algorithm figures to benefit signal coincidence detection and integration, bidirectional synaptic plasticity, and other vital cell functions by rapidly selecting, ordering, and/or counting optional response regulation choices. PMID:24860419

Homomorphic encryption experiments on IBM's cloud quantum computing platform

NASA Astrophysics Data System (ADS)

Huang, He-Liang; Zhao, You-Wei; Li, Tan; Li, Feng-Guang; Du, Yu-Tao; Fu, Xiang-Qun; Zhang, Shuo; Wang, Xiang; Bao, Wan-Su

2017-02-01

Quantum computing has undergone rapid development in recent years. Owing to limitations on scalability, personal quantum computers still seem slightly unrealistic in the near future. The first practical quantum computer for ordinary users is likely to be on the cloud. However, the adoption of cloud computing is possible only if security is ensured. Homomorphic encryption is a cryptographic protocol that allows computation to be performed on encrypted data without decrypting them, so it is well suited to cloud computing. Here, we first applied homomorphic encryption on IBM's cloud quantum computer platform. In our experiments, we successfully implemented a quantum algorithm for linear equations while protecting our privacy. This demonstration opens a feasible path to the next stage of development of cloud quantum information technology.

The Applicability of Emerging Quantum Computing Capabilities to Exo-Planet Research

NASA Astrophysics Data System (ADS)

Correll, Randall; Worden, S.

2014-01-01

In conjunction with the Universities Space Research Association and Google, Inc. NASA Ames has acquired a quantum computing device built by DWAVE Systems with approximately 512 “qubits.” Quantum computers have the feature that their capabilities to find solutions to problems with large numbers of variables scale linearly with the number of variables rather than exponentially with that number. These devices may have significant applicability to detection of exoplanet signals in noisy data. We have therefore explored the application of quantum computing to analyse stellar transiting exoplanet data from NASA’s Kepler Mission. The analysis of the case studies was done using the DWAVE Systems’s BlackBox compiler software emulator, although one dataset was run successfully on the DWAVE Systems’s 512 qubit Vesuvius machine. The approach first extracts a list of candidate transits from the photometric lightcurve of a given Kepler target, and then applies a quantum annealing algorithm to find periodicity matches between subsets of the candidate transit list. We examined twelve case studies and were successful in reproducing the results of the Kepler science pipeline in finding validated exoplanets, and matched the results for a pair of candidate exoplanets. We conclude that the current implementation of the algorithm is not sufficiently challenging to require a quantum computer as opposed to a conventional computer. We are developing more robust algorithms better tailored to the quantum computer and do believe that our approach has the potential to extract exoplanet transits in some cases where a conventional approach would not in Kepler data. Additionally, we believe the new quantum capabilities may have even greater relevance for new exoplanet data sets such as that contemplated for NASA’s Transiting Exoplanet Survey Satellite (TESS) and other astrophysics data sets.

A programmable two-qubit quantum processor in silicon.

PubMed

Watson, T F; Philips, S G J; Kawakami, E; Ward, D R; Scarlino, P; Veldhorst, M; Savage, D E; Lagally, M G; Friesen, Mark; Coppersmith, S N; Eriksson, M A; Vandersypen, L M K

2018-03-29

Now that it is possible to achieve measurement and control fidelities for individual quantum bits (qubits) above the threshold for fault tolerance, attention is moving towards the difficult task of scaling up the number of physical qubits to the large numbers that are needed for fault-tolerant quantum computing. In this context, quantum-dot-based spin qubits could have substantial advantages over other types of qubit owing to their potential for all-electrical operation and ability to be integrated at high density onto an industrial platform. Initialization, readout and single- and two-qubit gates have been demonstrated in various quantum-dot-based qubit representations. However, as seen with small-scale demonstrations of quantum computers using other types of qubit, combining these elements leads to challenges related to qubit crosstalk, state leakage, calibration and control hardware. Here we overcome these challenges by using carefully designed control techniques to demonstrate a programmable two-qubit quantum processor in a silicon device that can perform the Deutsch-Josza algorithm and the Grover search algorithm-canonical examples of quantum algorithms that outperform their classical analogues. We characterize the entanglement in our processor by using quantum-state tomography of Bell states, measuring state fidelities of 85-89 per cent and concurrences of 73-82 per cent. These results pave the way for larger-scale quantum computers that use spins confined to quantum dots.

Implementation of ternary Shor’s algorithm based on vibrational states of an ion in anharmonic potential

NASA Astrophysics Data System (ADS)

Liu, Wei; Chen, Shu-Ming; Zhang, Jian; Wu, Chun-Wang; Wu, Wei; Chen, Ping-Xing

2015-03-01

It is widely believed that Shor’s factoring algorithm provides a driving force to boost the quantum computing research. However, a serious obstacle to its binary implementation is the large number of quantum gates. Non-binary quantum computing is an efficient way to reduce the required number of elemental gates. Here, we propose optimization schemes for Shor’s algorithm implementation and take a ternary version for factorizing 21 as an example. The optimized factorization is achieved by a two-qutrit quantum circuit, which consists of only two single qutrit gates and one ternary controlled-NOT gate. This two-qutrit quantum circuit is then encoded into the nine lower vibrational states of an ion trapped in a weakly anharmonic potential. Optimal control theory (OCT) is employed to derive the manipulation electric field for transferring the encoded states. The ternary Shor’s algorithm can be implemented in one single step. Numerical simulation results show that the accuracy of the state transformations is about 0.9919. Project supported by the National Natural Science Foundation of China (Grant No. 61205108) and the High Performance Computing (HPC) Foundation of National University of Defense Technology, China.

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.

Adiabatic quantum computation

NASA Astrophysics Data System (ADS)

Albash, Tameem; Lidar, Daniel A.

2018-01-01

Adiabatic quantum computing (AQC) started as an approach to solving optimization problems and has evolved into an important universal alternative to the standard circuit model of quantum computing, with deep connections to both classical and quantum complexity theory and condensed matter physics. This review gives an account of the major theoretical developments in the field, while focusing on the closed-system setting. The review is organized around a series of topics that are essential to an understanding of the underlying principles of AQC, its algorithmic accomplishments and limitations, and its scope in the more general setting of computational complexity theory. Several variants are presented of the adiabatic theorem, the cornerstone of AQC, and examples are given of explicit AQC algorithms that exhibit a quantum speedup. An overview of several proofs of the universality of AQC and related Hamiltonian quantum complexity theory is given. Considerable space is devoted to stoquastic AQC, the setting of most AQC work to date, where obstructions to success and their possible resolutions are discussed.

ASCR Workshop on Quantum Computing for Science

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

Aspuru-Guzik, Alan; Van Dam, Wim; Farhi, Edward

This report details the findings of the DOE ASCR Workshop on Quantum Computing for Science that was organized to assess the viability of quantum computing technologies to meet the computational requirements of the DOE’s science and energy mission, and to identify the potential impact of quantum technologies. The workshop was held on February 17-18, 2015, in Bethesda, MD, to solicit input from members of the quantum computing community. The workshop considered models of quantum computation and programming environments, physical science applications relevant to DOE's science mission as well as quantum simulation, and applied mathematics topics including potential quantum algorithms formore » linear algebra, graph theory, and machine learning. This report summarizes these perspectives into an outlook on the opportunities for quantum computing to impact problems relevant to the DOE’s mission as well as the additional research required to bring quantum computing to the point where it can have such impact.« 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.

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.

Use of non-adiabatic geometric phase for quantum computing by NMR.

PubMed

Das, Ranabir; Kumar, S K Karthick; Kumar, Anil

2005-12-01

Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of error. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using the non-adiabatic geometric phase we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system.

Possible quantum algorithm for the Lipshitz-Sarkar-Steenrod square for Khovanov homology

NASA Astrophysics Data System (ADS)

Ospina, Juan

2013-05-01

Recently the celebrated Khovanov Homology was introduced as a target for Topological Quantum Computation given that the Khovanov Homology provides a generalization of the Jones polynomal and then it is possible to think about of a generalization of the Aharonov.-Jones-Landau algorithm. Recently, Lipshitz and Sarkar introduced a space-level refinement of Khovanov homology. which is called Khovanov Homotopy. This refinement induces a Steenrod square operation Sq2 on Khovanov homology which they describe explicitly and then some computations of Sq2 were presented. Particularly, examples of links with identical integral Khovanov homology but with distinct Khovanov homotopy types were showed. In the presente work we will introduce possible quantum algorithms for the Lipshitz- Sarkar-Steenrod square for Khovanov Homolog and their possible simulations using computer algebra.

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

Blind topological measurement-based quantum computation

PubMed Central

Morimae, Tomoyuki; Fujii, Keisuke

2012-01-01

Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantum computation in realistic noisy conditions. Here we show that fault-tolerant blind quantum computation is possible in a topologically protected manner using the Raussendorf–Harrington–Goyal scheme. The error threshold of our scheme is 4.3×10−3, which is comparable to that (7.5×10−3) of non-blind topological quantum computation. As the error per gate of the order 10−3 was already achieved in some experimental systems, our result implies that secure cloud quantum computation is within reach. PMID:22948818

Experimental Realization of a Quantum Support Vector Machine

NASA Astrophysics Data System (ADS)

Li, Zhaokai; Liu, Xiaomei; Xu, Nanyang; Du, Jiangfeng

2015-04-01

The fundamental principle of artificial intelligence is the ability of machines to learn from previous experience and do future work accordingly. In the age of big data, classical learning machines often require huge computational resources in many practical cases. Quantum machine learning algorithms, on the other hand, could be exponentially faster than their classical counterparts by utilizing quantum parallelism. Here, we demonstrate a quantum machine learning algorithm to implement handwriting recognition on a four-qubit NMR test bench. The quantum machine learns standard character fonts and then recognizes handwritten characters from a set with two candidates. Because of the wide spread importance of artificial intelligence and its tremendous consumption of computational resources, quantum speedup would be extremely attractive against the challenges of big data.

Quantum adiabatic computation with a constant gap is not useful in one dimension.

PubMed

Hastings, M B

2009-07-31

We show that it is possible to use a classical computer to efficiently simulate the adiabatic evolution of a quantum system in one dimension with a constant spectral gap, starting the adiabatic evolution from a known initial product state. The proof relies on a recently proven area law for such systems, implying the existence of a good matrix product representation of the ground state, combined with an appropriate algorithm to update the matrix product state as the Hamiltonian is changed. This implies that adiabatic evolution with such Hamiltonians is not useful for universal quantum computation. Therefore, adiabatic algorithms which are useful for universal quantum computation either require a spectral gap tending to zero or need to be implemented in more than one dimension (we leave open the question of the computational power of adiabatic simulation with a constant gap in more than one dimension).

Entanglement-Based Machine Learning on a Quantum Computer

NASA Astrophysics Data System (ADS)

Cai, X.-D.; Wu, D.; Su, Z.-E.; Chen, M.-C.; Wang, X.-L.; Li, Li; Liu, N.-L.; Lu, C.-Y.; Pan, J.-W.

2015-03-01

Machine learning, a branch of artificial intelligence, learns from previous experience to optimize performance, which is ubiquitous in various fields such as computer sciences, financial analysis, robotics, and bioinformatics. A challenge is that machine learning with the rapidly growing "big data" could become intractable for classical computers. Recently, quantum machine learning algorithms [Lloyd, Mohseni, and Rebentrost, arXiv.1307.0411] were proposed which could offer an exponential speedup over classical algorithms. Here, we report the first experimental entanglement-based classification of two-, four-, and eight-dimensional vectors to different clusters using a small-scale photonic quantum computer, which are then used to implement supervised and unsupervised machine learning. The results demonstrate the working principle of using quantum computers to manipulate and classify high-dimensional vectors, the core mathematical routine in machine learning. The method can, in principle, be scaled to larger numbers of qubits, and may provide a new route to accelerate machine learning.

Application of Blind Quantum Computation to Two-Party Quantum Computation

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan; Li, Qin; Yu, Fang; Chan, Wai Hong

2018-06-01

Blind quantum computation (BQC) allows a client who has only limited quantum power to achieve quantum computation with the help of a remote quantum server and still keep the client's input, output, and algorithm private. Recently, Kashefi and Wallden extended BQC to achieve two-party quantum computation which allows two parties Alice and Bob to perform a joint unitary transform upon their inputs. However, in their protocol Alice has to prepare rotated single qubits and perform Pauli operations, and Bob needs to have a powerful quantum computer. In this work, we also utilize the idea of BQC to put forward an improved two-party quantum computation protocol in which the operations of both Alice and Bob are simplified since Alice only needs to apply Pauli operations and Bob is just required to prepare and encrypt his input qubits.

Application of Blind Quantum Computation to Two-Party Quantum Computation

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan; Li, Qin; Yu, Fang; Chan, Wai Hong

2018-03-01

Blind quantum computation (BQC) allows a client who has only limited quantum power to achieve quantum computation with the help of a remote quantum server and still keep the client's input, output, and algorithm private. Recently, Kashefi and Wallden extended BQC to achieve two-party quantum computation which allows two parties Alice and Bob to perform a joint unitary transform upon their inputs. However, in their protocol Alice has to prepare rotated single qubits and perform Pauli operations, and Bob needs to have a powerful quantum computer. In this work, we also utilize the idea of BQC to put forward an improved two-party quantum computation protocol in which the operations of both Alice and Bob are simplified since Alice only needs to apply Pauli operations and Bob is just required to prepare and encrypt his input qubits.

Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Motta, Mario; Zhang, Shiwei

2018-05-01

We propose an algorithm for accurate, systematic, and scalable computation of interatomic forces within the auxiliary-field quantum Monte Carlo (AFQMC) method. The algorithm relies on the Hellmann-Feynman theorem and incorporates Pulay corrections in the presence of atomic orbital basis sets. We benchmark the method for small molecules by comparing the computed forces with the derivatives of the AFQMC potential energy surface and by direct comparison with other quantum chemistry methods. We then perform geometry optimizations using the steepest descent algorithm in larger molecules. With realistic basis sets, we obtain equilibrium geometries in agreement, within statistical error bars, with experimental values. The increase in computational cost for computing forces in this approach is only a small prefactor over that of calculating the total energy. This paves the way for a general and efficient approach for geometry optimization and molecular dynamics within AFQMC.

Bravyi-Kitaev Superfast simulation of electronic structure on a quantum computer.

PubMed

Setia, Kanav; Whitfield, James D

2018-04-28

Present quantum computers often work with distinguishable qubits as their computational units. In order to simulate indistinguishable fermionic particles, it is first required to map the fermionic state to the state of the qubits. The Bravyi-Kitaev Superfast (BKSF) algorithm can be used to accomplish this mapping. The BKSF mapping has connections to quantum error correction and opens the door to new ways of understanding fermionic simulation in a topological context. Here, we present the first detailed exposition of the BKSF algorithm for molecular simulation. We provide the BKSF transformed qubit operators and report on our implementation of the BKSF fermion-to-qubits transform in OpenFermion. In this initial study of a hydrogen molecule we have compared BKSF, Jordan-Wigner, and Bravyi-Kitaev transforms under the Trotter approximation. The gate count to implement BKSF is lower than Jordan-Wigner but higher than Bravyi-Kitaev. We considered different orderings of the exponentiated terms and found lower Trotter errors than the previously reported for Jordan-Wigner and Bravyi-Kitaev algorithms. These results open the door to the further study of the BKSF algorithm for quantum simulation.

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.

De-quantisation

NASA Astrophysics Data System (ADS)

Gruska, Jozef

2012-06-01

One of the most basic tasks in quantum information processing, communication and security (QIPCC) research, theoretically deep and practically important, is to find bounds on how really important are inherently quantum resources for speeding up computations. This area of research is bringing a variety of results that imply, often in a very unexpected and counter-intuitive way, that: (a) surprisingly large classes of quantum circuits and algorithms can be efficiently simulated on classical computers; (b) the border line between quantum processes that can and cannot be efficiently simulated on classical computers is often surprisingly thin; (c) the addition of a seemingly very simple resource or a tool often enormously increases the power of available quantum tools. These discoveries have put also a new light on our understanding of quantum phenomena and quantum physics and on the potential of its inherently quantum and often mysteriously looking phenomena. The paper motivates and surveys research and its outcomes in the area of de-quantisation, especially presents various approaches and their outcomes concerning efficient classical simulations of various families of quantum circuits and algorithms. To motivate this area of research some outcomes in the area of de-randomization of classical randomized computations.

Restoration for Noise Removal in Quantum Images

NASA Astrophysics Data System (ADS)

Liu, Kai; Zhang, Yi; Lu, Kai; Wang, Xiaoping

2017-09-01

Quantum computation has become increasingly attractive in the past few decades due to its extraordinary performance. As a result, some studies focusing on image representation and processing via quantum mechanics have been done. However, few of them have considered the quantum operations for images restoration. To address this problem, three noise removal algorithms are proposed in this paper based on the novel enhanced quantum representation model, oriented to two kinds of noise pollution (Salt-and-Pepper noise and Gaussian noise). For the first algorithm Q-Mean, it is designed to remove the Salt-and-Pepper noise. The noise points are extracted through comparisons with the adjacent pixel values, after which the restoration operation is finished by mean filtering. As for the second method Q-Gauss, a special mask is applied to weaken the Gaussian noise pollution. The third algorithm Q-Adapt is effective for the source image containing unknown noise. The type of noise can be judged through the quantum statistic operations for the color value of the whole image, and then different noise removal algorithms are used to conduct image restoration respectively. Performance analysis reveals that our methods can offer high restoration quality and achieve significant speedup through inherent parallelism of quantum computation.

Experimental demonstration of blind quantum computing

NASA Astrophysics Data System (ADS)

Barz, Stefanie; Kashefi, Elham; Broadbent, Anne; Fitzsimons, Joe; Zeilinger, Anton; Walther, Philip

2012-02-01

Quantum computers are among the most promising applications of quantum-enhanced technologies. Quantum effects such as superposition and entanglement enable computational speed-ups that are unattainable using classical computers. The challenges in realising quantum computers suggest that in the near future, only a few facilities worldwide will be capable of operating such devices. In order to exploit these computers, users would seemingly have to give up their privacy. It was recently shown that this is not the case and that, via the universal blind quantum computation protocol, quantum mechanics provides a way to guarantee that the user's data remain private. Here, we demonstrate the first experimental version of this protocol using polarisation-entangled photonic qubits. We demonstrate various blind one- and two-qubit gate operations as well as blind versions of the Deutsch's and Grover's algorithms. When the technology to build quantum computers becomes available, this will become an important privacy-preserving feature of quantum information processing.

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).

Reversibility and measurement in quantum computing

NASA Astrophysics Data System (ADS)

Leãao, J. P.

1998-03-01

The relation between computation and measurement at a fundamental physical level is yet to be understood. Rolf Landauer was perhaps the first to stress the strong analogy between these two concepts. His early queries have regained pertinence with the recent efforts to developed realizable models of quantum computers. In this context the irreversibility of quantum measurement appears in conflict with the requirement of reversibility of the overall computation associated with the unitary dynamics of quantum evolution. The latter in turn is responsible for the features of superposition and entanglement which make some quantum algorithms superior to classical ones for the same task in speed and resource demand. In this article we advocate an approach to this question which relies on a model of computation designed to enforce the analogy between the two concepts instead of demarcating them as it has been the case so far. The model is introduced as a symmetrization of the classical Turing machine model and is then carried on to quantum mechanics, first as a an abstract local interaction scheme (symbolic measurement) and finally in a nonlocal noninteractive implementation based on Aharonov-Bohm potentials and modular variables. It is suggested that this implementation leads to the most ubiquitous of quantum algorithms: the Discrete Fourier Transform.

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.

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.

Polynomial-time quantum algorithm for the simulation of chemical dynamics

PubMed Central

Kassal, Ivan; Jordan, Stephen P.; Love, Peter J.; Mohseni, Masoud; Aspuru-Guzik, Alán

2008-01-01

The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can be applied only to small systems. By contrast, we demonstrate that quantum computers could exactly simulate chemical reactions in polynomial time. Our algorithm uses the split-operator approach and explicitly simulates all electron-nuclear and interelectronic interactions in quadratic time. Surprisingly, this treatment is not only more accurate than the Born–Oppenheimer approximation but faster and more efficient as well, for all reactions with more than about four atoms. This is the case even though the entire electronic wave function is propagated on a grid with appropriately short time steps. Although the preparation and measurement of arbitrary states on a quantum computer is inefficient, here we demonstrate how to prepare states of chemical interest efficiently. We also show how to efficiently obtain chemically relevant observables, such as state-to-state transition probabilities and thermal reaction rates. Quantum computers using these techniques could outperform current classical computers with 100 qubits. PMID:19033207

Simulating chemistry using quantum computers.

PubMed

Kassal, Ivan; Whitfield, James D; Perdomo-Ortiz, Alejandro; Yung, Man-Hong; Aspuru-Guzik, Alán

2011-01-01

The difficulty of simulating quantum systems, well known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks. Although theory is still ahead of experiment, we outline recent advances that have led to the first chemical calculations on small quantum information processors.

A Comparison of Approaches for Solving Hard Graph-Theoretic Problems

DTIC Science & Technology

2015-05-01

collaborative effort “ Adiabatic Quantum Computing Applications Research” (14-RI-CRADA-02) between the Information Directorate and Lock- 3 Algorithm 3...using Matlab, a quantum annealing approach using the D-Wave computer , and lastly using satisfiability modulo theory (SMT) and corresponding SMT...methods are explored and consist of a parallel computing approach using Matlab, a quantum annealing approach using the D-Wave computer , and lastly using

Research on Quantum Algorithms at the Institute for Quantum Information

DTIC Science & Technology

2009-10-17

accuracy threshold theorem for the one-way quantum computer. Their proof is based on a novel scheme, in which a noisy cluster state in three spatial...detected. The proof applies to independent stochastic noise but (in contrast to proofs of the quantum accuracy threshold theorem based on concatenated...proved quantum threshold theorems for long-range correlated non-Markovian noise, for leakage faults, for the one-way quantum computer, for postselected

Application of fermionic marginal constraints to hybrid quantum algorithms

NASA Astrophysics Data System (ADS)

Rubin, Nicholas C.; Babbush, Ryan; McClean, Jarrod

2018-05-01

Many quantum algorithms, including recently proposed hybrid classical/quantum algorithms, make use of restricted tomography of the quantum state that measures the reduced density matrices, or marginals, of the full state. The most straightforward approach to this algorithmic step estimates each component of the marginal independently without making use of the algebraic and geometric structure of the marginals. Within the field of quantum chemistry, this structure is termed the fermionic n-representability conditions, and is supported by a vast amount of literature on both theoretical and practical results related to their approximations. In this work, we introduce these conditions in the language of quantum computation, and utilize them to develop several techniques to accelerate and improve practical applications for quantum chemistry on quantum computers. As a general result, we demonstrate how these marginals concentrate to diagonal quantities when measured on random quantum states. We also show that one can use fermionic n-representability conditions to reduce the total number of measurements required by more than an order of magnitude for medium sized systems in chemistry. As a practical demonstration, we simulate an efficient restoration of the physicality of energy curves for the dilation of a four qubit diatomic hydrogen system in the presence of three distinct one qubit error channels, providing evidence these techniques are useful for pre-fault tolerant quantum chemistry experiments.

Hybrid Quantum-Classical Approach to Quantum Optimal Control.

PubMed

Li, Jun; Yang, Xiaodong; Peng, Xinhua; Sun, Chang-Pu

2017-04-14

A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal control problem. We show that the most computationally demanding part of gradient-based algorithms, namely, computing the fitness function and its gradient for a control input, can be accomplished by the process of evolution and measurement on a quantum simulator. By posing queries to and receiving answers from the quantum simulator, classical computing devices update the control parameters until an optimal control solution is found. To demonstrate the quantum-classical scheme in experiment, we use a seven-qubit nuclear magnetic resonance system, on which we have succeeded in optimizing state preparation without involving classical computation of the large Hilbert space evolution.

Efficient quantum algorithm for computing n-time correlation functions.

PubMed

Pedernales, J S; Di Candia, R; Egusquiza, I L; Casanova, J; Solano, E

2014-07-11

We propose a method for computing n-time correlation functions of arbitrary spinorial, fermionic, and bosonic operators, consisting of an efficient quantum algorithm that encodes these correlations in an initially added ancillary qubit for probe and control tasks. For spinorial and fermionic systems, the reconstruction of arbitrary n-time correlation functions requires the measurement of two ancilla observables, while for bosonic variables time derivatives of the same observables are needed. Finally, we provide examples applicable to different quantum platforms in the frame of the linear response theory.

Computational nuclear quantum many-body problem: The UNEDF project

NASA Astrophysics Data System (ADS)

Bogner, S.; Bulgac, A.; Carlson, J.; Engel, J.; Fann, G.; Furnstahl, R. J.; Gandolfi, S.; Hagen, G.; Horoi, M.; Johnson, C.; Kortelainen, M.; Lusk, E.; Maris, P.; Nam, H.; Navratil, P.; Nazarewicz, W.; Ng, E.; Nobre, G. P. A.; Ormand, E.; Papenbrock, T.; Pei, J.; Pieper, S. C.; Quaglioni, S.; Roche, K. J.; Sarich, J.; Schunck, N.; Sosonkina, M.; Terasaki, J.; Thompson, I.; Vary, J. P.; Wild, S. M.

2013-10-01

The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. The primary focus of the project was on constructing, validating, and applying an optimized nuclear energy density functional, which entailed a wide range of pioneering developments in microscopic nuclear structure and reactions, algorithms, high-performance computing, and uncertainty quantification. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.

Computing quantum discord is NP-complete

NASA Astrophysics Data System (ADS)

Huang, Yichen

2014-03-01

We study the computational complexity of quantum discord (a measure of quantum correlation beyond entanglement), and prove that computing quantum discord is NP-complete. Therefore, quantum discord is computationally intractable: the running time of any algorithm for computing quantum discord is believed to grow exponentially with the dimension of the Hilbert space so that computing quantum discord in a quantum system of moderate size is not possible in practice. As by-products, some entanglement measures (namely entanglement cost, entanglement of formation, relative entropy of entanglement, squashed entanglement, classical squashed entanglement, conditional entanglement of mutual information, and broadcast regularization of mutual information) and constrained Holevo capacity are NP-hard/NP-complete to compute. These complexity-theoretic results are directly applicable in common randomness distillation, quantum state merging, entanglement distillation, superdense coding, and quantum teleportation; they may offer significant insights into quantum information processing. Moreover, we prove the NP-completeness of two typical problems: linear optimization over classical states and detecting classical states in a convex set, providing evidence that working with classical states is generically computationally intractable.

Parameters Free Computational Characterization of Defects in Transition Metal Oxides with Diffusion Quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Santana, Juan A.; Krogel, Jaron T.; Kent, Paul R.; Reboredo, Fernando

Materials based on transition metal oxides (TMO's) are among the most challenging systems for computational characterization. Reliable and practical computations are possible by directly solving the many-body problem for TMO's with quantum Monte Carlo (QMC) methods. These methods are very computationally intensive, but recent developments in algorithms and computational infrastructures have enabled their application to real materials. We will show our efforts on the application of the diffusion quantum Monte Carlo (DMC) method to study the formation of defects in binary and ternary TMO and heterostructures of TMO. We will also outline current limitations in hardware and algorithms. This work is supported by the Materials Sciences & Engineering Division of the Office of Basic Energy Sciences, U.S. Department of Energy (DOE).

A Novel Color Image Encryption Algorithm Based on Quantum Chaos Sequence

NASA Astrophysics Data System (ADS)

Liu, Hui; Jin, Cong

2017-03-01

In this paper, a novel algorithm of image encryption based on quantum chaotic is proposed. The keystreams are generated by the two-dimensional logistic map as initial conditions and parameters. And then general Arnold scrambling algorithm with keys is exploited to permute the pixels of color components. In diffusion process, a novel encryption algorithm, folding algorithm, is proposed to modify the value of diffused pixels. In order to get the high randomness and complexity, the two-dimensional logistic map and quantum chaotic map are coupled with nearest-neighboring coupled-map lattices. Theoretical analyses and computer simulations confirm that the proposed algorithm has high level of security.

Visualizing a silicon quantum computer

NASA Astrophysics Data System (ADS)

Sanders, Barry C.; Hollenberg, Lloyd C. L.; Edmundson, Darran; Edmundson, Andrew

2008-12-01

Quantum computation is a fast-growing, multi-disciplinary research field. The purpose of a quantum computer is to execute quantum algorithms that efficiently solve computational problems intractable within the existing paradigm of 'classical' computing built on bits and Boolean gates. While collaboration between computer scientists, physicists, chemists, engineers, mathematicians and others is essential to the project's success, traditional disciplinary boundaries can hinder progress and make communicating the aims of quantum computing and future technologies difficult. We have developed a four minute animation as a tool for representing, understanding and communicating a silicon-based solid-state quantum computer to a variety of audiences, either as a stand-alone animation to be used by expert presenters or embedded into a longer movie as short animated sequences. The paper includes a generally applicable recipe for successful scientific animation production.

Demonstration of two-qubit algorithms with a superconducting quantum processor.

PubMed

DiCarlo, L; Chow, J M; Gambetta, J M; Bishop, Lev S; Johnson, B R; Schuster, D I; Majer, J; Blais, A; Frunzio, L; Girvin, S M; Schoelkopf, R J

2009-07-09

Quantum computers, which harness the superposition and entanglement of physical states, could outperform their classical counterparts in solving problems with technological impact-such as factoring large numbers and searching databases. A quantum processor executes algorithms by applying a programmable sequence of gates to an initialized register of qubits, which coherently evolves into a final state containing the result of the computation. Building a quantum processor is challenging because of the need to meet simultaneously requirements that are in conflict: state preparation, long coherence times, universal gate operations and qubit readout. Processors based on a few qubits have been demonstrated using nuclear magnetic resonance, cold ion trap and optical systems, but a solid-state realization has remained an outstanding challenge. Here we demonstrate a two-qubit superconducting processor and the implementation of the Grover search and Deutsch-Jozsa quantum algorithms. We use a two-qubit interaction, tunable in strength by two orders of magnitude on nanosecond timescales, which is mediated by a cavity bus in a circuit quantum electrodynamics architecture. This interaction allows the generation of highly entangled states with concurrence up to 94 per cent. Although this processor constitutes an important step in quantum computing with integrated circuits, continuing efforts to increase qubit coherence times, gate performance and register size will be required to fulfil the promise of a scalable technology.

Novel Image Encryption based on Quantum Walks

PubMed Central

Yang, Yu-Guang; Pan, Qing-Xiang; Sun, Si-Jia; Xu, Peng

2015-01-01

Quantum computation has achieved a tremendous success during the last decades. In this paper, we investigate the potential application of a famous quantum computation model, i.e., quantum walks (QW) in image encryption. It is found that QW can serve as an excellent key generator thanks to its inherent nonlinear chaotic dynamic behavior. Furthermore, we construct a novel QW-based image encryption algorithm. Simulations and performance comparisons show that the proposal is secure enough for image encryption and outperforms prior works. It also opens the door towards introducing quantum computation into image encryption and promotes the convergence between quantum computation and image processing. PMID:25586889

PLQP & Company: Decidable Logics for Quantum Algorithms

NASA Astrophysics Data System (ADS)

Baltag, Alexandru; Bergfeld, Jort; Kishida, Kohei; Sack, Joshua; Smets, Sonja; Zhong, Shengyang

2014-10-01

We introduce a probabilistic modal (dynamic-epistemic) quantum logic PLQP for reasoning about quantum algorithms. We illustrate its expressivity by using it to encode the correctness of the well-known quantum search algorithm, as well as of a quantum protocol known to solve one of the paradigmatic tasks from classical distributed computing (the leader election problem). We also provide a general method (extending an idea employed in the decidability proof in Dunn et al. (J. Symb. Log. 70:353-359, 2005)) for proving the decidability of a range of quantum logics, interpreted on finite-dimensional Hilbert spaces. We give general conditions for the applicability of this method, and in particular we apply it to prove the decidability of PLQP.

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.

Requirements for fault-tolerant factoring on an atom-optics quantum computer.

PubMed

Devitt, Simon J; Stephens, Ashley M; Munro, William J; Nemoto, Kae

2013-01-01

Quantum information processing and its associated technologies have reached a pivotal stage in their development, with many experiments having established the basic building blocks. Moving forward, the challenge is to scale up to larger machines capable of performing computational tasks not possible today. This raises questions that need to be urgently addressed, such as what resources these machines will consume and how large will they be. Here we estimate the resources required to execute Shor's factoring algorithm on an atom-optics quantum computer architecture. We determine the runtime and size of the computer as a function of the problem size and physical error rate. Our results suggest that once the physical error rate is low enough to allow quantum error correction, optimization to reduce resources and increase performance will come mostly from integrating algorithms and circuits within the error correction environment, rather than from improving the physical hardware.

Quantum neural networks: Current status and prospects for development

NASA Astrophysics Data System (ADS)

Altaisky, M. V.; Kaputkina, N. E.; Krylov, V. A.

2014-11-01

The idea of quantum artificial neural networks, first formulated in [34], unites the artificial neural network concept with the quantum computation paradigm. Quantum artificial neural networks were first systematically considered in the PhD thesis by T. Menneer (1998). Based on the works of Menneer and Narayanan [42, 43], Kouda, Matsui, and Nishimura [35, 36], Altaisky [2, 68], Zhou [67], and others, quantum-inspired learning algorithms for neural networks were developed, and are now used in various training programs and computer games [29, 30]. The first practically realizable scaled hardware-implemented model of the quantum artificial neural network is obtained by D-Wave Systems, Inc. [33]. It is a quantum Hopfield network implemented on the basis of superconducting quantum interference devices (SQUIDs). In this work we analyze possibilities and underlying principles of an alternative way to implement quantum neural networks on the basis of quantum dots. A possibility of using quantum neural network algorithms in automated control systems, associative memory devices, and in modeling biological and social networks is examined.

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.

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

Spectral implementation of some quantum algorithms by one- and two-dimensional nuclear magnetic resonance

NASA Astrophysics Data System (ADS)

Das, Ranabir; Kumar, Anil

2004-10-01

Quantum information processing has been effectively demonstrated on a small number of qubits by nuclear magnetic resonance. An important subroutine in any computing is the readout of the output. "Spectral implementation" originally suggested by Z. L. Madi, R. Bruschweiler, and R. R. Ernst [J. Chem. Phys. 109, 10603 (1999)], provides an elegant method of readout with the use of an extra "observer" qubit. At the end of computation, detection of the observer qubit provides the output via the multiplet structure of its spectrum. In spectral implementation by two-dimensional experiment the observer qubit retains the memory of input state during computation, thereby providing correlated information on input and output, in the same spectrum. Spectral implementation of Grover's search algorithm, approximate quantum counting, a modified version of Berstein-Vazirani problem, and Hogg's algorithm are demonstrated here in three- and four-qubit systems.

An algorithmic approach to solving polynomial equations associated with quantum circuits

NASA Astrophysics Data System (ADS)

Gerdt, V. P.; Zinin, M. V.

2009-12-01

In this paper we present two algorithms for reducing systems of multivariate polynomial equations over the finite field F 2 to the canonical triangular form called lexicographical Gröbner basis. This triangular form is the most appropriate for finding solutions of the system. On the other hand, the system of polynomials over F 2 whose variables also take values in F 2 (Boolean polynomials) completely describes the unitary matrix generated by a quantum circuit. In particular, the matrix itself can be computed by counting the number of solutions (roots) of the associated polynomial system. Thereby, efficient construction of the lexicographical Gröbner bases over F 2 associated with quantum circuits gives a method for computing their circuit matrices that is alternative to the direct numerical method based on linear algebra. We compare our implementation of both algorithms with some other software packages available for computing Gröbner bases over F 2.

Experimental superposition of orders of quantum gates

PubMed Central

Procopio, Lorenzo M.; Moqanaki, Amir; Araújo, Mateus; Costa, Fabio; Alonso Calafell, Irati; Dowd, Emma G.; Hamel, Deny R.; Rozema, Lee A.; Brukner, Časlav; Walther, Philip

2015-01-01

Quantum computers achieve a speed-up by placing quantum bits (qubits) in superpositions of different states. However, it has recently been appreciated that quantum mechanics also allows one to ‘superimpose different operations'. Furthermore, it has been shown that using a qubit to coherently control the gate order allows one to accomplish a task—determining if two gates commute or anti-commute—with fewer gate uses than any known quantum algorithm. Here we experimentally demonstrate this advantage, in a photonic context, using a second qubit to control the order in which two gates are applied to a first qubit. We create the required superposition of gate orders by using additional degrees of freedom of the photons encoding our qubits. The new resource we exploit can be interpreted as a superposition of causal orders, and could allow quantum algorithms to be implemented with an efficiency unlikely to be achieved on a fixed-gate-order quantum computer. PMID:26250107

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).

Modeling the Gross-Pitaevskii Equation Using the Quantum Lattice Gas Method

NASA Astrophysics Data System (ADS)

Oganesov, Armen

We present an improved Quantum Lattice Gas (QLG) algorithm as a mesoscopic unitary perturbative representation of the mean field Gross Pitaevskii (GP) equation for Bose-Einstein Condensates (BECs). The method employs an interleaved sequence of unitary collide and stream operators. QLG is applicable to many different scalar potentials in the weak interaction regime and has been used to model the Korteweg-de Vries (KdV), Burgers and GP equations. It can be implemented on both quantum and classical computers and is extremely scalable. We present results for 1D soliton solutions with positive and negative internal interactions, as well as vector solitons with inelastic scattering. In higher dimensions we look at the behavior of vortex ring reconnection. A further improvement is considered with a proper operator splitting technique via a Fourier transformation. This is great for quantum computers since the quantum FFT is exponentially faster than its classical counterpart which involves non-local data on the entire lattice (Quantum FFT is the backbone of the Shor algorithm for quantum factorization). We also present an imaginary time method in which we transform the Schrodinger equation into a diffusion equation for recovering ground state initial conditions of a quantum system suitable for the QLG algorithm.

Contextuality supplies the 'magic' for quantum computation.

PubMed

Howard, Mark; Wallman, Joel; Veitch, Victor; Emerson, Joseph

2014-06-19

Quantum computers promise dramatic advantages over their classical counterparts, but the source of the power in quantum computing has remained elusive. Here we prove a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via 'magic state' distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer. This is a conceptually satisfying link, because contextuality, which precludes a simple 'hidden variable' model of quantum mechanics, provides one of the fundamental characterizations of uniquely quantum phenomena. Furthermore, this connection suggests a unifying paradigm for the resources of quantum information: the non-locality of quantum theory is a particular kind of contextuality, and non-locality is already known to be a critical resource for achieving advantages with quantum communication. In addition to clarifying these fundamental issues, this work advances the resource framework for quantum computation, which has a number of practical applications, such as characterizing the efficiency and trade-offs between distinct theoretical and experimental schemes for achieving robust quantum computation, and putting bounds on the overhead cost for the classical simulation of quantum algorithms.

Irreversibility and entanglement spectrum statistics in quantum circuits

NASA Astrophysics Data System (ADS)

Shaffer, Daniel; Chamon, Claudio; Hamma, Alioscia; Mucciolo, Eduardo R.

2014-12-01

We show that in a quantum system evolving unitarily under a stochastic quantum circuit the notions of irreversibility, universality of computation, and entanglement are closely related. As the state evolves from an initial product state, it gets asymptotically maximally entangled. We define irreversibility as the failure of searching for a disentangling circuit using a Metropolis-like algorithm. We show that irreversibility corresponds to Wigner-Dyson statistics in the level spacing of the entanglement eigenvalues, and that this is obtained from a quantum circuit made from a set of universal gates for quantum computation. If, on the other hand, the system is evolved with a non-universal set of gates, the statistics of the entanglement level spacing deviates from Wigner-Dyson and the disentangling algorithm succeeds. These results open a new way to characterize irreversibility in quantum systems.

Quantum computing without wavefunctions: time-dependent density functional theory for universal quantum computation.

PubMed

Tempel, David G; Aspuru-Guzik, Alán

2012-01-01

We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms.

Mathematical Theory of Generalized Duality Quantum Computers Acting on Vector-States

NASA Astrophysics Data System (ADS)

Cao, Huai-Xin; Long, Gui-Lu; Guo, Zhi-Hua; Chen, Zheng-Li

2013-06-01

Following the idea of duality quantum computation, a generalized duality quantum computer (GDQC) acting on vector-states is defined as a tuple consisting of a generalized quantum wave divider (GQWD) and a finite number of unitary operators as well as a generalized quantum wave combiner (GQWC). It is proved that the GQWD and GQWC of a GDQC are an isometry and a co-isometry, respectively, and mutually dual. It is also proved that every GDQC gives a contraction, called a generalized duality quantum gate (GDQG). A classification of GDQCs is given and the properties of GDQGs are discussed. Some applications are obtained, including two orthogonal duality quantum computer algorithms for unsorted database search and an understanding of the Mach-Zehnder interferometer.

Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes.

PubMed

Cafaro, Carlo; Alsing, Paul M

2018-04-01

The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is characterized by its decrease along the solutions of the Boltzmann equation for Maxwellian molecules in the two-dimensional case. From a quantum mechanical standpoint, the output state in Grover's quantum search algorithm follows a geodesic path obtained from the Fubini-Study metric on the manifold of Hilbert-space rays. Additionally, Grover's algorithm is specified by constant Fisher information. In this paper, we present an information geometric characterization of the oscillatory or monotonic behavior of statistically parametrized squared probability amplitudes originating from special functional forms of the Fisher information function: constant, exponential decay, and power-law decay. Furthermore, for each case, we compute both the computational speed and the availability loss of the corresponding physical processes by exploiting a convenient Riemannian geometrization of useful thermodynamical concepts. Finally, we briefly comment on the possibility of using the proposed methods of information geometry to help identify a suitable trade-off between speed and thermodynamic efficiency in quantum search algorithms.

Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes

NASA Astrophysics Data System (ADS)

Cafaro, Carlo; Alsing, Paul M.

2018-04-01

The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is characterized by its decrease along the solutions of the Boltzmann equation for Maxwellian molecules in the two-dimensional case. From a quantum mechanical standpoint, the output state in Grover's quantum search algorithm follows a geodesic path obtained from the Fubini-Study metric on the manifold of Hilbert-space rays. Additionally, Grover's algorithm is specified by constant Fisher information. In this paper, we present an information geometric characterization of the oscillatory or monotonic behavior of statistically parametrized squared probability amplitudes originating from special functional forms of the Fisher information function: constant, exponential decay, and power-law decay. Furthermore, for each case, we compute both the computational speed and the availability loss of the corresponding physical processes by exploiting a convenient Riemannian geometrization of useful thermodynamical concepts. Finally, we briefly comment on the possibility of using the proposed methods of information geometry to help identify a suitable trade-off between speed and thermodynamic efficiency in quantum search algorithms.

Quantum Search in Hilbert Space

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

A proposed quantum-computing algorithm would perform a search for an item of information in a database stored in a Hilbert-space memory structure. The algorithm is intended to make it possible to search relatively quickly through a large database under conditions in which available computing resources would otherwise be considered inadequate to perform such a task. The algorithm would apply, more specifically, to a relational database in which information would be stored in a set of N complex orthonormal vectors, each of N dimensions (where N can be exponentially large). Each vector would constitute one row of a unitary matrix, from which one would derive the Hamiltonian operator (and hence the evolutionary operator) of a quantum system. In other words, all the stored information would be mapped onto a unitary operator acting on a quantum state that would represent the item of information to be retrieved. Then one could exploit quantum parallelism: one could pose all search queries simultaneously by performing a quantum measurement on the system. In so doing, one would effectively solve the search problem in one computational step. One could exploit the direct- and inner-product decomposability of the unitary matrix to make the dimensionality of the memory space exponentially large by use of only linear resources. However, inasmuch as the necessary preprocessing (the mapping of the stored information into a Hilbert space) could be exponentially expensive, the proposed algorithm would likely be most beneficial in applications in which the resources available for preprocessing were much greater than those available for searching.

ProjectQ: Compiling quantum programs for various backends

NASA Astrophysics Data System (ADS)

Haener, Thomas; Steiger, Damian S.; Troyer, Matthias

In order to control quantum computers beyond the current generation, a high level quantum programming language and optimizing compilers will be essential. Therefore, we have developed ProjectQ - an open source software framework to facilitate implementing and running quantum algorithms both in software and on actual quantum hardware. Here, we introduce the backends available in ProjectQ. This includes a high-performance simulator and emulator to test and debug quantum algorithms, tools for resource estimation, and interfaces to several small-scale quantum devices. We demonstrate the workings of the framework and show how easily it can be further extended to control upcoming quantum hardware.

Efficient quantum walk on a quantum processor

PubMed Central

Qiang, Xiaogang; Loke, Thomas; Montanaro, Ashley; Aungskunsiri, Kanin; Zhou, Xiaoqi; O'Brien, Jeremy L.; Wang, Jingbo B.; Matthews, Jonathan C. F.

2016-01-01

The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor. PMID:27146471

Parallel algorithms for quantum chemistry. I. Integral transformations on a hypercube multiprocessor

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

Whiteside, R.A.; Binkley, J.S.; Colvin, M.E.

1987-02-15

For many years it has been recognized that fundamental physical constraints such as the speed of light will limit the ultimate speed of single processor computers to less than about three billion floating point operations per second (3 GFLOPS). This limitation is becoming increasingly restrictive as commercially available machines are now within an order of magnitude of this asymptotic limit. A natural way to avoid this limit is to harness together many processors to work on a single computational problem. In principle, these parallel processing computers have speeds limited only by the number of processors one chooses to acquire. Themore » usefulness of potentially unlimited processing speed to a computationally intensive field such as quantum chemistry is obvious. If these methods are to be applied to significantly larger chemical systems, parallel schemes will have to be employed. For this reason we have developed distributed-memory algorithms for a number of standard quantum chemical methods. We are currently implementing these on a 32 processor Intel hypercube. In this paper we present our algorithm and benchmark results for one of the bottleneck steps in quantum chemical calculations: the four index integral transformation.« less

Experimental Adiabatic Quantum Factorization under Ambient Conditions Based on a Solid-State Single Spin System.

PubMed

Xu, Kebiao; Xie, Tianyu; Li, Zhaokai; Xu, Xiangkun; Wang, Mengqi; Ye, Xiangyu; Kong, Fei; Geng, Jianpei; Duan, Changkui; Shi, Fazhan; Du, Jiangfeng

2017-03-31

The adiabatic quantum computation is a universal and robust method of quantum computing. In this architecture, the problem can be solved by adiabatically evolving the quantum processor from the ground state of a simple initial Hamiltonian to that of a final one, which encodes the solution of the problem. Adiabatic quantum computation has been proved to be a compatible candidate for scalable quantum computation. In this Letter, we report on the experimental realization of an adiabatic quantum algorithm on a single solid spin system under ambient conditions. All elements of adiabatic quantum computation, including initial state preparation, adiabatic evolution (simulated by optimal control), and final state read-out, are realized experimentally. As an example, we found the ground state of the problem Hamiltonian S_{z}I_{z} on our adiabatic quantum processor, which can be mapped to the factorization of 35 into its prime factors 5 and 7.

Experimental Adiabatic Quantum Factorization under Ambient Conditions Based on a Solid-State Single Spin System

NASA Astrophysics Data System (ADS)

Xu, Kebiao; Xie, Tianyu; Li, Zhaokai; Xu, Xiangkun; Wang, Mengqi; Ye, Xiangyu; Kong, Fei; Geng, Jianpei; Duan, Changkui; Shi, Fazhan; Du, Jiangfeng

2017-03-01

The adiabatic quantum computation is a universal and robust method of quantum computing. In this architecture, the problem can be solved by adiabatically evolving the quantum processor from the ground state of a simple initial Hamiltonian to that of a final one, which encodes the solution of the problem. Adiabatic quantum computation has been proved to be a compatible candidate for scalable quantum computation. In this Letter, we report on the experimental realization of an adiabatic quantum algorithm on a single solid spin system under ambient conditions. All elements of adiabatic quantum computation, including initial state preparation, adiabatic evolution (simulated by optimal control), and final state read-out, are realized experimentally. As an example, we found the ground state of the problem Hamiltonian SzIz on our adiabatic quantum processor, which can be mapped to the factorization of 35 into its prime factors 5 and 7.

Implementation of a three-qubit refined Deutsch Jozsa algorithm using SFG quantum logic gates

NASA Astrophysics Data System (ADS)

DelDuce, A.; Savory, S.; Bayvel, P.

2006-05-01

In this paper we present a quantum logic circuit which can be used for the experimental demonstration of a three-qubit solid state quantum computer based on a recent proposal of optically driven quantum logic gates. In these gates, the entanglement of randomly placed electron spin qubits is manipulated by optical excitation of control electrons. The circuit we describe solves the Deutsch problem with an improved algorithm called the refined Deutsch-Jozsa algorithm. We show that it is possible to select optical pulses that solve the Deutsch problem correctly, and do so without losing quantum information to the control electrons, even though the gate parameters vary substantially from one gate to another.

Optimally stopped variational quantum algorithms

NASA Astrophysics Data System (ADS)

Vinci, Walter; Shabani, Alireza

2018-04-01

Quantum processors promise a paradigm shift in high-performance computing which needs to be assessed by accurate benchmarking measures. In this article, we introduce a benchmark for the variational quantum algorithm (VQA), recently proposed as a heuristic algorithm for small-scale quantum processors. In VQA, a classical optimization algorithm guides the processor's quantum dynamics to yield the best solution for a given problem. A complete assessment of the scalability and competitiveness of VQA should take into account both the quality and the time of dynamics optimization. The method of optimal stopping, employed here, provides such an assessment by explicitly including time as a cost factor. Here, we showcase this measure for benchmarking VQA as a solver for some quadratic unconstrained binary optimization. Moreover, we show that a better choice for the cost function of the classical routine can significantly improve the performance of the VQA algorithm and even improve its scaling properties.

An entangling-probe attack on Shor's algorithm for factorization

NASA Astrophysics Data System (ADS)

Azuma, Hiroo

2018-02-01

We investigate how to attack Shor's quantum algorithm for factorization with an entangling probe. We show that an attacker can steal an exact solution of Shor's algorithm outside an institute where the quantum computer is installed if he replaces its initialized quantum register with entangled qubits, namely the entangling probe. He can apply arbitrary local operations to his own probe. Moreover, we assume that there is an unauthorized person who helps the attacker to commit a crime inside the institute. He tells garbage data obtained from measurements of the quantum register to the attacker secretly behind a legitimate user's back. If the attacker succeeds in cracking Shor's algorithm, the legitimate user obtains a random answer and does not notice the attacker's illegal acts. We discuss how to detect the attacker. Finally, we estimate a probability that the quantum algorithm inevitably makes an error, of which the attacker can take advantage.

Noise-tolerant parity learning with one quantum bit

NASA Astrophysics Data System (ADS)

Park, Daniel K.; Rhee, June-Koo K.; Lee, Soonchil

2018-03-01

Demonstrating quantum advantage with less powerful but more realistic devices is of great importance in modern quantum information science. Recently, a significant quantum speedup was achieved in the problem of learning a hidden parity function with noise. However, if all data qubits at the query output are completely depolarized, the algorithm fails. In this work, we present a quantum parity learning algorithm that exhibits quantum advantage as long as one qubit is provided with nonzero polarization in each query. In this scenario, the quantum parity learning naturally becomes deterministic quantum computation with one qubit. Then the hidden parity function can be revealed by performing a set of operations that can be interpreted as measuring nonlocal observables on the auxiliary result qubit having nonzero polarization and each data qubit. We also discuss the source of the quantum advantage in our algorithm from the resource-theoretic point of view.

Parallel Photonic Quantum Computation Assisted by Quantum Dots in One-Side Optical Microcavities

PubMed Central

Luo, Ming-Xing; Wang, Xiaojun

2014-01-01

Universal quantum logic gates are important elements for a quantum computer. In contrast to previous constructions on one degree of freedom (DOF) of quantum systems, we investigate the possibility of parallel quantum computations dependent on two DOFs of photon systems. We construct deterministic hyper-controlled-not (hyper-CNOT) gates operating on the spatial-mode and the polarization DOFs of two-photon or one-photon systems by exploring the giant optical circular birefringence induced by quantum-dot spins in one-sided optical microcavities. These hyper-CNOT gates show that the quantum states of two DOFs can be viewed as independent qubits without requiring auxiliary DOFs in theory. This result can reduce the quantum resources by half for quantum applications with large qubit systems, such as the quantum Shor algorithm. PMID:25030424

Parallel photonic quantum computation assisted by quantum dots in one-side optical microcavities.

PubMed

Luo, Ming-Xing; Wang, Xiaojun

2014-07-17

Universal quantum logic gates are important elements for a quantum computer. In contrast to previous constructions on one degree of freedom (DOF) of quantum systems, we investigate the possibility of parallel quantum computations dependent on two DOFs of photon systems. We construct deterministic hyper-controlled-not (hyper-CNOT) gates operating on the spatial-mode and the polarization DOFs of two-photon or one-photon systems by exploring the giant optical circular birefringence induced by quantum-dot spins in one-sided optical microcavities. These hyper-CNOT gates show that the quantum states of two DOFs can be viewed as independent qubits without requiring auxiliary DOFs in theory. This result can reduce the quantum resources by half for quantum applications with large qubit systems, such as the quantum Shor algorithm.

Intermediate quantum maps for quantum computation

NASA Astrophysics Data System (ADS)

Giraud, O.; Georgeot, B.

2005-10-01

We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity decay or spectral statistics. We study their matrix elements and entanglement production and show that they converge with time to distributions which differ from random matrix predictions. A randomized version of these maps can be implemented even more economically and yields pseudorandom operators with original properties, enabling, for example, one to produce fractal random vectors. These algorithms are within reach of present-day quantum computers.

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.

Quantum simulation of quantum field theory using continuous variables

DOE PAGES

Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; ...

2015-12-14

Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonicmore » quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.« less

Quantum simulation of quantum field theory using continuous variables

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

Marshall, Kevin; Pooser, Raphael C.; Siopsis, George

Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonicmore » quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.« less

Classical simulation of infinite-size quantum lattice systems in two spatial dimensions.

PubMed

Jordan, J; Orús, R; Vidal, G; Verstraete, F; Cirac, J I

2008-12-19

We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066] and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)10.1103/PhysRevLett.98.070201]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.

Computing on quantum shared secrets

NASA Astrophysics Data System (ADS)

Ouyang, Yingkai; Tan, Si-Hui; Zhao, Liming; Fitzsimons, Joseph F.

2017-11-01

A (k ,n )-threshold secret-sharing scheme allows for a string to be split into n shares in such a way that any subset of at least k shares suffices to recover the secret string, but such that any subset of at most k -1 shares contains no information about the secret. Quantum secret-sharing schemes extend this idea to the sharing of quantum states. Here we propose a method of performing computation securely on quantum shared secrets. We introduce a (n ,n )-quantum secret sharing scheme together with a set of algorithms that allow quantum circuits to be evaluated securely on the shared secret without the need to decode the secret. We consider a multipartite setting, with each participant holding a share of the secret. We show that if there exists at least one honest participant, no group of dishonest participants can recover any information about the shared secret, independent of their deviations from the algorithm.

Multiple feature fusion via covariance matrix for visual tracking

NASA Astrophysics Data System (ADS)

Jin, Zefenfen; Hou, Zhiqiang; Yu, Wangsheng; Wang, Xin; Sun, Hui

2018-04-01

Aiming at the problem of complicated dynamic scenes in visual target tracking, a multi-feature fusion tracking algorithm based on covariance matrix is proposed to improve the robustness of the tracking algorithm. In the frame-work of quantum genetic algorithm, this paper uses the region covariance descriptor to fuse the color, edge and texture features. It also uses a fast covariance intersection algorithm to update the model. The low dimension of region covariance descriptor, the fast convergence speed and strong global optimization ability of quantum genetic algorithm, and the fast computation of fast covariance intersection algorithm are used to improve the computational efficiency of fusion, matching, and updating process, so that the algorithm achieves a fast and effective multi-feature fusion tracking. The experiments prove that the proposed algorithm can not only achieve fast and robust tracking but also effectively handle interference of occlusion, rotation, deformation, motion blur and so on.

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.

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 algorithms on Walsh transform and Hamming distance for Boolean functions

NASA Astrophysics Data System (ADS)

Xie, Zhengwei; Qiu, Daowen; Cai, Guangya

2018-06-01

Walsh spectrum or Walsh transform is an alternative description of Boolean functions. In this paper, we explore quantum algorithms to approximate the absolute value of Walsh transform W_f at a single point z0 (i.e., |W_f(z0)|) for n-variable Boolean functions with probability at least 8/π 2 using the number of O(1/|W_f(z_{0)|ɛ }) queries, promised that the accuracy is ɛ , while the best known classical algorithm requires O(2n) queries. The Hamming distance between Boolean functions is used to study the linearity testing and other important problems. We take advantage of Walsh transform to calculate the Hamming distance between two n-variable Boolean functions f and g using O(1) queries in some cases. Then, we exploit another quantum algorithm which converts computing Hamming distance between two Boolean functions to quantum amplitude estimation (i.e., approximate counting). If Ham(f,g)=t≠0, we can approximately compute Ham( f, g) with probability at least 2/3 by combining our algorithm and {Approx-Count(f,ɛ ) algorithm} using the expected number of Θ( √{N/(\\lfloor ɛ t\\rfloor +1)}+√{t(N-t)}/\\lfloor ɛ t\\rfloor +1) queries, promised that the accuracy is ɛ . Moreover, our algorithm is optimal, while the exact query complexity for the above problem is Θ(N) and the query complexity with the accuracy ɛ is O(1/ɛ 2N/(t+1)) in classical algorithm, where N=2n. Finally, we present three exact quantum query algorithms for two promise problems on Hamming distance using O(1) queries, while any classical deterministic algorithm solving the problem uses Ω(2n) queries.

Neural implementation of operations used in quantum cognition.

PubMed

Busemeyer, Jerome R; Fakhari, Pegah; Kvam, Peter

2017-11-01

Quantum probability theory has been successfully applied outside of physics to account for numerous findings from psychology regarding human judgement and decision making behavior. However, the researchers who have made these applications do not rely on the hypothesis that the brain is some type of quantum computer. This raises the question of how could the brain implement quantum algorithms other than quantum physical operations. This article outlines one way that a neural based system could perform the computations required by applications of quantum probability to human behavior. Copyright © 2017 Elsevier Ltd. All rights reserved.

The theory of variational hybrid quantum-classical algorithms

NASA Astrophysics Data System (ADS)

McClean, Jarrod R.; Romero, Jonathan; Babbush, Ryan; Aspuru-Guzik, Alán

2016-02-01

Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as ‘the quantum variational eigensolver’ was developed (Peruzzo et al 2014 Nat. Commun. 5 4213) with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through a relaxation of exponential operator splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.

Graphene-based room-temperature implementation of a modified Deutsch-Jozsa quantum algorithm.

PubMed

Dragoman, Daniela; Dragoman, Mircea

2015-12-04

We present an implementation of a one-qubit and two-qubit modified Deutsch-Jozsa quantum algorithm based on graphene ballistic devices working at room temperature. The modified Deutsch-Jozsa algorithm decides whether a function, equivalent to the effect of an energy potential distribution on the wave function of ballistic charge carriers, is constant or not, without measuring the output wave function. The function need not be Boolean. Simulations confirm that the algorithm works properly, opening the way toward quantum computing at room temperature based on the same clean-room technologies as those used for fabrication of very-large-scale integrated circuits.

Quantum Algorithm for K-Nearest Neighbors Classification Based on the Metric of Hamming Distance

NASA Astrophysics Data System (ADS)

Ruan, Yue; Xue, Xiling; Liu, Heng; Tan, Jianing; Li, Xi

2017-11-01

K-nearest neighbors (KNN) algorithm is a common algorithm used for classification, and also a sub-routine in various complicated machine learning tasks. In this paper, we presented a quantum algorithm (QKNN) for implementing this algorithm based on the metric of Hamming distance. We put forward a quantum circuit for computing Hamming distance between testing sample and each feature vector in the training set. Taking advantage of this method, we realized a good analog for classical KNN algorithm by setting a distance threshold value t to select k - n e a r e s t neighbors. As a result, QKNN achieves O( n 3) performance which is only relevant to the dimension of feature vectors and high classification accuracy, outperforms Llyod's algorithm (Lloyd et al. 2013) and Wiebe's algorithm (Wiebe et al. 2014).

Post-quantum cryptography.

PubMed

Bernstein, Daniel J; Lange, Tanja

2017-09-13

Cryptography is essential for the security of online communication, cars and implanted medical devices. However, many commonly used cryptosystems will be completely broken once large quantum computers exist. Post-quantum cryptography is cryptography under the assumption that the attacker has a large quantum computer; post-quantum cryptosystems strive to remain secure even in this scenario. This relatively young research area has seen some successes in identifying mathematical operations for which quantum algorithms offer little advantage in speed, and then building cryptographic systems around those. The central challenge in post-quantum cryptography is to meet demands for cryptographic usability and flexibility without sacrificing confidence.

Post-quantum cryptography

NASA Astrophysics Data System (ADS)

Bernstein, Daniel J.; Lange, Tanja

2017-09-01

Cryptography is essential for the security of online communication, cars and implanted medical devices. However, many commonly used cryptosystems will be completely broken once large quantum computers exist. Post-quantum cryptography is cryptography under the assumption that the attacker has a large quantum computer; post-quantum cryptosystems strive to remain secure even in this scenario. This relatively young research area has seen some successes in identifying mathematical operations for which quantum algorithms offer little advantage in speed, and then building cryptographic systems around those. The central challenge in post-quantum cryptography is to meet demands for cryptographic usability and flexibility without sacrificing confidence.

Efficient universal quantum channel simulation in IBM's cloud quantum computer

NASA Astrophysics Data System (ADS)

Wei, Shi-Jie; Xin, Tao; Long, Gui-Lu

2018-07-01

The study of quantum channels is an important field and promises a wide range of applications, because any physical process can be represented as a quantum channel that transforms an initial state into a final state. Inspired by the method of performing non-unitary operators by the linear combination of unitary operations, we proposed a quantum algorithm for the simulation of the universal single-qubit channel, described by a convex combination of "quasi-extreme" channels corresponding to four Kraus operators, and is scalable to arbitrary higher dimension. We demonstrated the whole algorithm experimentally using the universal IBM cloud-based quantum computer and studied the properties of different qubit quantum channels. We illustrated the quantum capacity of the general qubit quantum channels, which quantifies the amount of quantum information that can be protected. The behavior of quantum capacity in different channels revealed which types of noise processes can support information transmission, and which types are too destructive to protect information. There was a general agreement between the theoretical predictions and the experiments, which strongly supports our method. By realizing the arbitrary qubit channel, this work provides a universally- accepted way to explore various properties of quantum channels and novel prospect for quantum communication.

Greenberger-Horne-Zeilinger states-based blind quantum computation with entanglement concentration.

PubMed

Zhang, Xiaoqian; Weng, Jian; Lu, Wei; Li, Xiaochun; Luo, Weiqi; Tan, Xiaoqing

2017-09-11

In blind quantum computation (BQC) protocol, the quantum computability of servers are complicated and powerful, while the clients are not. It is still a challenge for clients to delegate quantum computation to servers and keep the clients' inputs, outputs and algorithms private. Unfortunately, quantum channel noise is unavoidable in the practical transmission. In this paper, a novel BQC protocol based on maximally entangled Greenberger-Horne-Zeilinger (GHZ) states is proposed which doesn't need a trusted center. The protocol includes a client and two servers, where the client only needs to own quantum channels with two servers who have full-advantage quantum computers. Two servers perform entanglement concentration used to remove the noise, where the success probability can almost reach 100% in theory. But they learn nothing in the process of concentration because of the no-signaling principle, so this BQC protocol is secure and feasible.

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

A programmable two-qubit quantum processor in silicon

NASA Astrophysics Data System (ADS)

Watson, T. F.; Philips, S. G. J.; Kawakami, E.; Ward, D. R.; Scarlino, P.; Veldhorst, M.; Savage, D. E.; Lagally, M. G.; Friesen, Mark; Coppersmith, S. N.; Eriksson, M. A.; Vandersypen, L. M. K.

2018-03-01

Now that it is possible to achieve measurement and control fidelities for individual quantum bits (qubits) above the threshold for fault tolerance, attention is moving towards the difficult task of scaling up the number of physical qubits to the large numbers that are needed for fault-tolerant quantum computing. In this context, quantum-dot-based spin qubits could have substantial advantages over other types of qubit owing to their potential for all-electrical operation and ability to be integrated at high density onto an industrial platform. Initialization, readout and single- and two-qubit gates have been demonstrated in various quantum-dot-based qubit representations. However, as seen with small-scale demonstrations of quantum computers using other types of qubit, combining these elements leads to challenges related to qubit crosstalk, state leakage, calibration and control hardware. Here we overcome these challenges by using carefully designed control techniques to demonstrate a programmable two-qubit quantum processor in a silicon device that can perform the Deutsch–Josza algorithm and the Grover search algorithm—canonical examples of quantum algorithms that outperform their classical analogues. We characterize the entanglement in our processor by using quantum-state tomography of Bell states, measuring state fidelities of 85–89 per cent and concurrences of 73–82 per cent. These results pave the way for larger-scale quantum computers that use spins confined to quantum dots.

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

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.

Electron-Phonon Systems on a Universal Quantum Computer

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

Macridin, Alexandru; Spentzouris, Panagiotis; Amundson, James

We present an algorithm that extends existing quantum algorithms forsimulating fermion systems in quantum chemistry and condensed matter physics toinclude phonons. The phonon degrees of freedom are represented with exponentialaccuracy on a truncated Hilbert space with a size that increases linearly withthe cutoff of the maximum phonon number. The additional number of qubitsrequired by the presence of phonons scales linearly with the size of thesystem. The additional circuit depth is constant for systems with finite-rangeelectron-phonon and phonon-phonon interactions and linear for long-rangeelectron-phonon interactions. Our algorithm for a Holstein polaron problem wasimplemented on an Atos Quantum Learning Machine (QLM) quantum simulatoremployingmore » the Quantum Phase Estimation method. The energy and the phonon numberdistribution of the polaron state agree with exact diagonalization results forweak, intermediate and strong electron-phonon coupling regimes.« less

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.

Quantum and classical dynamics in adiabatic computation

NASA Astrophysics Data System (ADS)

Crowley, P. J. D.; Äńurić, T.; Vinci, W.; Warburton, P. A.; Green, A. G.

2014-10-01

Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in a readily initialized state and then slowly changing its Hamiltonian, one may achieve quantum states that would otherwise be inaccessible. Moreover, a judicious choice of final Hamiltonian whose ground state encodes the solution to a problem allows adiabatic transport to be used for universal quantum computation. However, the dephasing effects of the environment limit the quantum correlations that an open system can support and degrade the power of such adiabatic computation. We quantify this effect by allowing the system to evolve over a restricted set of quantum states, providing a link between physically inspired classical optimization algorithms and quantum adiabatic optimization. This perspective allows us to develop benchmarks to bound the quantum correlations harnessed by an adiabatic computation. We apply these to the D-Wave Vesuvius machine with revealing—though inconclusive—results.

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.

Implementing the Deutsch-Jozsa algorithm with macroscopic ensembles

NASA Astrophysics Data System (ADS)

Semenenko, Henry; Byrnes, Tim

2016-05-01

Quantum computing implementations under consideration today typically deal with systems with microscopic degrees of freedom such as photons, ions, cold atoms, and superconducting circuits. The quantum information is stored typically in low-dimensional Hilbert spaces such as qubits, as quantum effects are strongest in such systems. It has, however, been demonstrated that quantum effects can be observed in mesoscopic and macroscopic systems, such as nanomechanical systems and gas ensembles. While few-qubit quantum information demonstrations have been performed with such macroscopic systems, a quantum algorithm showing exponential speedup over classical algorithms is yet to be shown. Here, we show that the Deutsch-Jozsa algorithm can be implemented with macroscopic ensembles. The encoding that we use avoids the detrimental effects of decoherence that normally plagues macroscopic implementations. We discuss two mapping procedures which can be chosen depending upon the constraints of the oracle and the experiment. Both methods have an exponential speedup over the classical case, and only require control of the ensembles at the level of the total spin of the ensembles. It is shown that both approaches reproduce the qubit Deutsch-Jozsa algorithm, and are robust under decoherence.

Experimental implementation of heat-bath algorithmic cooling using solid-state nuclear magnetic resonance.

PubMed

Baugh, J; Moussa, O; Ryan, C A; Nayak, A; Laflamme, R

2005-11-24

The counter-intuitive properties of quantum mechanics have the potential to revolutionize information processing by enabling the development of efficient algorithms with no known classical counterparts. Harnessing this power requires the development of a set of building blocks, one of which is a method to initialize the set of quantum bits (qubits) to a known state. Additionally, fresh ancillary qubits must be available during the course of computation to achieve fault tolerance. In any physical system used to implement quantum computation, one must therefore be able to selectively and dynamically remove entropy from the part of the system that is to be mapped to qubits. One such method is an 'open-system' cooling protocol in which a subset of qubits can be brought into contact with an external system of large heat capacity. Theoretical efforts have led to an implementation-independent cooling procedure, namely heat-bath algorithmic cooling. These efforts have culminated with the proposal of an optimal algorithm, the partner-pairing algorithm, which was used to compute the physical limits of heat-bath algorithmic cooling. Here we report the experimental realization of multi-step cooling of a quantum system via heat-bath algorithmic cooling. The experiment was carried out using nuclear magnetic resonance of a solid-state ensemble three-qubit system. We demonstrate the repeated repolarization of a particular qubit to an effective spin-bath temperature, and alternating logical operations within the three-qubit subspace to ultimately cool a second qubit below this temperature. Demonstration of the control necessary for these operations represents an important step forward in the manipulation of solid-state nuclear magnetic resonance qubits.

Efficient state initialization by a quantum spectral filtering algorithm

NASA Astrophysics Data System (ADS)

Fillion-Gourdeau, François; MacLean, Steve; Laflamme, Raymond

2017-04-01

An algorithm that initializes a quantum register to a state with a specified energy range is given, corresponding to a quantum implementation of the celebrated Feit-Fleck method. This is performed by introducing a nondeterministic quantum implementation of a standard spectral filtering procedure combined with an apodization technique, allowing for accurate state initialization. It is shown that the implementation requires only two ancilla qubits. A lower bound for the total probability of success of this algorithm is derived, showing that this scheme can be realized using a finite, relatively low number of trials. Assuming the time evolution can be performed efficiently and using a trial state polynomially close to the desired states, it is demonstrated that the number of operations required scales polynomially with the number of qubits. Tradeoffs between accuracy and performance are demonstrated in a simple example: the harmonic oscillator. This algorithm would be useful for the initialization phase of the simulation of quantum systems on digital quantum computers.

Quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices

NASA Astrophysics Data System (ADS)

Chakhmakhchyan, L.; Cerf, N. J.; Garcia-Patron, R.

2017-08-01

We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the permanent of a Hermitian positive semidefinite matrix can be expressed in terms of the expected value of a random variable, which stands for a specific photon-counting probability when measuring a linear-optically evolved random multimode coherent state. Our algorithm then approximates the matrix permanent from the corresponding sample mean and is shown to run in polynomial time for various sets of Hermitian positive semidefinite matrices, achieving a precision that improves over known techniques. This work illustrates how quantum optics may benefit algorithm development.

Prime factorization using quantum annealing and computational algebraic geometry

NASA Astrophysics Data System (ADS)

Dridi, Raouf; Alghassi, Hedayat

2017-02-01

We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gröbner bases. We present a novel autonomous algorithm which combines the two approaches and leads to the factorization of all bi-primes up to just over 200000, the largest number factored to date using a quantum processor. We also explain how Gröbner bases can be used to reduce the degree of Hamiltonians.

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method

NASA Astrophysics Data System (ADS)

Volokitin, V.; Liniov, A.; Meyerov, I.; Hartmann, M.; Ivanchenko, M.; Hänggi, P.; Denisov, S.

2017-11-01

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dim H =N ≲300 , while the direct long-time numerical integration of the master equation becomes increasingly problematic for N ≳400 , especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η1,η2,...,ηn} , one could propagate a quantum trajectory (with ηi's as norm thresholds) in a numerically exact way. By using a scalable N -particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N =2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method.

PubMed

Volokitin, V; Liniov, A; Meyerov, I; Hartmann, M; Ivanchenko, M; Hänggi, P; Denisov, S

2017-11-01

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dimH=N≲300, while the direct long-time numerical integration of the master equation becomes increasingly problematic for N≳400, especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η_{1},η_{2},...,η_{n}}, one could propagate a quantum trajectory (with η_{i}'s as norm thresholds) in a numerically exact way. By using a scalable N-particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N=2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.

Architecture Framework for Trapped-Ion Quantum Computer based on Performance Simulation Tool

NASA Astrophysics Data System (ADS)

Ahsan, Muhammad

The challenge of building scalable quantum computer lies in striking appropriate balance between designing a reliable system architecture from large number of faulty computational resources and improving the physical quality of system components. The detailed investigation of performance variation with physics of the components and the system architecture requires adequate performance simulation tool. In this thesis we demonstrate a software tool capable of (1) mapping and scheduling the quantum circuit on a realistic quantum hardware architecture with physical resource constraints, (2) evaluating the performance metrics such as the execution time and the success probability of the algorithm execution, and (3) analyzing the constituents of these metrics and visualizing resource utilization to identify system components which crucially define the overall performance. Using this versatile tool, we explore vast design space for modular quantum computer architecture based on trapped ions. We find that while success probability is uniformly determined by the fidelity of physical quantum operation, the execution time is a function of system resources invested at various layers of design hierarchy. At physical level, the number of lasers performing quantum gates, impact the latency of the fault-tolerant circuit blocks execution. When these blocks are used to construct meaningful arithmetic circuit such as quantum adders, the number of ancilla qubits for complicated non-clifford gates and entanglement resources to establish long-distance communication channels, become major performance limiting factors. Next, in order to factorize large integers, these adders are assembled into modular exponentiation circuit comprising bulk of Shor's algorithm. At this stage, the overall scaling of resource-constraint performance with the size of problem, describes the effectiveness of chosen design. By matching the resource investment with the pace of advancement in hardware technology, we find optimal designs for different types of quantum adders. Conclusively, we show that 2,048-bit Shor's algorithm can be reliably executed within the resource budget of 1.5 million qubits.

Two-spectral Yang-Baxter operators in topological quantum computation

NASA Astrophysics Data System (ADS)

Sanchez, William F.

2011-05-01

One of the current trends in quantum computing is the application of algebraic topological methods in the design of new algorithms and quantum computers, giving rise to topological quantum computing. One of the tools used in it is the Yang-Baxter equation whose solutions are interpreted as universal quantum gates. Lately, more general Yang-Baxter equations have been investigated, making progress as two-spectral equations and Yang-Baxter systems. This paper intends to apply these new findings to the field of topological quantum computation, more specifically, the proposition of the two-spectral Yang-Baxter operators as universal quantum gates for 2 qubits and 2 qutrits systems, obtaining 4x4 and 9x9 matrices respectively, and further elaboration of the corresponding Hamiltonian by the use of computer algebra software Mathematica® and its Qucalc package. In addition, possible physical systems to which the Yang-Baxter operators obtained can be applied are considered. In the present work it is demonstrated the utility of the Yang-Baxter equation to generate universal quantum gates and the power of computer algebra to design them; it is expected that these mathematical studies contribute to the further development of quantum computers

Quantum Information Theory - an Invitation

NASA Astrophysics Data System (ADS)

Werner, Reinhard F.

Quantum information and quantum computers have received a lot of public attention recently. Quantum computers have been advertised as a kind of warp drive for computing, and indeed the promise of the algorithms of Shor and Grover is to perform computations which are extremely hard or even provably impossible on any merely ``classical'' computer.In this article I shall give an account of the basic concepts of quantum information theory is given, staying as much as possible in the area of general agreement.The article is divided into two parts. The first (up to the end of Sect. 2.5) is mostly in plain English, centered around the exploration of what can or cannot be done with quantum systems as information carriers. The second part, Sect. 2.6, then gives a description of the mathematical structures and of some of the tools needed to develop the theory.

Quantum Hash function and its application to privacy amplification in quantum key distribution, pseudo-random number generation and image encryption

NASA Astrophysics Data System (ADS)

Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min

2016-01-01

Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information.

Quantum Hash function and its application to privacy amplification in quantum key distribution, pseudo-random number generation and image encryption

PubMed Central

Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min

2016-01-01

Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information. PMID:26823196

Quantum Hash function and its application to privacy amplification in quantum key distribution, pseudo-random number generation and image encryption.

PubMed

Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min

2016-01-29

Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information.

FermiLib v0.1

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

MCCLEAN, JARROD; HANER, THOMAS; STEIGER, DAMIAN

FermiLib is an open source software package designed to facilitate the development and testing of algorithms for simulations of fermionic systems on quantum computers. Fermionic simulations represent an important application of early quantum devices with a lot of potential high value targets, such as quantum chemistry for the development of new catalysts. This software strives to provide a link between the required domain expertise in specific fermionic applications and quantum computing to enable more users to directly interface with, and develop for, these applications. It is an extensible Python library designed to interface with the high performance quantum simulator, ProjectQ,more » as well as application specific software such as PSI4 from the domain of quantum chemistry. Such software is key to enabling effective user facilities in quantum computation research.« less

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

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.

Massively parallel quantum computer simulator

NASA Astrophysics Data System (ADS)

De Raedt, K.; Michielsen, K.; De Raedt, H.; Trieu, B.; Arnold, G.; Richter, M.; Lippert, Th.; Watanabe, H.; Ito, N.

2007-01-01

We describe portable software to simulate universal quantum computers on massive parallel computers. We illustrate the use of the simulation software by running various quantum algorithms on different computer architectures, such as a IBM BlueGene/L, a IBM Regatta p690+, a Hitachi SR11000/J1, a Cray X1E, a SGI Altix 3700 and clusters of PCs running Windows XP. We study the performance of the software by simulating quantum computers containing up to 36 qubits, using up to 4096 processors and up to 1 TB of memory. Our results demonstrate that the simulator exhibits nearly ideal scaling as a function of the number of processors and suggest that the simulation software described in this paper may also serve as benchmark for testing high-end parallel computers.

Prime factorization using quantum annealing and computational algebraic geometry

PubMed Central

Dridi, Raouf; Alghassi, Hedayat

2017-01-01

We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gröbner bases. We present a novel autonomous algorithm which combines the two approaches and leads to the factorization of all bi-primes up to just over 200000, the largest number factored to date using a quantum processor. We also explain how Gröbner bases can be used to reduce the degree of Hamiltonians. PMID:28220854

Interferometric Computation Beyond Quantum Theory

NASA Astrophysics Data System (ADS)

Garner, Andrew J. P.

2018-03-01

There are quantum solutions for computational problems that make use of interference at some stage in the algorithm. These stages can be mapped into the physical setting of a single particle travelling through a many-armed interferometer. There has been recent foundational interest in theories beyond quantum theory. Here, we present a generalized formulation of computation in the context of a many-armed interferometer, and explore how theories can differ from quantum theory and still perform distributed calculations in this set-up. We shall see that quaternionic quantum theory proves a suitable candidate, whereas box-world does not. We also find that a classical hidden variable model first presented by Spekkens (Phys Rev A 75(3): 32100, 2007) can also be used for this type of computation due to the epistemic restriction placed on the hidden variable.

Quantum discord of two-qubit X states

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

Chen Qing; Yu Sixia; Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026 Anhui

Quantum discord provides a measure for quantifying quantum correlations beyond entanglement and is very hard to compute even for two-qubit states because of the minimization over all possible measurements. Recently a simple algorithm to evaluate the quantum discord for two-qubit X states was proposed by Ali, Rau, and Alber [Phys. Rev. A 81, 042105 (2010)] with minimization taken over only a few cases. Here we shall at first identify a class of X states, whose quantum discord can be evaluated analytically without any minimization, for which their algorithm is valid, and also identify a family of X states for whichmore » their algorithm fails. And then we demonstrate that this special family of X states provides furthermore an explicit example for the inequivalence between the minimization over positive operator-valued measures and that over von Neumann measurements.« less

Protecting Information

NASA Astrophysics Data System (ADS)

Loepp, Susan; Wootters, William K.

2006-09-01

For many everyday transmissions, it is essential to protect digital information from noise or eavesdropping. This undergraduate introduction to error correction and cryptography is unique in devoting several chapters to quantum cryptography and quantum computing, thus providing a context in which ideas from mathematics and physics meet. By covering such topics as Shor's quantum factoring algorithm, this text informs the reader about current thinking in quantum information theory and encourages an appreciation of the connections between mathematics and science.Of particular interest are the potential impacts of quantum physics:(i) a quantum computer, if built, could crack our currently used public-key cryptosystems; and (ii) quantum cryptography promises to provide an alternative to these cryptosystems, basing its security on the laws of nature rather than on computational complexity. No prior knowledge of quantum mechanics is assumed, but students should have a basic knowledge of complex numbers, vectors, and matrices. Accessible to readers familiar with matrix algebra, vector spaces and complex numbers First undergraduate text to cover cryptography, error-correction, and quantum computation together Features exercises designed to enhance understanding, including a number of computational problems, available from www.cambridge.org/9780521534765

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.

Quantum ensembles of quantum classifiers.

PubMed

Schuld, Maria; Petruccione, Francesco

2018-02-09

Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are implementations of quantum classifiers, or models for the classification of data inputs with a quantum computer. Following the success of collective decision making with ensembles in classical machine learning, this paper introduces the concept of quantum ensembles of quantum classifiers. Creating the ensemble corresponds to a state preparation routine, after which the quantum classifiers are evaluated in parallel and their combined decision is accessed by a single-qubit measurement. This framework naturally allows for exponentially large ensembles in which - similar to Bayesian learning - the individual classifiers do not have to be trained. As an example, we analyse an exponentially large quantum ensemble in which each classifier is weighed according to its performance in classifying the training data, leading to new results for quantum as well as classical machine learning.

Quantum Linear System Algorithm for Dense Matrices.

PubMed

Wossnig, Leonard; Zhao, Zhikuan; Prakash, Anupam

2018-02-02

Solving linear systems of equations is a frequently encountered problem in machine learning and optimization. Given a matrix A and a vector b the task is to find the vector x such that Ax=b. We describe a quantum algorithm that achieves a sparsity-independent runtime scaling of O(κ^{2}sqrt[n]polylog(n)/ε) for an n×n dimensional A with bounded spectral norm, where κ denotes the condition number of A, and ε is the desired precision parameter. This amounts to a polynomial improvement over known quantum linear system algorithms when applied to dense matrices, and poses a new state of the art for solving dense linear systems on a quantum computer. Furthermore, an exponential improvement is achievable if the rank of A is polylogarithmic in the matrix dimension. Our algorithm is built upon a singular value estimation subroutine, which makes use of a memory architecture that allows for efficient preparation of quantum states that correspond to the rows of A and the vector of Euclidean norms of the rows of A.

Characterizing quantum supremacy in near-term devices

NASA Astrophysics Data System (ADS)

Boixo, Sergio; Isakov, Sergei V.; Smelyanskiy, Vadim N.; Babbush, Ryan; Ding, Nan; Jiang, Zhang; Bremner, Michael J.; Martinis, John M.; Neven, Hartmut

2018-06-01

A critical question for quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of supercomputers. Such a demonstration of what is referred to as quantum supremacy requires a reliable evaluation of the resources required to solve tasks with classical approaches. Here, we propose the task of sampling from the output distribution of random quantum circuits as a demonstration of quantum supremacy. We extend previous results in computational complexity to argue that this sampling task must take exponential time in a classical computer. We introduce cross-entropy benchmarking to obtain the experimental fidelity of complex multiqubit dynamics. This can be estimated and extrapolated to give a success metric for a quantum supremacy demonstration. We study the computational cost of relevant classical algorithms and conclude that quantum supremacy can be achieved with circuits in a two-dimensional lattice of 7 × 7 qubits and around 40 clock cycles. This requires an error rate of around 0.5% for two-qubit gates (0.05% for one-qubit gates), and it would demonstrate the basic building blocks for a fault-tolerant quantum computer.

Quantum population and entanglement evolution in photosynthetic process

NASA Astrophysics Data System (ADS)

Zhu, Jing

Applications of the concepts of quantum information theory are usually related to the powerful and counter-intuitive quantum mechanical effects of superposition, interference and entanglement. In this thesis, I examine the role of coherence and entanglement in complex chemical systems. The research has focused mainly on two related projects: The first project is developing a theoretical model to explain the recent ultrafast experiments on excitonic migration in photosynthetic complexes that show long-lived coherence of the order of hundreds of femtoseconds and the second project developing the Grover algorithm for global optimization of complex systems. The first part can be divided into two sections. The first section is investigating the theoretical frame about the transfer of electronic excitation energy through the Fenna-Matthews-Olson (FMO) pigment-protein complex. The new developed modified scaled hierarchical equation of motion (HEOM) approach is employed for simulating the open quantum system. The second section is investigating the evolution of entanglement in the FMO complex based on the simulation result via scaled HEOM approach. We examine the role of multipartite entanglement in the FMO complex by direct computation of the convex roof optimization for a number of different measures, including pairwise, triplet, quadruple and quintuple sites entanglement. Our results support the hypothesis that multipartite entanglement is maximum primary along the two distinct electronic energy transfer pathways. The second part of this thesis can be separated into two sections. The first section demonstrated that a modified Grover's quantum algorithm can be applied to real problems of finding a global minimum using modest numbers of quantum bits. Calculations of the global minimum of simple test functions and Lennard-Jones clusters have been carried out on a quantum computer simulator using a modified Grover's algorithm. The second section is implementing the basic quantum logical gates upon arrays of trapped ultracold polar molecules as qubits for the quantum computer. Utilized herein is the Multi-Target Optimal Control Theory (MTOCT) as a means of manipulating the initial-to-target transition probability via external laser field. The detailed calculation is applied for the SrO molecule, an ideal candidate in proposed quantum computers using arrays of trapped ultra-cold polar molecules.

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.

Quantum Simulation of Helium Hydride Cation in a Solid-State Spin Register.

PubMed

Wang, Ya; Dolde, Florian; Biamonte, Jacob; Babbush, Ryan; Bergholm, Ville; Yang, Sen; Jakobi, Ingmar; Neumann, Philipp; Aspuru-Guzik, Alán; Whitfield, James D; Wrachtrup, Jörg

2015-08-25

Ab initio computation of molecular properties is one of the most promising applications of quantum computing. While this problem is widely believed to be intractable for classical computers, efficient quantum algorithms exist which have the potential to vastly accelerate research throughput in fields ranging from material science to drug discovery. Using a solid-state quantum register realized in a nitrogen-vacancy (NV) defect in diamond, we compute the bond dissociation curve of the minimal basis helium hydride cation, HeH(+). Moreover, we report an energy uncertainty (given our model basis) of the order of 10(-14) hartree, which is 10 orders of magnitude below the desired chemical precision. As NV centers in diamond provide a robust and straightforward platform for quantum information processing, our work provides an important step toward a fully scalable solid-state implementation of a quantum chemistry simulator.

Numerical approach of the quantum circuit theory

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

Silva, J.J.B., E-mail: jaedsonfisica@hotmail.com; Duarte-Filho, G.C.; Almeida, F.A.G.

2017-03-15

In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency formore » a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.« less

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.

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

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.

Hard decoding algorithm for optimizing thresholds under general Markovian noise

NASA Astrophysics Data System (ADS)

Chamberland, Christopher; Wallman, Joel; Beale, Stefanie; Laflamme, Raymond

2017-04-01

Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of error-correcting codes have been obtained. However, realistic quantum systems can undergo noise processes that differ significantly from Pauli noise. In this paper, we present an efficient hard decoding algorithm for optimizing thresholds and lowering failure rates of an error-correcting code under general completely positive and trace-preserving (i.e., Markovian) noise. We use our hard decoding algorithm to study the performance of several error-correcting codes under various non-Pauli noise models by computing threshold values and failure rates for these codes. We compare the performance of our hard decoding algorithm to decoders optimized for depolarizing noise and show improvements in thresholds and reductions in failure rates by several orders of magnitude. Our hard decoding algorithm can also be adapted to take advantage of a code's non-Pauli transversal gates to further suppress noise. For example, we show that using the transversal gates of the 5-qubit code allows arbitrary rotations around certain axes to be perfectly corrected. Furthermore, we show that Pauli twirling can increase or decrease the threshold depending upon the code properties. Lastly, we show that even if the physical noise model differs slightly from the hypothesized noise model used to determine an optimized decoder, failure rates can still be reduced by applying our hard decoding algorithm.

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 algorithm for linear regression

NASA Astrophysics Data System (ADS)

Wang, Guoming

2017-07-01

We present a quantum algorithm for fitting a linear regression model to a given data set using the least-squares approach. Differently from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs these numbers in the classical form. So by running it once, one completely determines the fitted model and then can use it to make predictions on new data at little cost. Moreover, our algorithm works in the standard oracle model, and can handle data sets with nonsparse design matrices. It runs in time poly( log2(N ) ,d ,κ ,1 /ɛ ) , where N is the size of the data set, d is the number of adjustable parameters, κ is the condition number of the design matrix, and ɛ is the desired precision in the output. We also show that the polynomial dependence on d and κ is necessary. Thus, our algorithm cannot be significantly improved. Furthermore, we also give a quantum algorithm that estimates the quality of the least-squares fit (without computing its parameters explicitly). This algorithm runs faster than the one for finding this fit, and can be used to check whether the given data set qualifies for linear regression in the first place.

Quantum Support Vector Machine for Big Data Classification

NASA Astrophysics Data System (ADS)

Rebentrost, Patrick; Mohseni, Masoud; Lloyd, Seth

2014-09-01

Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the number of training examples. In cases where classical sampling algorithms require polynomial time, an exponential speedup is obtained. At the core of this quantum big data algorithm is a nonsparse matrix exponentiation technique for efficiently performing a matrix inversion of the training data inner-product (kernel) matrix.

Belief propagation decoding of quantum channels by passing quantum messages

NASA Astrophysics Data System (ADS)

Renes, Joseph M.

2017-07-01

The belief propagation (BP) algorithm is a powerful tool in a wide range of disciplines from statistical physics to machine learning to computational biology, and is ubiquitous in decoding classical error-correcting codes. The algorithm works by passing messages between nodes of the factor graph associated with the code and enables efficient decoding of the channel, in some cases even up to the Shannon capacity. Here we construct the first BP algorithm which passes quantum messages on the factor graph and is capable of decoding the classical-quantum channel with pure state outputs. This gives explicit decoding circuits whose number of gates is quadratic in the code length. We also show that this decoder can be modified to work with polar codes for the pure state channel and as part of a decoder for transmitting quantum information over the amplitude damping channel. These represent the first explicit capacity-achieving decoders for non-Pauli channels.

Research on Quantum Algorithms at the Institute for Quantum Information and Matter

DTIC Science & Technology

2016-05-29

local quantum computation with applications to position-based cryptography , New Journal of Physics, (09 2011): 0. doi: 10.1088/1367-2630/13/9/093036... cryptography , such as the ability to turn private-key encryption into public-key encryption. While ad hoc obfuscators exist, theoretical progress has mainly...to device-independent quantum cryptography , to quantifying entanglement, and to the classification of quantum phases of matter. Exact synthesis

Computational applications of the many-interacting-worlds interpretation of quantum mechanics.

PubMed

Sturniolo, Simone

2018-05-01

While historically many quantum-mechanical simulations of molecular dynamics have relied on the Born-Oppenheimer approximation to separate electronic and nuclear behavior, recently a great deal of interest has arisen in quantum effects in nuclear dynamics as well. Due to the computational difficulty of solving the Schrödinger equation in full, these effects are often treated with approximate methods. In this paper, we present an algorithm to tackle these problems using an extension to the many-interacting-worlds approach to quantum mechanics. This technique uses a kernel function to rebuild the probability density, and therefore, in contrast with the approximation presented in the original paper, it can be naturally extended to n-dimensional systems. This opens up the possibility of performing quantum ground-state searches with steepest-descent methods, and it could potentially lead to real-time quantum molecular-dynamics simulations. The behavior of the algorithm is studied in different potentials and numbers of dimensions and compared both to the original approach and to exact Schrödinger equation solutions whenever possible.

Artificial Bee Colony Optimization of Capping Potentials for Hybrid Quantum Mechanical/Molecular Mechanical Calculations.

PubMed

Schiffmann, Christoph; Sebastiani, Daniel

2011-05-10

We present an algorithmic extension of a numerical optimization scheme for analytic capping potentials for use in mixed quantum-classical (quantum mechanical/molecular mechanical, QM/MM) ab initio calculations. Our goal is to minimize bond-cleavage-induced perturbations in the electronic structure, measured by means of a suitable penalty functional. The optimization algorithm-a variant of the artificial bee colony (ABC) algorithm, which relies on swarm intelligence-couples deterministic (downhill gradient) and stochastic elements to avoid local minimum trapping. The ABC algorithm outperforms the conventional downhill gradient approach, if the penalty hypersurface exhibits wiggles that prevent a straight minimization pathway. We characterize the optimized capping potentials by computing NMR chemical shifts. This approach will increase the accuracy of QM/MM calculations of complex biomolecules.

Quantum Machine Learning over Infinite Dimensions

DOE PAGES

Lau, Hoi-Kwan; Pooser, Raphael; Siopsis, George; ...

2017-02-21

Machine learning is a fascinating and exciting eld within computer science. Recently, this ex- citement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the nite-dimensional substrate of discrete variables. Here we generalize quantum machine learning to the more complex, but still remarkably practi- cal, in nite-dimensional systems. We present the critical subroutines of quantum machine learning algorithms for an all-photonic continuous-variable quantum computer that achieve an exponential speedup compared to their equivalent classical counterparts. Finally, we also map out an experi- mental implementation which can be used as amore » blueprint for future photonic demonstrations.« less

Quantum Machine Learning over Infinite Dimensions

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

Lau, Hoi-Kwan; Pooser, Raphael; Siopsis, George

Machine learning is a fascinating and exciting eld within computer science. Recently, this ex- citement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the nite-dimensional substrate of discrete variables. Here we generalize quantum machine learning to the more complex, but still remarkably practi- cal, in nite-dimensional systems. We present the critical subroutines of quantum machine learning algorithms for an all-photonic continuous-variable quantum computer that achieve an exponential speedup compared to their equivalent classical counterparts. Finally, we also map out an experi- mental implementation which can be used as amore » blueprint for future photonic demonstrations.« less

Quantum supercharger library: hyper-parallelism of the Hartree-Fock method.

PubMed

Fernandes, Kyle D; Renison, C Alicia; Naidoo, Kevin J

2015-07-05

We present here a set of algorithms that completely rewrites the Hartree-Fock (HF) computations common to many legacy electronic structure packages (such as GAMESS-US, GAMESS-UK, and NWChem) into a massively parallel compute scheme that takes advantage of hardware accelerators such as Graphical Processing Units (GPUs). The HF compute algorithm is core to a library of routines that we name the Quantum Supercharger Library (QSL). We briefly evaluate the QSL's performance and report that it accelerates a HF 6-31G Self-Consistent Field (SCF) computation by up to 20 times for medium sized molecules (such as a buckyball) when compared with mature Central Processing Unit algorithms available in the legacy codes in regular use by researchers. It achieves this acceleration by massive parallelization of the one- and two-electron integrals and optimization of the SCF and Direct Inversion in the Iterative Subspace routines through the use of GPU linear algebra libraries. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Quantum exhaustive key search with simplified-DES as a case study.

PubMed

Almazrooie, Mishal; Samsudin, Azman; Abdullah, Rosni; Mutter, Kussay N

2016-01-01

To evaluate the security of a symmetric cryptosystem against any quantum attack, the symmetric algorithm must be first implemented on a quantum platform. In this study, a quantum implementation of a classical block cipher is presented. A quantum circuit for a classical block cipher of a polynomial size of quantum gates is proposed. The entire work has been tested on a quantum mechanics simulator called libquantum. First, the functionality of the proposed quantum cipher is verified and the experimental results are compared with those of the original classical version. Then, quantum attacks are conducted by using Grover's algorithm to recover the secret key. The proposed quantum cipher is used as a black box for the quantum search. The quantum oracle is then queried over the produced ciphertext to mark the quantum state, which consists of plaintext and key qubits. The experimental results show that for a key of n-bit size and key space of N such that [Formula: see text], the key can be recovered in [Formula: see text] computational steps.

Natural three-qubit interactions in one-way quantum computing

NASA Astrophysics Data System (ADS)

Tame, M. S.; Paternostro, M.; Kim, M. S.; Vedral, V.

2006-02-01

We address the effects of natural three-qubit interactions on the computational power of one-way quantum computation. A benefit of using more sophisticated entanglement structures is the ability to construct compact and economic simulations of quantum algorithms with limited resources. We show that the features of our study are embodied by suitably prepared optical lattices, where effective three-spin interactions have been theoretically demonstrated. We use this to provide a compact construction for the Toffoli gate. Information flow and two-qubit interactions are also outlined, together with a brief analysis of relevant sources of imperfection.

Quantum Computing Architectural Design

NASA Astrophysics Data System (ADS)

West, Jacob; Simms, Geoffrey; Gyure, Mark

2006-03-01

Large scale quantum computers will invariably require scalable architectures in addition to high fidelity gate operations. Quantum computing architectural design (QCAD) addresses the problems of actually implementing fault-tolerant algorithms given physical and architectural constraints beyond those of basic gate-level fidelity. Here we introduce a unified framework for QCAD that enables the scientist to study the impact of varying error correction schemes, architectural parameters including layout and scheduling, and physical operations native to a given architecture. Our software package, aptly named QCAD, provides compilation, manipulation/transformation, multi-paradigm simulation, and visualization tools. We demonstrate various features of the QCAD software package through several examples.

Counterfactual quantum computation through quantum interrogation

NASA Astrophysics Data System (ADS)

Hosten, Onur; Rakher, Matthew T.; Barreiro, Julio T.; Peters, Nicholas A.; Kwiat, Paul G.

2006-02-01

The logic underlying the coherent nature of quantum information processing often deviates from intuitive reasoning, leading to surprising effects. Counterfactual computation constitutes a striking example: the potential outcome of a quantum computation can be inferred, even if the computer is not run. Relying on similar arguments to interaction-free measurements (or quantum interrogation), counterfactual computation is accomplished by putting the computer in a superposition of `running' and `not running' states, and then interfering the two histories. Conditional on the as-yet-unknown outcome of the computation, it is sometimes possible to counterfactually infer information about the solution. Here we demonstrate counterfactual computation, implementing Grover's search algorithm with an all-optical approach. It was believed that the overall probability of such counterfactual inference is intrinsically limited, so that it could not perform better on average than random guesses. However, using a novel `chained' version of the quantum Zeno effect, we show how to boost the counterfactual inference probability to unity, thereby beating the random guessing limit. Our methods are general and apply to any physical system, as illustrated by a discussion of trapped-ion systems. Finally, we briefly show that, in certain circumstances, counterfactual computation can eliminate errors induced by decoherence.

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.

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

Implementation and characterization of active feed-forward for deterministic linear optics quantum computing

NASA Astrophysics Data System (ADS)

Böhi, P.; Prevedel, R.; Jennewein, T.; Stefanov, A.; Tiefenbacher, F.; Zeilinger, A.

2007-12-01

In general, quantum computer architectures which are based on the dynamical evolution of quantum states, also require the processing of classical information, obtained by measurements of the actual qubits that make up the computer. This classical processing involves fast, active adaptation of subsequent measurements and real-time error correction (feed-forward), so that quantum gates and algorithms can be executed in a deterministic and hence error-free fashion. This is also true in the linear optical regime, where the quantum information is stored in the polarization state of photons. The adaptation of the photon’s polarization can be achieved in a very fast manner by employing electro-optical modulators, which change the polarization of a trespassing photon upon appliance of a high voltage. In this paper we discuss techniques for implementing fast, active feed-forward at the single photon level and we present their application in the context of photonic quantum computing. This includes the working principles and the characterization of the EOMs as well as a description of the switching logics, both of which allow quantum computation at an unprecedented speed.

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

Quantum reinforcement learning.

PubMed

Dong, Daoyi; Chen, Chunlin; Li, Hanxiong; Tarn, Tzyh-Jong

2008-10-01

The key approaches for machine learning, particularly learning in unknown probabilistic environments, are new representations and computation mechanisms. In this paper, a novel quantum reinforcement learning (QRL) method is proposed by combining quantum theory and reinforcement learning (RL). Inspired by the state superposition principle and quantum parallelism, a framework of a value-updating algorithm is introduced. The state (action) in traditional RL is identified as the eigen state (eigen action) in QRL. The state (action) set can be represented with a quantum superposition state, and the eigen state (eigen action) can be obtained by randomly observing the simulated quantum state according to the collapse postulate of quantum measurement. The probability of the eigen action is determined by the probability amplitude, which is updated in parallel according to rewards. Some related characteristics of QRL such as convergence, optimality, and balancing between exploration and exploitation are also analyzed, which shows that this approach makes a good tradeoff between exploration and exploitation using the probability amplitude and can speedup learning through the quantum parallelism. To evaluate the performance and practicability of QRL, several simulated experiments are given, and the results demonstrate the effectiveness and superiority of the QRL algorithm for some complex problems. This paper is also an effective exploration on the application of quantum computation to artificial intelligence.

Trapping photons on the line: controllable dynamics of a quantum walk

NASA Astrophysics Data System (ADS)

Xue, Peng; Qin, Hao; Tang, Bao

2014-04-01

Optical interferometers comprising birefringent-crystal beam displacers, wave plates, and phase shifters serve as stable devices for simulating quantum information processes such as heralded coined quantum walks. Quantum walks are important for quantum algorithms, universal quantum computing circuits, quantum transport in complex systems, and demonstrating intriguing nonlinear dynamical quantum phenomena. We introduce fully controllable polarization-independent phase shifters in optical pathes in order to realize site-dependent phase defects. The effectiveness of our interferometer is demonstrated through realizing single-photon quantum-walk dynamics in one dimension. By applying site-dependent phase defects, the translational symmetry of an ideal standard quantum walk is broken resulting in localization effect in a quantum walk architecture. The walk is realized for different site-dependent phase defects and coin settings, indicating the strength of localization signature depends on the level of phase due to site-dependent phase defects and coin settings and opening the way for the implementation of a quantum-walk-based algorithm.

QPSO-Based Adaptive DNA Computing Algorithm

PubMed Central

Karakose, Mehmet; Cigdem, Ugur

2013-01-01

DNA (deoxyribonucleic acid) computing that is a new computation model based on DNA molecules for information storage has been increasingly used for optimization and data analysis in recent years. However, DNA computing algorithm has some limitations in terms of convergence speed, adaptability, and effectiveness. In this paper, a new approach for improvement of DNA computing is proposed. This new approach aims to perform DNA computing algorithm with adaptive parameters towards the desired goal using quantum-behaved particle swarm optimization (QPSO). Some contributions provided by the proposed QPSO based on adaptive DNA computing algorithm are as follows: (1) parameters of population size, crossover rate, maximum number of operations, enzyme and virus mutation rate, and fitness function of DNA computing algorithm are simultaneously tuned for adaptive process, (2) adaptive algorithm is performed using QPSO algorithm for goal-driven progress, faster operation, and flexibility in data, and (3) numerical realization of DNA computing algorithm with proposed approach is implemented in system identification. Two experiments with different systems were carried out to evaluate the performance of the proposed approach with comparative results. Experimental results obtained with Matlab and FPGA demonstrate ability to provide effective optimization, considerable convergence speed, and high accuracy according to DNA computing algorithm. PMID:23935409

Blind quantum computation over a collective-noise channel

NASA Astrophysics Data System (ADS)

Takeuchi, Yuki; Fujii, Keisuke; Ikuta, Rikizo; Yamamoto, Takashi; Imoto, Nobuyuki

2016-05-01

Blind quantum computation (BQC) allows a client (Alice), who only possesses relatively poor quantum devices, to delegate universal quantum computation to a server (Bob) in such a way that Bob cannot know Alice's inputs, algorithm, and outputs. The quantum channel between Alice and Bob is noisy, and the loss over the long-distance quantum communication should also be taken into account. Here we propose to use decoherence-free subspace (DFS) to overcome the collective noise in the quantum channel for BQC, which we call DFS-BQC. We propose three variations of DFS-BQC protocols. One of them, a coherent-light-assisted DFS-BQC protocol, allows Alice to faithfully send the signal photons with a probability proportional to a transmission rate of the quantum channel. In all cases, we combine the ideas based on DFS and the Broadbent-Fitzsimons-Kashefi protocol, which is one of the BQC protocols, without degrading unconditional security. The proposed DFS-based schemes are generic and hence can be applied to other BQC protocols where Alice sends quantum states to Bob.

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

Numerical method for computing Maass cusp forms on triply punctured two-sphere

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

Chan, K. T.; Kamari, H. M.; Zainuddin, H.

2014-03-05

A quantum mechanical system on a punctured surface modeled on hyperbolic space has always been an important subject of research in mathematics and physics. This corresponding quantum system is governed by the Schrödinger equation whose solutions are the Maass waveforms. Spectral studies on these Maass waveforms are known to contain both continuous and discrete eigenvalues. The discrete eigenfunctions are usually called the Maass Cusp Forms (MCF) where their discrete eigenvalues are not known analytically. We introduce a numerical method based on Hejhal and Then algorithm using GridMathematica for computing MCF on a punctured surface with three cusps namely the triplymore » punctured two-sphere. We also report on a pullback algorithm for the punctured surface and a point locater algorithm to facilitate the complete pullback which are essential parts of the main algorithm.« less

Optimal subsystem approach to multi-qubit quantum state discrimination and experimental investigation

NASA Astrophysics Data System (ADS)

Xue, ShiChuan; Wu, JunJie; Xu, Ping; Yang, XueJun

2018-02-01

Quantum computing is a significant computing capability which is superior to classical computing because of its superposition feature. Distinguishing several quantum states from quantum algorithm outputs is often a vital computational task. In most cases, the quantum states tend to be non-orthogonal due to superposition; quantum mechanics has proved that perfect outcomes could not be achieved by measurements, forcing repetitive measurement. Hence, it is important to determine the optimum measuring method which requires fewer repetitions and a lower error rate. However, extending current measurement approaches mainly aiming at quantum cryptography to multi-qubit situations for quantum computing confronts challenges, such as conducting global operations which has considerable costs in the experimental realm. Therefore, in this study, we have proposed an optimum subsystem method to avoid these difficulties. We have provided an analysis of the comparison between the reduced subsystem method and the global minimum error method for two-qubit problems; the conclusions have been verified experimentally. The results showed that the subsystem method could effectively discriminate non-orthogonal two-qubit states, such as separable states, entangled pure states, and mixed states; the cost of the experimental process had been significantly reduced, in most circumstances, with acceptable error rate. We believe the optimal subsystem method is the most valuable and promising approach for multi-qubit quantum computing applications.

Heat-bath algorithmic cooling with correlated qubit-environment interactions

NASA Astrophysics Data System (ADS)

Rodríguez-Briones, Nayeli A.; Li, Jun; Peng, Xinhua; Mor, Tal; Weinstein, Yossi; Laflamme, Raymond

2017-11-01

Cooling techniques are essential to understand fundamental thermodynamic questions of the low-energy states of physical systems, furthermore they are at the core of practical applications of quantum information science. In quantum computing, this controlled preparation of highly pure quantum states is required from the state initialization of most quantum algorithms to a reliable supply of ancilla qubits that satisfy the fault-tolerance threshold for quantum error correction. Heat-bath algorithmic cooling has been shown to purify qubits by controlled redistribution of entropy and multiple contact with a bath, not only for ensemble implementations but also for technologies with strong but imperfect measurements. In this paper, we show that correlated relaxation processes between the system and environment during rethermalization when we reset hot ancilla qubits, can be exploited to enhance purification. We show that a long standing upper bound on the limits of algorithmic cooling Schulman et al (2005 Phys. Rev. Lett. 94, 120501) can be broken by exploiting these correlations. We introduce a new tool for cooling algorithms, which we call ‘state-reset’, obtained when the coupling to the environment is generalized from individual-qubits relaxation to correlated-qubit relaxation. Furthermore, we present explicit improved cooling algorithms which lead to an increase of purity beyond all the previous work, and relate our results to the Nuclear Overhauser Effect.

Creating Very True Quantum Algorithms for Quantum Energy Based Computing

NASA Astrophysics Data System (ADS)

Nagata, Koji; Nakamura, Tadao; Geurdes, Han; Batle, Josep; Abdalla, Soliman; Farouk, Ahmed; Diep, Do Ngoc

2018-04-01

An interpretation of quantum mechanics is discussed. It is assumed that quantum is energy. An algorithm by means of the energy interpretation is discussed. An algorithm, based on the energy interpretation, for fast determining a homogeneous linear function f( x) := s. x = s 1 x 1 + s 2 x 2 + ⋯ + s N x N is proposed. Here x = ( x 1, … , x N ), x j ∈ R and the coefficients s = ( s 1, … , s N ), s j ∈ N. Given the interpolation values (f(1), f(2),...,f(N))=ěc {y}, the unknown coefficients s = (s1(ěc {y}),\\dots , sN(ěc {y})) of the linear function shall be determined, simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of N. Our method is based on the generalized Bernstein-Vazirani algorithm to qudit systems. Next, by using M parallel quantum systems, M homogeneous linear functions are determined, simultaneously. The speed of obtaining the set of M homogeneous linear functions is shown to outperform the classical case by a factor of N × M.

Creating Very True Quantum Algorithms for Quantum Energy Based Computing

NASA Astrophysics Data System (ADS)

Nagata, Koji; Nakamura, Tadao; Geurdes, Han; Batle, Josep; Abdalla, Soliman; Farouk, Ahmed; Diep, Do Ngoc

2017-12-01

An interpretation of quantum mechanics is discussed. It is assumed that quantum is energy. An algorithm by means of the energy interpretation is discussed. An algorithm, based on the energy interpretation, for fast determining a homogeneous linear function f(x) := s.x = s 1 x 1 + s 2 x 2 + ⋯ + s N x N is proposed. Here x = (x 1, … , x N ), x j ∈ R and the coefficients s = (s 1, … , s N ), s j ∈ N. Given the interpolation values (f(1), f(2),...,f(N))=ěc {y}, the unknown coefficients s = (s1(ěc {y}),\\dots , sN(ěc {y})) of the linear function shall be determined, simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of N. Our method is based on the generalized Bernstein-Vazirani algorithm to qudit systems. Next, by using M parallel quantum systems, M homogeneous linear functions are determined, simultaneously. The speed of obtaining the set of M homogeneous linear functions is shown to outperform the classical case by a factor of N × M.

Quantum Linear System Algorithm for Dense Matrices

NASA Astrophysics Data System (ADS)

Wossnig, Leonard; Zhao, Zhikuan; Prakash, Anupam

2018-02-01

Solving linear systems of equations is a frequently encountered problem in machine learning and optimization. Given a matrix A and a vector b the task is to find the vector x such that A x =b . We describe a quantum algorithm that achieves a sparsity-independent runtime scaling of O (κ2√{n }polylog(n )/ɛ ) for an n ×n dimensional A with bounded spectral norm, where κ denotes the condition number of A , and ɛ is the desired precision parameter. This amounts to a polynomial improvement over known quantum linear system algorithms when applied to dense matrices, and poses a new state of the art for solving dense linear systems on a quantum computer. Furthermore, an exponential improvement is achievable if the rank of A is polylogarithmic in the matrix dimension. Our algorithm is built upon a singular value estimation subroutine, which makes use of a memory architecture that allows for efficient preparation of quantum states that correspond to the rows of A and the vector of Euclidean norms of the rows of A .

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.

Using quantum chemistry muscle to flex massive systems: How to respond to something perturbing

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

Bertoni, Colleen

Computational chemistry uses the theoretical advances of quantum mechanics and the algorithmic and hardware advances of computer science to give insight into chemical problems. It is currently possible to do highly accurate quantum chemistry calculations, but the most accurate methods are very computationally expensive. Thus it is only feasible to do highly accurate calculations on small molecules, since typically more computationally efficient methods are also less accurate. The overall goal of my dissertation work has been to try to decrease the computational expense of calculations without decreasing the accuracy. In particular, my dissertation work focuses on fragmentation methods, intermolecular interactionsmore » methods, analytic gradients, and taking advantage of new hardware.« less

Connes distance function on fuzzy sphere and the connection between geometry and statistics

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

Devi, Yendrembam Chaoba, E-mail: chaoba@bose.res.in; Chakraborty, Biswajit, E-mail: biswajit@bose.res.in; Prajapat, Shivraj, E-mail: shraprajapat@gmail.com

An algorithm to compute Connes spectral distance, adaptable to the Hilbert-Schmidt operatorial formulation of non-commutative quantum mechanics, was developed earlier by introducing the appropriate spectral triple and used to compute infinitesimal distances in the Moyal plane, revealing a deep connection between geometry and statistics. In this paper, using the same algorithm, the Connes spectral distance has been calculated in the Hilbert-Schmidt operatorial formulation for the fuzzy sphere whose spatial coordinates satisfy the su(2) algebra. This has been computed for both the discrete and the Perelemov’s SU(2) coherent state. Here also, we get a connection between geometry and statistics which ismore » shown by computing the infinitesimal distance between mixed states on the quantum Hilbert space of a particular fuzzy sphere, indexed by n ∈ ℤ/2.« less

Efficient experimental design of high-fidelity three-qubit quantum gates via genetic programming

NASA Astrophysics Data System (ADS)

Devra, Amit; Prabhu, Prithviraj; Singh, Harpreet; Arvind; Dorai, Kavita

2018-03-01

We have designed efficient quantum circuits for the three-qubit Toffoli (controlled-controlled-NOT) and the Fredkin (controlled-SWAP) gate, optimized via genetic programming methods. The gates thus obtained were experimentally implemented on a three-qubit NMR quantum information processor, with a high fidelity. Toffoli and Fredkin gates in conjunction with the single-qubit Hadamard gates form a universal gate set for quantum computing and are an essential component of several quantum algorithms. Genetic algorithms are stochastic search algorithms based on the logic of natural selection and biological genetics and have been widely used for quantum information processing applications. We devised a new selection mechanism within the genetic algorithm framework to select individuals from a population. We call this mechanism the "Luck-Choose" mechanism and were able to achieve faster convergence to a solution using this mechanism, as compared to existing selection mechanisms. The optimization was performed under the constraint that the experimentally implemented pulses are of short duration and can be implemented with high fidelity. We demonstrate the advantage of our pulse sequences by comparing our results with existing experimental schemes and other numerical optimization methods.

Gradient Optimization for Analytic conTrols - GOAT

NASA Astrophysics Data System (ADS)

Assémat, Elie; Machnes, Shai; Tannor, David; Wilhelm-Mauch, Frank

Quantum optimal control becomes a necessary step in a number of studies in the quantum realm. Recent experimental advances showed that superconducting qubits can be controlled with an impressive accuracy. However, most of the standard optimal control algorithms are not designed to manage such high accuracy. To tackle this issue, a novel quantum optimal control algorithm have been introduced: the Gradient Optimization for Analytic conTrols (GOAT). It avoids the piecewise constant approximation of the control pulse used by standard algorithms. This allows an efficient implementation of very high accuracy optimization. It also includes a novel method to compute the gradient that provides many advantages, e.g. the absence of backpropagation or the natural route to optimize the robustness of the control pulses. This talk will present the GOAT algorithm and a few applications to transmons systems.

pyCTQW: A continuous-time quantum walk simulator on distributed memory computers

NASA Astrophysics Data System (ADS)

Izaac, Josh A.; Wang, Jingbo B.

2015-01-01

In the general field of quantum information and computation, quantum walks are playing an increasingly important role in constructing physical models and quantum algorithms. We have recently developed a distributed memory software package pyCTQW, with an object-oriented Python interface, that allows efficient simulation of large multi-particle CTQW (continuous-time quantum walk)-based systems. In this paper, we present an introduction to the Python and Fortran interfaces of pyCTQW, discuss various numerical methods of calculating the matrix exponential, and demonstrate the performance behavior of pyCTQW on a distributed memory cluster. In particular, the Chebyshev and Krylov-subspace methods for calculating the quantum walk propagation are provided, as well as methods for visualization and data analysis.

Multi-AUV autonomous task planning based on the scroll time domain quantum bee colony optimization algorithm in uncertain environment

PubMed Central

Zhang, Rubo; Yang, Yu

2017-01-01

Research on distributed task planning model for multi-autonomous underwater vehicle (MAUV). A scroll time domain quantum artificial bee colony (STDQABC) optimization algorithm is proposed to solve the multi-AUV optimal task planning scheme. In the uncertain marine environment, the rolling time domain control technique is used to realize a numerical optimization in a narrowed time range. Rolling time domain control is one of the better task planning techniques, which can greatly reduce the computational workload and realize the tradeoff between AUV dynamics, environment and cost. Finally, a simulation experiment was performed to evaluate the distributed task planning performance of the scroll time domain quantum bee colony optimization algorithm. The simulation results demonstrate that the STDQABC algorithm converges faster than the QABC and ABC algorithms in terms of both iterations and running time. The STDQABC algorithm can effectively improve MAUV distributed tasking planning performance, complete the task goal and get the approximate optimal solution. PMID:29186166

Multi-AUV autonomous task planning based on the scroll time domain quantum bee colony optimization algorithm in uncertain environment.

PubMed

Li, Jianjun; Zhang, Rubo; Yang, Yu

2017-01-01

Research on distributed task planning model for multi-autonomous underwater vehicle (MAUV). A scroll time domain quantum artificial bee colony (STDQABC) optimization algorithm is proposed to solve the multi-AUV optimal task planning scheme. In the uncertain marine environment, the rolling time domain control technique is used to realize a numerical optimization in a narrowed time range. Rolling time domain control is one of the better task planning techniques, which can greatly reduce the computational workload and realize the tradeoff between AUV dynamics, environment and cost. Finally, a simulation experiment was performed to evaluate the distributed task planning performance of the scroll time domain quantum bee colony optimization algorithm. The simulation results demonstrate that the STDQABC algorithm converges faster than the QABC and ABC algorithms in terms of both iterations and running time. The STDQABC algorithm can effectively improve MAUV distributed tasking planning performance, complete the task goal and get the approximate optimal solution.

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.

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.

Versatile microwave-driven trapped ion spin system for quantum information processing

PubMed Central

Piltz, Christian; Sriarunothai, Theeraphot; Ivanov, Svetoslav S.; Wölk, Sabine; Wunderlich, Christof

2016-01-01

Using trapped atomic ions, we demonstrate a tailored and versatile effective spin system suitable for quantum simulations and universal quantum computation. By simply applying microwave pulses, selected spins can be decoupled from the remaining system and, thus, can serve as a quantum memory, while simultaneously, other coupled spins perform conditional quantum dynamics. Also, microwave pulses can change the sign of spin-spin couplings, as well as their effective strength, even during the course of a quantum algorithm. Taking advantage of the simultaneous long-range coupling between three spins, a coherent quantum Fourier transform—an essential building block for many quantum algorithms—is efficiently realized. This approach, which is based on microwave-driven trapped ions and is complementary to laser-based methods, opens a new route to overcoming technical and physical challenges in the quest for a quantum simulator and a quantum computer. PMID:27419233

Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm

DOE PAGES

Colless, J. I.; Ramasesh, V. V.; Dahlen, D.; ...

2018-02-12

Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite coherent lifetimes. Hybrid algorithms, such as the variational quantum eigensolver (VQE), leverage classical resources to reduce the required number of quantum gates. Experimental demonstrations of VQE have resulted in calculation of Hamiltonian ground states, and a new theoretical approach based on a quantum subspace expansion (QSE) has outlined a procedure for determining excited states that are central to dynamical processes. Here, we use a superconducting-qubit-based processor to apply the QSE approach to the H 2 molecule, extracting both groundmore » and excited states without the need for auxiliary qubits or additional minimization. Further, we show that this extended protocol can mitigate the effects of incoherent errors, potentially enabling larger-scale quantum simulations without the need for complex error-correction techniques.« less

Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm

NASA Astrophysics Data System (ADS)

Colless, J. I.; Ramasesh, V. V.; Dahlen, D.; Blok, M. S.; Kimchi-Schwartz, M. E.; McClean, J. R.; Carter, J.; de Jong, W. A.; Siddiqi, I.

2018-02-01

Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite coherent lifetimes. Hybrid algorithms, such as the variational quantum eigensolver (VQE), leverage classical resources to reduce the required number of quantum gates. Experimental demonstrations of VQE have resulted in calculation of Hamiltonian ground states, and a new theoretical approach based on a quantum subspace expansion (QSE) has outlined a procedure for determining excited states that are central to dynamical processes. We use a superconducting-qubit-based processor to apply the QSE approach to the H2 molecule, extracting both ground and excited states without the need for auxiliary qubits or additional minimization. Further, we show that this extended protocol can mitigate the effects of incoherent errors, potentially enabling larger-scale quantum simulations without the need for complex error-correction techniques.

Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm

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

Colless, J. I.; Ramasesh, V. V.; Dahlen, D.

Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite coherent lifetimes. Hybrid algorithms, such as the variational quantum eigensolver (VQE), leverage classical resources to reduce the required number of quantum gates. Experimental demonstrations of VQE have resulted in calculation of Hamiltonian ground states, and a new theoretical approach based on a quantum subspace expansion (QSE) has outlined a procedure for determining excited states that are central to dynamical processes. Here, we use a superconducting-qubit-based processor to apply the QSE approach to the H 2 molecule, extracting both groundmore » and excited states without the need for auxiliary qubits or additional minimization. Further, we show that this extended protocol can mitigate the effects of incoherent errors, potentially enabling larger-scale quantum simulations without the need for complex error-correction techniques.« less

Element distinctness revisited

NASA Astrophysics Data System (ADS)

Portugal, Renato

2018-07-01

The element distinctness problem is the problem of determining whether the elements of a list are distinct, that is, if x=(x_1,\\ldots ,x_N) is a list with N elements, we ask whether the elements of x are distinct or not. The solution in a classical computer requires N queries because it uses sorting to check whether there are equal elements. In the quantum case, it is possible to solve the problem in O(N^{2/3}) queries. There is an extension which asks whether there are k colliding elements, known as element k-distinctness problem. This work obtains optimal values of two critical parameters of Ambainis' seminal quantum algorithm (SIAM J Comput 37(1):210-239, 2007). The first critical parameter is the number of repetitions of the algorithm's main block, which inverts the phase of the marked elements and calls a subroutine. The second parameter is the number of quantum walk steps interlaced by oracle queries. We show that, when the optimal values of the parameters are used, the algorithm's success probability is 1-O(N^{1/(k+1)}), quickly approaching 1. The specification of the exact running time and success probability is important in practical applications of this algorithm.

Quantum Molecular Dynamics Simulations of Nanotube Tip Assisted Reactions

NASA Technical Reports Server (NTRS)

Menon, Madhu

1998-01-01

In this report we detail the development and application of an efficient quantum molecular dynamics computational algorithm and its application to the nanotube-tip assisted reactions on silicon and diamond surfaces. The calculations shed interesting insights into the microscopic picture of tip surface interactions.

Symmetry-conserving purification of quantum states within the density matrix renormalization group

DOE PAGES

Nocera, Alberto; Alvarez, Gonzalo

2016-01-28

The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero-temperature or ground-state properties of one-dimensional strongly correlated quantum systems. The development of the algorithm at finite temperature has been a topic of much interest, because of the usefulness of thermodynamics quantities in understanding the physics of condensed matter systems, and because of the increased complexity associated with efficiently computing temperature-dependent properties. The ancilla method is a DMRG technique that enables the computation of these thermodynamic quantities. In this paper, we review the ancilla method, and improve its performance by working on reduced Hilbert spaces andmore » using canonical approaches. Furthermore we explore its applicability beyond spins systems to t-J and Hubbard models.« less

Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle

DOE PAGES

Yang, Zhi -Cheng; Rahmani, Armin; Shabani, Alireza; ...

2017-05-18

We use Pontryagin’s minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian decoherence. Our findings support the choice of evolution ansatz in the recently proposed quantum approximate optimization algorithm. Focusing on the Sherrington-Kirkpatrick spin glass as an example, we find a system-size independent distribution of the duration of pulses, with characteristic time scale set by the inverse of the coupling constants in the Hamiltonian. The optimality of the bang-bang protocols and the characteristic time scale ofmore » the pulses provide an efficient parametrization of the protocol and inform the search for effective hybrid (classical and quantum) schemes for tackling combinatorial optimization problems. Moreover, we find that the success rates of our optimal bang-bang protocols remain high even in the presence of weak external noise and coupling to a thermal bath.« less

Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle

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

Yang, Zhi -Cheng; Rahmani, Armin; Shabani, Alireza

We use Pontryagin’s minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian decoherence. Our findings support the choice of evolution ansatz in the recently proposed quantum approximate optimization algorithm. Focusing on the Sherrington-Kirkpatrick spin glass as an example, we find a system-size independent distribution of the duration of pulses, with characteristic time scale set by the inverse of the coupling constants in the Hamiltonian. The optimality of the bang-bang protocols and the characteristic time scale ofmore » the pulses provide an efficient parametrization of the protocol and inform the search for effective hybrid (classical and quantum) schemes for tackling combinatorial optimization problems. Moreover, we find that the success rates of our optimal bang-bang protocols remain high even in the presence of weak external noise and coupling to a thermal bath.« less

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.

Quantum hydrodynamics: capturing a reactive scattering resonance.

PubMed

Derrickson, Sean W; Bittner, Eric R; Kendrick, Brian K

2005-08-01

The hydrodynamic equations of motion associated with the de Broglie-Bohm formulation of quantum mechanics are solved using a meshless method based upon a moving least-squares approach. An arbitrary Lagrangian-Eulerian frame of reference and a regridding algorithm which adds and deletes computational points are used to maintain a uniform and nearly constant interparticle spacing. The methodology also uses averaged fields to maintain unitary time evolution. The numerical instabilities associated with the formation of nodes in the reflected portion of the wave packet are avoided by adding artificial viscosity to the equations of motion. A new and more robust artificial viscosity algorithm is presented which gives accurate scattering results and is capable of capturing quantum resonances. The methodology is applied to a one-dimensional model chemical reaction that is known to exhibit a quantum resonance. The correlation function approach is used to compute the reactive scattering matrix, reaction probability, and time delay as a function of energy. Excellent agreement is obtained between the scattering results based upon the quantum hydrodynamic approach and those based upon standard quantum mechanics. This is the first clear demonstration of the ability of moving grid approaches to accurately and robustly reproduce resonance structures in a scattering system.

Blind quantum computation with identity authentication

NASA Astrophysics Data System (ADS)

Li, Qin; Li, Zhulin; Chan, Wai Hong; Zhang, Shengyu; Liu, Chengdong

2018-04-01

Blind quantum computation (BQC) allows a client with relatively few quantum resources or poor quantum technologies to delegate his computational problem to a quantum server such that the client's input, output, and algorithm are kept private. However, all existing BQC protocols focus on correctness verification of quantum computation but neglect authentication of participants' identity which probably leads to man-in-the-middle attacks or denial-of-service attacks. In this work, we use quantum identification to overcome such two kinds of attack for BQC, which will be called QI-BQC. We propose two QI-BQC protocols based on a typical single-server BQC protocol and a double-server BQC protocol. The two protocols can ensure both data integrity and mutual identification between participants with the help of a third trusted party (TTP). In addition, an unjammable public channel between a client and a server which is indispensable in previous BQC protocols is unnecessary, although it is required between TTP and each participant at some instant. Furthermore, the method to achieve identity verification in the presented protocols is general and it can be applied to other similar BQC protocols.

Quantum Correlations in Nonlocal Boson Sampling.

PubMed

Shahandeh, Farid; Lund, Austin P; Ralph, Timothy C

2017-09-22

Determination of the quantum nature of correlations between two spatially separated systems plays a crucial role in quantum information science. Of particular interest is the questions of if and how these correlations enable quantum information protocols to be more powerful. Here, we report on a distributed quantum computation protocol in which the input and output quantum states are considered to be classically correlated in quantum informatics. Nevertheless, we show that the correlations between the outcomes of the measurements on the output state cannot be efficiently simulated using classical algorithms. Crucially, at the same time, local measurement outcomes can be efficiently simulated on classical computers. We show that the only known classicality criterion violated by the input and output states in our protocol is the one used in quantum optics, namely, phase-space nonclassicality. As a result, we argue that the global phase-space nonclassicality inherent within the output state of our protocol represents true quantum correlations.

Computation of energy states of hydrogenic quantum dot with two-electrons

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

Yakar, Y., E-mail: yuyakar@yahoo.com; Özmen, A., E-mail: aozmen@selcuk.edu.tr; Çakır, B., E-mail: bcakir@selcuk.edu.tr

2016-03-25

In this study we have investigated the electronic structure of the hydrogenic quantum dot with two electrons inside an impenetrable potential surface. The energy eigenvalues and wavefunctions of the ground and excited states of spherical quantum dot have been calculated by using the Quantum Genetic Algorithm (QGA) and Hartree-Fock Roothaan (HFR) method, and the energies are investigated as a function of dot radius. The results show that as dot radius increases, the energy of quantum dot decreases.

Secure and Efficient Signature Scheme Based on NTRU for Mobile Payment

NASA Astrophysics Data System (ADS)

Xia, Yunhao; You, Lirong; Sun, Zhe; Sun, Zhixin

2017-10-01

Mobile payment becomes more and more popular, however the traditional public-key encryption algorithm has higher requirements for hardware which is not suitable for mobile terminals of limited computing resources. In addition, these public-key encryption algorithms do not have the ability of anti-quantum computing. This paper researches public-key encryption algorithm NTRU for quantum computation through analyzing the influence of parameter q and k on the probability of generating reasonable signature value. Two methods are proposed to improve the probability of generating reasonable signature value. Firstly, increase the value of parameter q. Secondly, add the authentication condition that meet the reasonable signature requirements during the signature phase. Experimental results show that the proposed signature scheme can realize the zero leakage of the private key information of the signature value, and increase the probability of generating the reasonable signature value. It also improve rate of the signature, and avoid the invalid signature propagation in the network, but the scheme for parameter selection has certain restrictions.

Faster quantum searching with almost any diffusion operator

NASA Astrophysics Data System (ADS)

Tulsi, Avatar

2015-05-01

Grover's search algorithm drives a quantum system from an initial state |s > to a desired final state |t > by using selective phase inversions of these two states. Earlier, we studied a generalization of Grover's algorithm that relaxes the assumption of the efficient implementation of Is, the selective phase inversion of the initial state, also known as a diffusion operator. This assumption is known to become a serious handicap in cases of physical interest. Our general search algorithm works with almost any diffusion operator Ds with the only restriction of having |s > as one of its eigenstates. The price that we pay for using any operator is an increase in the number of oracle queries by a factor of O (B ) , where B is a characteristic of the eigenspectrum of Ds and can be large in some situations. Here we show that by using a quantum Fourier transform, we can regain the optimal query complexity of Grover's algorithm without losing the freedom of using any diffusion operator for quantum searching. However, the total number of operators required by the algorithm is still O (B ) times more than that of Grover's algorithm. So our algorithm offers an advantage only if the oracle operator is computationally more expensive than the diffusion operator, which is true in most search problems.

The limits of predictability: Indeterminism and undecidability in classical and quantum physics

NASA Astrophysics Data System (ADS)

Korolev, Alexandre V.

This thesis is a collection of three case studies, investigating various sources of indeterminism and undecidability as they bear upon in principle unpredictability of the behaviour of mechanistic systems in both classical and quantum physics. I begin by examining the sources of indeterminism and acausality in classical physics. Here I discuss the physical significance of an often overlooked and yet important Lipschitz condition, the violation of which underlies the existence of anomalous non-trivial solutions in the Norton-type indeterministic systems. I argue that the singularity arising from the violation of the Lipschitz condition in the systems considered appears to be so fragile as to be easily destroyed by slightly relaxing certain (infinite) idealizations required by these models. In particular, I show that the idealization of an absolutely nondeformable, or infinitely rigid, dome appears to be an essential assumption for anomalous motion to begin; any slightest elastic deformations of the dome due to finite rigidity of the dome destroy the shape of the dome required for indeterminism to obtain. I also consider several modifications of the original Norton's example and show that indeterminism in these cases, too, critically depends on the nature of certain idealizations pertaining to elastic properties of the bodies in these models. As a result, I argue that indeterminism of the Norton-type Lipschitz-indeterministic systems should rather be viewed as an artefact of certain (infinite) idealizations essential for the models, depriving the examples of much of their intended metaphysical import, as, for example, in Norton's antifundamentalist programme. Second, I examine the predictive computational limitations of a classical Laplace's demon. I demonstrate that in situations of self-fulfilling prognoses the class of undecidable propositions about certain future events, in general, is not empty; any Laplace's demon having all the information about the world now will be unable to predict all the future. In order to answer certain questions about the future it needs to resort occasionally to, or to consult with, a demon of a higher order in the computational hierarchy whose computational powers are beyond that of any Turing machine. In computer science such power is attributed to a theoretical device called an Oracle---a device capable of looking through an infinite domain in a finite time. I also discuss the distinction between ontological and epistemological views of determinism, and how adopting Wheeler-Landauer view of physical laws can entangle these aspects on a more fundamental level. Thirdly, I examine a recent proposal from the area of quantum computation purporting to utilize peculiarities of quantum reality to perform hypercomputation. While the current view is that quantum algorithms (such as Shor's) lead to re-description of the complexity space for computational problems, recently it has been argued (by Kieu) that certain novel quantum adiabatic algorithms may even require reconsideration of the whole notion of computability, by being able to break the Turing limit and "compute the non-computable". If implemented, such algorithms could serve as a physical realization of an Oracle needed for a Laplacian demon to accomplish its job. I critically review this latter proposal by exposing the weaknesses of Kieu's quantum adiabatic demon, pointing out its failure to deliver the purported hypercomputation. Regardless of whether the class of hypercomputers is non-empty, Kieu's proposed algorithm is not a member of this distinguished club, and a quantum computer powered Laplace's demon can do no more than its ordinary classical counterpart.

Hamiltonian lattice field theory: Computer calculations using variational methods

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

Zako, Robert L.

1991-12-03

I develop a variational method for systematic numerical computation of physical quantities -- bound state energies and scattering amplitudes -- in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. I present an algorithm for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. I also show how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato`s generalizations of Temple`s formula. The algorithm could bemore » adapted to systems such as atoms and molecules. I show how to compute Green`s functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green`s functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. I discuss the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, I do not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. I apply the method to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. I describe a computer implementation of the method and present numerical results for simple quantum mechanical systems.« less

Quantum neuromorphic hardware for quantum artificial intelligence

NASA Astrophysics Data System (ADS)

Prati, Enrico

2017-08-01

The development of machine learning methods based on deep learning boosted the field of artificial intelligence towards unprecedented achievements and application in several fields. Such prominent results were made in parallel with the first successful demonstrations of fault tolerant hardware for quantum information processing. To which extent deep learning can take advantage of the existence of a hardware based on qubits behaving as a universal quantum computer is an open question under investigation. Here I review the convergence between the two fields towards implementation of advanced quantum algorithms, including quantum deep learning.

Efficient method for computing the maximum-likelihood quantum state from measurements with additive Gaussian noise.

PubMed

Smolin, John A; Gambetta, Jay M; Smith, Graeme

2012-02-17

We provide an efficient method for computing the maximum-likelihood mixed quantum state (with density matrix ρ) given a set of measurement outcomes in a complete orthonormal operator basis subject to Gaussian noise. Our method works by first changing basis yielding a candidate density matrix μ which may have nonphysical (negative) eigenvalues, and then finding the nearest physical state under the 2-norm. Our algorithm takes at worst O(d(4)) for the basis change plus O(d(3)) for finding ρ where d is the dimension of the quantum state. In the special case where the measurement basis is strings of Pauli operators, the basis change takes only O(d(3)) as well. The workhorse of the algorithm is a new linear-time method for finding the closest probability distribution (in Euclidean distance) to a set of real numbers summing to one.

SALUTE Grid Application using Message-Oriented Middleware

NASA Astrophysics Data System (ADS)

Atanassov, E.; Dimitrov, D. Sl.; Gurov, T.

2009-10-01

Stochastic ALgorithms for Ultra-fast Transport in sEmiconductors (SALUTE) is a grid application developed for solving various computationally intensive problems which describe ultra-fast carrier transport in semiconductors. SALUTE studies memory and quantum effects during the relaxation process due to electronphonon interaction in one-band semiconductors or quantum wires. Formally, SALUTE integrates a set of novel Monte Carlo, quasi-Monte Carlo and hybrid algorithms for solving various computationally intensive problems which describe the femtosecond relaxation process of optically excited carriers in one-band semiconductors or quantum wires. In this paper we present application-specific job submission and reservation management tool named a Job Track Server (JTS). It is developed using Message-Oriented middleware to implement robust, versatile job submission and tracing mechanism, which can be tailored to application specific failover and quality of service requirements. Experience from using the JTS for submission of SALUTE jobs is presented.

Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics

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

Kube, Susanna; Lasser, Caroline; Weber, Marcus

2009-04-01

The article addresses the achievable accuracy for a Monte Carlo sampling of Wigner functions in combination with a surface hopping algorithm for non-adiabatic quantum dynamics. The approximation of Wigner functions is realized by an adaption of the Metropolis algorithm for real-valued functions with disconnected support. The integration, which is necessary for computing values of the Wigner function, uses importance sampling with a Gaussian weight function. The numerical experiments agree with theoretical considerations and show an error of 2-3%.

Quantum simulation from the bottom up: the case of rebits

NASA Astrophysics Data System (ADS)

Enshan Koh, Dax; Yuezhen Niu, Murphy; Yoder, Theodore J.

2018-05-01

Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schrödinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately narrow point of view. Just as a classical computer can simulate highly nonlinear functions of classical states, so too can the more general quantum computer simulate nonlinear evolutions of quantum states. We detail one particular simulation of nonlinearity on a quantum computer, showing how the entire class of -unitary evolutions (on n qubits) can be simulated using a unitary, real-amplitude quantum computer (consisting of n  +  1 qubits in total). These operators can be represented as the sum of a linear and antilinear operator, and add an intriguing new set of nonlinear quantum gates to the toolbox of the quantum algorithm designer. Furthermore, a subgroup of these nonlinear evolutions, called the -Cliffords, can be efficiently classically simulated, by making use of the fact that Clifford operators can simulate non-Clifford (in fact, non-linear) operators. This perspective of using the physical operators that we have to simulate non-physical ones that we do not is what we call bottom-up simulation, and we give some examples of its broader implications.

Including Memory Friction in Single- and Two-State Quantum Dynamics Simulations.

PubMed

Brown, Paul A; Messina, Michael

2016-03-03

We present a simple computational algorithm that allows for the inclusion of memory friction in a quantum dynamics simulation of a small, quantum, primary system coupled to many atoms in the surroundings. We show how including a memory friction operator, F̂, in the primary quantum system's Hamiltonian operator builds memory friction into the dynamics of the primary quantum system. We show that, in the harmonic, semi-classical limit, this friction operator causes the classical phase-space centers of a wavepacket to evolve exactly as if it were a classical particle experiencing memory friction. We also show that this friction operator can be used to include memory friction in the quantum dynamics of an anharmonic primary system. We then generalize the algorithm so that it can be used to treat a primary quantum system that is evolving, non-adiabatically on two coupled potential energy surfaces, i.e., a model that can be used to model H atom transfer, for example. We demonstrate this approach's computational ease and flexibility by showing numerical results for both harmonic and anharmonic primary quantum systems in the single surface case. Finally, we present numerical results for a model of non-adiabatic H atom transfer between a reactant and product state that includes memory friction on one or both of the non-adiabatic potential energy surfaces and uncover some interesting dynamical effects of non-memory friction on the H atom transfer process.

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

Comparing, optimizing, and benchmarking quantum-control algorithms in a unifying programming framework

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

Machnes, S.; Institute for Theoretical Physics, University of Ulm, D-89069 Ulm; Sander, U.

2011-08-15

For paving the way to novel applications in quantum simulation, computation, and technology, increasingly large quantum systems have to be steered with high precision. It is a typical task amenable to numerical optimal control to turn the time course of pulses, i.e., piecewise constant control amplitudes, iteratively into an optimized shape. Here, we present a comparative study of optimal-control algorithms for a wide range of finite-dimensional applications. We focus on the most commonly used algorithms: GRAPE methods which update all controls concurrently, and Krotov-type methods which do so sequentially. Guidelines for their use are given and open research questions aremore » pointed out. Moreover, we introduce a unifying algorithmic framework, DYNAMO (dynamic optimization platform), designed to provide the quantum-technology community with a convenient matlab-based tool set for optimal control. In addition, it gives researchers in optimal-control techniques a framework for benchmarking and comparing newly proposed algorithms with the state of the art. It allows a mix-and-match approach with various types of gradients, update and step-size methods as well as subspace choices. Open-source code including examples is made available at http://qlib.info.« less

Quantum Computation using Arrays of N Polar Molecules in Pendular States.

PubMed

Wei, Qi; Cao, Yudong; Kais, Sabre; Friedrich, Bretislav; Herschbach, Dudley

2016-11-18

We investigate several aspects of realizing quantum computation using entangled polar molecules in pendular states. Quantum algorithms typically start from a product state |00⋯0⟩ and we show that up to a negligible error, the ground states of polar molecule arrays can be considered as the unentangled qubit basis state |00⋯0⟩ . This state can be prepared by simply allowing the system to reach thermal equilibrium at low temperature (<1 mK). We also evaluate entanglement, characterized by concurrence of pendular state qubits in dipole arrays as governed by the external electric field, dipole-dipole coupling and number N of molecules in the array. In the parameter regime that we consider for quantum computing, we find that qubit entanglement is modest, typically no greater than 10 -4 , confirming the negligible entanglement in the ground state. We discuss methods for realizing quantum computation in the gate model, measurement-based model, instantaneous quantum polynomial time circuits and the adiabatic model using polar molecules in pendular states. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Quantum computing gates via optimal control

NASA Astrophysics Data System (ADS)

Atia, Yosi; Elias, Yuval; Mor, Tal; Weinstein, Yossi

2014-10-01

We demonstrate the use of optimal control to design two entropy-manipulating quantum gates which are more complex than the corresponding, commonly used, gates, such as CNOT and Toffoli (CCNOT): A two-qubit gate called polarization exchange (PE) and a three-qubit gate called polarization compression (COMP) were designed using GRAPE, an optimal control algorithm. Both gates were designed for a three-spin system. Our design provided efficient and robust nuclear magnetic resonance (NMR) radio frequency (RF) pulses for 13C2-trichloroethylene (TCE), our chosen three-spin system. We then experimentally applied these two quantum gates onto TCE at the NMR lab. Such design of these gates and others could be relevant for near-future applications of quantum computing devices.

Low-Latency Digital Signal Processing for Feedback and Feedforward in Quantum Computing and Communication

NASA Astrophysics Data System (ADS)

Salathé, Yves; Kurpiers, Philipp; Karg, Thomas; Lang, Christian; Andersen, Christian Kraglund; Akin, Abdulkadir; Krinner, Sebastian; Eichler, Christopher; Wallraff, Andreas

2018-03-01

Quantum computing architectures rely on classical electronics for control and readout. Employing classical electronics in a feedback loop with the quantum system allows us to stabilize states, correct errors, and realize specific feedforward-based quantum computing and communication schemes such as deterministic quantum teleportation. These feedback and feedforward operations are required to be fast compared to the coherence time of the quantum system to minimize the probability of errors. We present a field-programmable-gate-array-based digital signal processing system capable of real-time quadrature demodulation, a determination of the qubit state, and a generation of state-dependent feedback trigger signals. The feedback trigger is generated with a latency of 110 ns with respect to the timing of the analog input signal. We characterize the performance of the system for an active qubit initialization protocol based on the dispersive readout of a superconducting qubit and discuss potential applications in feedback and feedforward algorithms.

The scalable implementation of quantum walks using classical light

NASA Astrophysics Data System (ADS)

Goyal, Sandeep K.; Roux, F. S.; Forbes, Andrew; Konrad, Thomas

2014-02-01

A quantum walk is the quantum analog of the classical random walks. Despite their simple structure they form a universal platform to implement any algorithm of quantum computation. However, it is very hard to realize quantum walks with a sufficient number of iterations in quantum systems due to their sensitivity to environmental influences and subsequent loss of coherence. Here we present a scalable implementation scheme for one-dimensional quantum walks for arbitrary number of steps using the orbital angular momentum modes of classical light beams. Furthermore, we show that using the same setup with a minor adjustment we can also realize electric quantum walks.

Entanglement by Path Identity.

PubMed

Krenn, Mario; Hochrainer, Armin; Lahiri, Mayukh; Zeilinger, Anton

2017-02-24

Quantum entanglement is one of the most prominent features of quantum mechanics and forms the basis of quantum information technologies. Here we present a novel method for the creation of quantum entanglement in multipartite and high-dimensional systems. The two ingredients are (i) superposition of photon pairs with different origins and (ii) aligning photons such that their paths are identical. We explain the experimentally feasible creation of various classes of multiphoton entanglement encoded in polarization as well as in high-dimensional Hilbert spaces-starting only from nonentangled photon pairs. For two photons, arbitrary high-dimensional entanglement can be created. The idea of generating entanglement by path identity could also apply to quantum entities other than photons. We discovered the technique by analyzing the output of a computer algorithm. This shows that computer designed quantum experiments can be inspirations for new techniques.

Entanglement by Path Identity

NASA Astrophysics Data System (ADS)

Krenn, Mario; Hochrainer, Armin; Lahiri, Mayukh; Zeilinger, Anton

2017-02-01

Quantum entanglement is one of the most prominent features of quantum mechanics and forms the basis of quantum information technologies. Here we present a novel method for the creation of quantum entanglement in multipartite and high-dimensional systems. The two ingredients are (i) superposition of photon pairs with different origins and (ii) aligning photons such that their paths are identical. We explain the experimentally feasible creation of various classes of multiphoton entanglement encoded in polarization as well as in high-dimensional Hilbert spaces—starting only from nonentangled photon pairs. For two photons, arbitrary high-dimensional entanglement can be created. The idea of generating entanglement by path identity could also apply to quantum entities other than photons. We discovered the technique by analyzing the output of a computer algorithm. This shows that computer designed quantum experiments can be inspirations for new techniques.

Automated Design of Quantum Circuits

NASA Technical Reports Server (NTRS)

Williams, Colin P.; Gray, Alexander G.

2000-01-01

In order to design a quantum circuit that performs a desired quantum computation, it is necessary to find a decomposition of the unitary matrix that represents that computation in terms of a sequence of quantum gate operations. To date, such designs have either been found by hand or by exhaustive enumeration of all possible circuit topologies. In this paper we propose an automated approach to quantum circuit design using search heuristics based on principles abstracted from evolutionary genetics, i.e. using a genetic programming algorithm adapted specially for this problem. We demonstrate the method on the task of discovering quantum circuit designs for quantum teleportation. We show that to find a given known circuit design (one which was hand-crafted by a human), the method considers roughly an order of magnitude fewer designs than naive enumeration. In addition, the method finds novel circuit designs superior to those previously known.

A quantum Fredkin gate.

PubMed

Patel, Raj B; Ho, Joseph; Ferreyrol, Franck; Ralph, Timothy C; Pryde, Geoff J

2016-03-01

Minimizing the resources required to build logic gates into useful processing circuits is key to realizing quantum computers. Although the salient features of a quantum computer have been shown in proof-of-principle experiments, difficulties in scaling quantum systems have made more complex operations intractable. This is exemplified in the classical Fredkin (controlled-SWAP) gate for which, despite theoretical proposals, no quantum analog has been realized. By adding control to the SWAP unitary, we use photonic qubit logic to demonstrate the first quantum Fredkin gate, which promises many applications in quantum information and measurement. We implement example algorithms and generate the highest-fidelity three-photon Greenberger-Horne-Zeilinger states to date. The technique we use allows one to add a control operation to a black-box unitary, something that is impossible in the standard circuit model. Our experiment represents the first use of this technique to control a two-qubit operation and paves the way for larger controlled circuits to be realized efficiently.

Google in a Quantum Network

PubMed Central

Paparo, G. D.; Martin-Delgado, M. A.

2012-01-01

We introduce the characterization of a class of quantum PageRank algorithms in a scenario in which some kind of quantum network is realizable out of the current classical internet web, but no quantum computer is yet available. This class represents a quantization of the PageRank protocol currently employed to list web pages according to their importance. We have found an instance of this class of quantum protocols that outperforms its classical counterpart and may break the classical hierarchy of web pages depending on the topology of the web. PMID:22685626

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.

Quantum logic gates based on ballistic transport in graphene

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

Dragoman, Daniela; Academy of Romanian Scientists, Splaiul Independentei 54, 050094 Bucharest; Dragoman, Mircea, E-mail: mircea.dragoman@imt.ro

2016-03-07

The paper presents various configurations for the implementation of graphene-based Hadamard, C-phase, controlled-NOT, and Toffoli gates working at room temperature. These logic gates, essential for any quantum computing algorithm, involve ballistic graphene devices for qubit generation and processing and can be fabricated using existing nanolithographical techniques. All quantum gate configurations are based on the very large mean-free-paths of carriers in graphene at room temperature.

Spin Glass Patch Planting

NASA Technical Reports Server (NTRS)

Wang, Wenlong; Mandra, Salvatore; Katzgraber, Helmut G.

2016-01-01

In this paper, we propose a patch planting method for creating arbitrarily large spin glass instances with known ground states. The scaling of the computational complexity of these instances with various block numbers and sizes is investigated and compared with random instances using population annealing Monte Carlo and the quantum annealing DW2X machine. The method can be useful for benchmarking tests for future generation quantum annealing machines, classical and quantum mechanical optimization algorithms.

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

Quantum Walk Schemes for Universal Quantum Computation

NASA Astrophysics Data System (ADS)

Underwood, Michael S.

Random walks are a powerful tool for the efficient implementation of algorithms in classical computation. Their quantum-mechanical analogues, called quantum walks, hold similar promise. Quantum walks provide a model of quantum computation that has recently been shown to be equivalent in power to the standard circuit model. As in the classical case, quantum walks take place on graphs and can undergo discrete or continuous evolution, though quantum evolution is unitary and therefore deterministic until a measurement is made. This thesis considers the usefulness of continuous-time quantum walks to quantum computation from the perspectives of both their fundamental power under various formulations, and their applicability in practical experiments. In one extant scheme, logical gates are effected by scattering processes. The results of an exhaustive search for single-qubit operations in this model are presented. It is shown that the number of distinct operations increases exponentially with the number of vertices in the scattering graph. A catalogue of all graphs on up to nine vertices that implement single-qubit unitaries at a specific set of momenta is included in an appendix. I develop a novel scheme for universal quantum computation called the discontinuous quantum walk, in which a continuous-time quantum walker takes discrete steps of evolution via perfect quantum state transfer through small 'widget' graphs. The discontinuous quantum-walk scheme requires an exponentially sized graph, as do prior discrete and continuous schemes. To eliminate the inefficient vertex resource requirement, a computation scheme based on multiple discontinuous walkers is presented. In this model, n interacting walkers inhabiting a graph with 2n vertices can implement an arbitrary quantum computation on an input of length n, an exponential savings over previous universal quantum walk schemes. This is the first quantum walk scheme that allows for the application of quantum error correction. The many-particle quantum walk can be viewed as a single quantum walk undergoing perfect state transfer on a larger weighted graph, obtained via equitable partitioning. I extend this formalism to non-simple graphs. Examples of the application of equitable partitioning to the analysis of quantum walks and many-particle quantum systems are discussed.

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

Rajbhandari, Samyam; NIkam, Akshay; Lai, Pai-Wei

Tensor contractions represent the most compute-intensive core kernels in ab initio computational quantum chemistry and nuclear physics. Symmetries in these tensor contractions makes them difficult to load balance and scale to large distributed systems. In this paper, we develop an efficient and scalable algorithm to contract symmetric tensors. We introduce a novel approach that avoids data redistribution in contracting symmetric tensors while also avoiding redundant storage and maintaining load balance. We present experimental results on two parallel supercomputers for several symmetric contractions that appear in the CCSD quantum chemistry method. We also present a novel approach to tensor redistribution thatmore » can take advantage of parallel hyperplanes when the initial distribution has replicated dimensions, and use collective broadcast when the final distribution has replicated dimensions, making the algorithm very efficient.« less

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.

Finding paths in tree graphs with a quantum walk

NASA Astrophysics Data System (ADS)

Koch, Daniel; Hillery, Mark

2018-01-01

We analyze the potential for different types of searches using the formalism of scattering random walks on quantum computers. Given a particular type of graph consisting of nodes and connections, a "tree maze," we would like to find a selected final node as quickly as possible, faster than any classical search algorithm. We show that this can be done using a quantum random walk, both through numerical calculations as well as by using the eigenvectors and eigenvalues of the quantum system.

In Vivo EPR Resolution Enhancement Using Techniques Known from Quantum Computing Spin Technology.

PubMed

Rahimi, Robabeh; Halpern, Howard J; Takui, Takeji

2017-01-01

A crucial issue with in vivo biological/medical EPR is its low signal-to-noise ratio, giving rise to the low spectroscopic resolution. We propose quantum hyperpolarization techniques based on 'Heat Bath Algorithmic Cooling', allowing possible approaches for improving the resolution in magnetic resonance spectroscopy and imaging.

Quantum phase transitions in a two-dimensional quantum XYX model: ground-state fidelity and entanglement.

PubMed

Li, Bo; Li, Sheng-Hao; Zhou, Huan-Qiang

2009-06-01

A systematic analysis is performed for quantum phase transitions in a two-dimensional anisotropic spin-1/2 antiferromagnetic XYX model in an external magnetic field. With the help of an innovative tensor network algorithm, we compute the fidelity per lattice site to demonstrate that the field-induced quantum phase transition is unambiguously characterized by a pinch point on the fidelity surface, marking a continuous phase transition. We also compute an entanglement estimator, defined as a ratio between the one-tangle and the sum of squared concurrences, to identify both the factorizing field and the critical point, resulting in a quantitative agreement with quantum Monte Carlo simulation. In addition, the local order parameter is "derived" from the tensor network representation of the system's ground-state wave functions.

Quantum Image Processing and Its Application to Edge Detection: Theory and Experiment

NASA Astrophysics Data System (ADS)

Yao, Xi-Wei; Wang, Hengyan; Liao, Zeyang; Chen, Ming-Cheng; Pan, Jian; Li, Jun; Zhang, Kechao; Lin, Xingcheng; Wang, Zhehui; Luo, Zhihuang; Zheng, Wenqiang; Li, Jianzhong; Zhao, Meisheng; Peng, Xinhua; Suter, Dieter

2017-07-01

Processing of digital images is continuously gaining in volume and relevance, with concomitant demands on data storage, transmission, and processing power. Encoding the image information in quantum-mechanical systems instead of classical ones and replacing classical with quantum information processing may alleviate some of these challenges. By encoding and processing the image information in quantum-mechanical systems, we here demonstrate the framework of quantum image processing, where a pure quantum state encodes the image information: we encode the pixel values in the probability amplitudes and the pixel positions in the computational basis states. Our quantum image representation reduces the required number of qubits compared to existing implementations, and we present image processing algorithms that provide exponential speed-up over their classical counterparts. For the commonly used task of detecting the edge of an image, we propose and implement a quantum algorithm that completes the task with only one single-qubit operation, independent of the size of the image. This demonstrates the potential of quantum image processing for highly efficient image and video processing in the big data era.

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

A formulation of a matrix sparsity approach for the quantum ordered search algorithm

NASA Astrophysics Data System (ADS)

Parmar, Jupinder; Rahman, Saarim; Thiara, Jaskaran

One specific subset of quantum algorithms is Grovers Ordered Search Problem (OSP), the quantum counterpart of the classical binary search algorithm, which utilizes oracle functions to produce a specified value within an ordered database. Classically, the optimal algorithm is known to have a log2N complexity; however, Grovers algorithm has been found to have an optimal complexity between the lower bound of ((lnN-1)/π≈0.221log2N) and the upper bound of 0.433log2N. We sought to lower the known upper bound of the OSP. With Farhi et al. MITCTP 2815 (1999), arXiv:quant-ph/9901059], we see that the OSP can be resolved into a translational invariant algorithm to create quantum query algorithm restraints. With these restraints, one can find Laurent polynomials for various k — queries — and N — database sizes — thus finding larger recursive sets to solve the OSP and effectively reducing the upper bound. These polynomials are found to be convex functions, allowing one to make use of convex optimization to find an improvement on the known bounds. According to Childs et al. [Phys. Rev. A 75 (2007) 032335], semidefinite programming, a subset of convex optimization, can solve the particular problem represented by the constraints. We were able to implement a program abiding to their formulation of a semidefinite program (SDP), leading us to find that it takes an immense amount of storage and time to compute. To combat this setback, we then formulated an approach to improve results of the SDP using matrix sparsity. Through the development of this approach, along with an implementation of a rudimentary solver, we demonstrate how matrix sparsity reduces the amount of time and storage required to compute the SDP — overall ensuring further improvements will likely be made to reach the theorized lower bound.

Complete Bell-state analysis for superconducting-quantum-interference-device qubits with a transitionless tracking algorithm

NASA Astrophysics Data System (ADS)

Kang, Yi-Hao; Chen, Ye-Hong; Shi, Zhi-Cheng; Huang, Bi-Hua; Song, Jie; Xia, Yan

2017-08-01

We propose a protocol for complete Bell-state analysis for two superconducting-quantum-interference-device qubits. The Bell-state analysis could be completed by using a sequence of microwave pulses designed by the transitionless tracking algorithm, which is a useful method in the technique of shortcut to adiabaticity. After the whole process, the information for distinguishing four Bell states will be encoded on two auxiliary qubits, while the Bell states remain unchanged. One can read out the information by detecting the auxiliary qubits. Thus the Bell-state analysis is nondestructive. The numerical simulations show that the protocol possesses a high success probability of distinguishing each Bell state with current experimental technology even when decoherence is taken into account. Thus, the protocol may have potential applications for the information readout in quantum communications and quantum computations in superconducting quantum networks.

QDENSITY—A Mathematica Quantum Computer simulation

NASA Astrophysics Data System (ADS)

Juliá-Díaz, Bruno; Burdis, Joseph M.; Tabakin, Frank

2006-06-01

This Mathematica 5.2 package is a simulation of a Quantum Computer. The program provides a modular, instructive approach for generating the basic elements that make up a quantum circuit. The main emphasis is on using the density matrix, although an approach using state vectors is also implemented in the package. The package commands are defined in Qdensity.m which contains the tools needed in quantum circuits, e.g., multiqubit kets, projectors, gates, etc. Selected examples of the basic commands are presented here and a tutorial notebook, Tutorial.nb is provided with the package (available on our website) that serves as a full guide to the package. Finally, application is made to a variety of relevant cases, including Teleportation, Quantum Fourier transform, Grover's search and Shor's algorithm, in separate notebooks: QFT.nb, Teleportation.nb, Grover.nb and Shor.nb where each algorithm is explained in detail. Finally, two examples of the construction and manipulation of cluster states, which are part of "one way computing" ideas, are included as an additional tool in the notebook Cluster.nb. A Mathematica palette containing most commands in QDENSITY is also included: QDENSpalette.nb. Program summaryTitle of program: QDENSITY Catalogue identifier: ADXH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXH_v1_0 Program available from: CPC Program Library, Queen's University of Belfast, N. Ireland Operating systems: Any which supports Mathematica; tested under Microsoft Windows XP, Macintosh OS X, and Linux FC4 Programming language used: Mathematica 5.2 No. of bytes in distributed program, including test data, etc.: 180 581 No. of lines in distributed program, including test data, etc.: 19 382 Distribution format: tar.gz Method of solution: A Mathematica package is provided which contains commands to create and analyze quantum circuits. Several Mathematica notebooks containing relevant examples: Teleportation, Shor's Algorithm and Grover's search are explained in detail. A tutorial, Tutorial.nb is also enclosed. QDENSITY is available at http://www.pitt.edu/~tabakin/QDENSITY.

Black hole state counting in loop quantum gravity: a number-theoretical approach.

PubMed

Agulló, Iván; Barbero G, J Fernando; Díaz-Polo, Jacobo; Fernández-Borja, Enrique; Villaseñor, Eduardo J S

2008-05-30

We give an efficient method, combining number-theoretic and combinatorial ideas, to exactly compute black hole entropy in the framework of loop quantum gravity. Along the way we provide a complete characterization of the relevant sector of the spectrum of the area operator, including degeneracies, and explicitly determine the number of solutions to the projection constraint. We use a computer implementation of the proposed algorithm to confirm and extend previous results on the detailed structure of the black hole degeneracy spectrum.

Design of automata theory of cubical complexes with applications to diagnosis and algorithmic description

NASA Technical Reports Server (NTRS)

Roth, J. P.

1972-01-01

Methods for development of logic design together with algorithms for failure testing, a method for design of logic for ultra-large-scale integration, extension of quantum calculus to describe the functional behavior of a mechanism component-by-component and to computer tests for failures in the mechanism using the diagnosis algorithm, and the development of an algorithm for the multi-output 2-level minimization problem are discussed.

Design of automata theory of cubical complexes with applications to diagnosis and algorithmic description

NASA Technical Reports Server (NTRS)

Roth, J. P.

1972-01-01

The following problems are considered: (1) methods for development of logic design together with algorithms, so that it is possible to compute a test for any failure in the logic design, if such a test exists, and developing algorithms and heuristics for the purpose of minimizing the computation for tests; and (2) a method of design of logic for ultra LSI (large scale integration). It was discovered that the so-called quantum calculus can be extended to render it possible: (1) to describe the functional behavior of a mechanism component by component, and (2) to compute tests for failures, in the mechanism, using the diagnosis algorithm. The development of an algorithm for the multioutput two-level minimization problem is presented and the program MIN 360 was written for this algorithm. The program has options of mode (exact minimum or various approximations), cost function, cost bound, etc., providing flexibility.

Adaptive quantum computation in changing environments using projective simulation

NASA Astrophysics Data System (ADS)

Tiersch, M.; Ganahl, E. J.; Briegel, H. J.

2015-08-01

Quantum information processing devices need to be robust and stable against external noise and internal imperfections to ensure correct operation. In a setting of measurement-based quantum computation, we explore how an intelligent agent endowed with a projective simulator can act as controller to adapt measurement directions to an external stray field of unknown magnitude in a fixed direction. We assess the agent’s learning behavior in static and time-varying fields and explore composition strategies in the projective simulator to improve the agent’s performance. We demonstrate the applicability by correcting for stray fields in a measurement-based algorithm for Grover’s search. Thereby, we lay out a path for adaptive controllers based on intelligent agents for quantum information tasks.

Adaptive quantum computation in changing environments using projective simulation

PubMed Central

Tiersch, M.; Ganahl, E. J.; Briegel, H. J.

2015-01-01

Quantum information processing devices need to be robust and stable against external noise and internal imperfections to ensure correct operation. In a setting of measurement-based quantum computation, we explore how an intelligent agent endowed with a projective simulator can act as controller to adapt measurement directions to an external stray field of unknown magnitude in a fixed direction. We assess the agent’s learning behavior in static and time-varying fields and explore composition strategies in the projective simulator to improve the agent’s performance. We demonstrate the applicability by correcting for stray fields in a measurement-based algorithm for Grover’s search. Thereby, we lay out a path for adaptive controllers based on intelligent agents for quantum information tasks. PMID:26260263

Quantum Error Correction with Biased Noise

NASA Astrophysics Data System (ADS)

Brooks, Peter

Quantum computing offers powerful new techniques for speeding up the calculation of many classically intractable problems. Quantum algorithms can allow for the efficient simulation of physical systems, with applications to basic research, chemical modeling, and drug discovery; other algorithms have important implications for cryptography and internet security. At the same time, building a quantum computer is a daunting task, requiring the coherent manipulation of systems with many quantum degrees of freedom while preventing environmental noise from interacting too strongly with the system. Fortunately, we know that, under reasonable assumptions, we can use the techniques of quantum error correction and fault tolerance to achieve an arbitrary reduction in the noise level. In this thesis, we look at how additional information about the structure of noise, or "noise bias," can improve or alter the performance of techniques in quantum error correction and fault tolerance. In Chapter 2, we explore the possibility of designing certain quantum gates to be extremely robust with respect to errors in their operation. This naturally leads to structured noise where certain gates can be implemented in a protected manner, allowing the user to focus their protection on the noisier unprotected operations. In Chapter 3, we examine how to tailor error-correcting codes and fault-tolerant quantum circuits in the presence of dephasing biased noise, where dephasing errors are far more common than bit-flip errors. By using an appropriately asymmetric code, we demonstrate the ability to improve the amount of error reduction and decrease the physical resources required for error correction. In Chapter 4, we analyze a variety of protocols for distilling magic states, which enable universal quantum computation, in the presence of faulty Clifford operations. Here again there is a hierarchy of noise levels, with a fixed error rate for faulty gates, and a second rate for errors in the distilled states which decreases as the states are distilled to better quality. The interplay of of these different rates sets limits on the achievable distillation and how quickly states converge to that limit.

High-Fidelity Single-Shot Toffoli Gate via Quantum Control.

PubMed

Zahedinejad, Ehsan; Ghosh, Joydip; Sanders, Barry C

2015-05-22

A single-shot Toffoli, or controlled-controlled-not, gate is desirable for classical and quantum information processing. The Toffoli gate alone is universal for reversible computing and, accompanied by the Hadamard gate, forms a universal gate set for quantum computing. The Toffoli gate is also a key ingredient for (nontopological) quantum error correction. Currently Toffoli gates are achieved by decomposing into sequentially implemented single- and two-qubit gates, which require much longer times and yields lower overall fidelities compared to a single-shot implementation. We develop a quantum-control procedure to construct a single-shot Toffoli gate for three nearest-neighbor-coupled superconducting transmon systems such that the fidelity is 99.9% and is as fast as an entangling two-qubit gate under the same realistic conditions. The gate is achieved by a nongreedy quantum control procedure using our enhanced version of the differential evolution algorithm.

Feedback quantum control of molecular electronic population transfer

NASA Astrophysics Data System (ADS)

Bardeen, Christopher J.; Yakovlev, Vladislav V.; Wilson, Kent R.; Carpenter, Scott D.; Weber, Peter M.; Warren, Warren S.

1997-11-01

Feedback quantum control, where the sample `teaches' a computer-controlled arbitrary lightform generator to find the optimal light field, is experimentally demonstrated for a molecular system. Femtosecond pulses tailored by a computer-controlled acousto-optic pulse shaper excite fluorescence from laser dye molecules in solution. Fluorescence and laser power are monitored, and the computer uses the experimental data and a genetic algorithm to optimize population transfer from ground to first excited state. Both efficiency (the ratio of excited state population to laser energy) and effectiveness (total excited state population) are optimized. Potential use as an `automated theory tester' is discussed.

Exploring Do-It-Yourself Approaches in Computational Quantum Chemistry: The Pedagogical Benefits of the Classical Boys Algorithm

ERIC Educational Resources Information Center

Orsini, Gabriele

2015-01-01

The ever-increasing impact of molecular quantum calculations over chemical sciences implies a strong and urgent need for the elaboration of proper teaching strategies in university curricula. In such perspective, this paper proposes an extensive project for a student-driven, cooperative, from-scratch implementation of a general Hartree-Fock…

Chemical application of diffusion quantum Monte Carlo

NASA Technical Reports Server (NTRS)

Reynolds, P. J.; Lester, W. A., Jr.

1984-01-01

The diffusion quantum Monte Carlo (QMC) method gives a stochastic solution to the Schroedinger equation. This approach is receiving increasing attention in chemical applications as a result of its high accuracy. However, reducing statistical uncertainty remains a priority because chemical effects are often obtained as small differences of large numbers. As an example, the single-triplet splitting of the energy of the methylene molecule CH sub 2 is given. The QMC algorithm was implemented on the CYBER 205, first as a direct transcription of the algorithm running on the VAX 11/780, and second by explicitly writing vector code for all loops longer than a crossover length C. The speed of the codes relative to one another as a function of C, and relative to the VAX, are discussed. The computational time dependence obtained versus the number of basis functions is discussed and this is compared with that obtained from traditional quantum chemistry codes and that obtained from traditional computer architectures.

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.

Towards non-classical walks with bright laser pulses

NASA Astrophysics Data System (ADS)

Sephton, B.; Dudley, A.; Forbes, A.

2017-08-01

In the avid search for means to increase computational power in comparison to that which is currently available, quantum walks (QWs) have become a promising option with derived quantum algorithms providing an associated speed up compared to what is currently used for implementation in classical computers. It has additionally been shown that the physical implementation of QWs will provide a successful computational basis for a quantum computer. It follows that considerable drive for finding such means has been occurring over the 20+ years since its introduction with phenomena such as electrons and photons being employed. Principal problems encountered with such quantum systems involve the vulnerability to environmental influence as well as scalability of the systems. Here we outline how to perform the QW due to interference characteristics inherent in the phenomenon, to mitigate these challenges. We utilize the properties of vector beams to physically implement such a walk in orbital angular momentum space by manipulating polarization and exploiting the non-separability of such beams.

Positive Wigner functions render classical simulation of quantum computation efficient.

PubMed

Mari, A; Eisert, J

2012-12-07

We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as discrete variable systems in odd prime dimensions, two cases which will be treated on entirely the same footing. Noting the fact that Clifford and Gaussian operations preserve the positivity of the Wigner function, our result generalizes the Gottesman-Knill theorem. Our algorithm provides a way of sampling from the output distribution of a computation or a simulation, including the efficient sampling from an approximate output distribution in the case of sampling imperfections for initial states, gates, or measurements. In this sense, this work highlights the role of the positive Wigner function as separating classically efficiently simulable systems from those that are potentially universal for quantum computing and simulation, and it emphasizes the role of negativity of the Wigner function as a computational resource.

Quantum Error Correction Protects Quantum Search Algorithms Against Decoherence

PubMed Central

Botsinis, Panagiotis; Babar, Zunaira; Alanis, Dimitrios; Chandra, Daryus; Nguyen, Hung; Ng, Soon Xin; Hanzo, Lajos

2016-01-01

When quantum computing becomes a wide-spread commercial reality, Quantum Search Algorithms (QSA) and especially Grover’s QSA will inevitably be one of their main applications, constituting their cornerstone. Most of the literature assumes that the quantum circuits are free from decoherence. Practically, decoherence will remain unavoidable as is the Gaussian noise of classic circuits imposed by the Brownian motion of electrons, hence it may have to be mitigated. In this contribution, we investigate the effect of quantum noise on the performance of QSAs, in terms of their success probability as a function of the database size to be searched, when decoherence is modelled by depolarizing channels’ deleterious effects imposed on the quantum gates. Moreover, we employ quantum error correction codes for limiting the effects of quantum noise and for correcting quantum flips. More specifically, we demonstrate that, when we search for a single solution in a database having 4096 entries using Grover’s QSA at an aggressive depolarizing probability of 10−3, the success probability of the search is 0.22 when no quantum coding is used, which is improved to 0.96 when Steane’s quantum error correction code is employed. Finally, apart from Steane’s code, the employment of Quantum Bose-Chaudhuri-Hocquenghem (QBCH) codes is also considered. PMID:27924865

Computation in generalised probabilisitic theories

NASA Astrophysics Data System (ADS)

Lee, Ciarán M.; Barrett, Jonathan

2015-08-01

From the general difficulty of simulating quantum systems using classical systems, and in particular the existence of an efficient quantum algorithm for factoring, it is likely that quantum computation is intrinsically more powerful than classical computation. At present, the best upper bound known for the power of quantum computation is that {{BQP}}\\subseteq {{AWPP}}, where {{AWPP}} is a classical complexity class (known to be included in {{PP}}, hence {{PSPACE}}). This work investigates limits on computational power that are imposed by simple physical, or information theoretic, principles. To this end, we define a circuit-based model of computation in a class of operationally-defined theories more general than quantum theory, and ask: what is the minimal set of physical assumptions under which the above inclusions still hold? We show that given only an assumption of tomographic locality (roughly, that multipartite states and transformations can be characterized by local measurements), efficient computations are contained in {{AWPP}}. This inclusion still holds even without assuming a basic notion of causality (where the notion is, roughly, that probabilities for outcomes cannot depend on future measurement choices). Following Aaronson, we extend the computational model by allowing post-selection on measurement outcomes. Aaronson showed that the corresponding quantum complexity class, {{PostBQP}}, is equal to {{PP}}. Given only the assumption of tomographic locality, the inclusion in {{PP}} still holds for post-selected computation in general theories. Hence in a world with post-selection, quantum theory is optimal for computation in the space of all operational theories. We then consider whether one can obtain relativized complexity results for general theories. It is not obvious how to define a sensible notion of a computational oracle in the general framework that reduces to the standard notion in the quantum case. Nevertheless, it is possible to define computation relative to a ‘classical oracle’. Then, we show there exists a classical oracle relative to which efficient computation in any theory satisfying the causality assumption does not include {{NP}}.

Entanglement spectroscopy on a quantum computer

NASA Astrophysics Data System (ADS)

Johri, Sonika; Steiger, Damian S.; Troyer, Matthias

2017-11-01

We present a quantum algorithm to compute the entanglement spectrum of arbitrary quantum states. The interesting universal part of the entanglement spectrum is typically contained in the largest eigenvalues of the density matrix which can be obtained from the lower Renyi entropies through the Newton-Girard method. Obtaining the p largest eigenvalues (λ1>λ2⋯>λp ) requires a parallel circuit depth of O [p (λ1/λp) p] and O [p log(N )] qubits where up to p copies of the quantum state defined on a Hilbert space of size N are needed as the input. We validate this procedure for the entanglement spectrum of the topologically ordered Laughlin wave function corresponding to the quantum Hall state at filling factor ν =1 /3 . Our scaling analysis exposes the tradeoffs between time and number of qubits for obtaining the entanglement spectrum in the thermodynamic limit using finite-size digital quantum computers. We also illustrate the utility of the second Renyi entropy in predicting a topological phase transition and in extracting the localization length in a many-body localized system.

QDENSITY—A Mathematica quantum computer simulation

NASA Astrophysics Data System (ADS)

Juliá-Díaz, Bruno; Burdis, Joseph M.; Tabakin, Frank

2009-03-01

This Mathematica 6.0 package is a simulation of a Quantum Computer. The program provides a modular, instructive approach for generating the basic elements that make up a quantum circuit. The main emphasis is on using the density matrix, although an approach using state vectors is also implemented in the package. The package commands are defined in Qdensity.m which contains the tools needed in quantum circuits, e.g., multiqubit kets, projectors, gates, etc. New version program summaryProgram title: QDENSITY 2.0 Catalogue identifier: ADXH_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXH_v2_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.: 26 055 No. of bytes in distributed program, including test data, etc.: 227 540 Distribution format: tar.gz Programming language: Mathematica 6.0 Operating system: Any which supports Mathematica; tested under Microsoft Windows XP, Macintosh OS X, and Linux FC4 Catalogue identifier of previous version: ADXH_v1_0 Journal reference of previous version: Comput. Phys. Comm. 174 (2006) 914 Classification: 4.15 Does the new version supersede the previous version?: Offers an alternative, more up to date, implementation Nature of problem: Analysis and design of quantum circuits, quantum algorithms and quantum clusters. Solution method: A Mathematica package is provided which contains commands to create and analyze quantum circuits. Several Mathematica notebooks containing relevant examples: Teleportation, Shor's Algorithm and Grover's search are explained in detail. A tutorial, Tutorial.nb is also enclosed. Reasons for new version: The package has been updated to make it fully compatible with Mathematica 6.0 Summary of revisions: The package has been updated to make it fully compatible with Mathematica 6.0 Running time: Most examples included in the package, e.g., the tutorial, Shor's examples, Teleportation examples and Grover's search, run in less than a minute on a Pentium 4 processor (2.6 GHz). The running time for a quantum computation depends crucially on the number of qubits employed.

Quantum simulation of dissipative processes without reservoir engineering

DOE PAGES

Di Candia, R.; Pedernales, J. S.; del Campo, A.; ...

2015-05-29

We present a quantum algorithm to simulate general finite dimensional Lindblad master equations without the requirement of engineering the system-environment interactions. The proposed method is able to simulate both Markovian and non-Markovian quantum dynamics. It consists in the quantum computation of the dissipative corrections to the unitary evolution of the system of interest, via the reconstruction of the response functions associated with the Lindblad operators. Our approach is equally applicable to dynamics generated by effectively non-Hermitian Hamiltonians. We confirm the quality of our method providing specific error bounds that quantify its accuracy.

Divide and conquer approach to quantum Hamiltonian simulation

NASA Astrophysics Data System (ADS)

Hadfield, Stuart; Papageorgiou, Anargyros

2018-04-01

We show a divide and conquer approach for simulating quantum mechanical systems on quantum computers. We can obtain fast simulation algorithms using Hamiltonian structure. Considering a sum of Hamiltonians we split them into groups, simulate each group separately, and combine the partial results. Simulation is customized to take advantage of the properties of each group, and hence yield refined bounds to the overall simulation cost. We illustrate our results using the electronic structure problem of quantum chemistry, where we obtain significantly improved cost estimates under very mild assumptions.

Exact Dynamics via Poisson Process: a unifying Monte Carlo paradigm

NASA Astrophysics Data System (ADS)

Gubernatis, James

2014-03-01

A common computational task is solving a set of ordinary differential equations (o.d.e.'s). A little known theorem says that the solution of any set of o.d.e.'s is exactly solved by the expectation value over a set of arbitary Poisson processes of a particular function of the elements of the matrix that defines the o.d.e.'s. The theorem thus provides a new starting point to develop real and imaginary-time continous-time solvers for quantum Monte Carlo algorithms, and several simple observations enable various quantum Monte Carlo techniques and variance reduction methods to transfer to a new context. I will state the theorem, note a transformation to a very simple computational scheme, and illustrate the use of some techniques from the directed-loop algorithm in context of the wavefunction Monte Carlo method that is used to solve the Lindblad master equation for the dynamics of open quantum systems. I will end by noting that as the theorem does not depend on the source of the o.d.e.'s coming from quantum mechanics, it also enables the transfer of continuous-time methods from quantum Monte Carlo to the simulation of various classical equations of motion heretofore only solved deterministically.

On the role of dealing with quantum coherence in amplitude amplification

NASA Astrophysics Data System (ADS)

Rastegin, Alexey E.

2018-07-01

Amplitude amplification is one of primary tools in building algorithms for quantum computers. This technique generalizes key ideas of the Grover search algorithm. Potentially useful modifications are connected with changing phases in the rotation operations and replacing the intermediate Hadamard transform with arbitrary unitary one. In addition, arbitrary initial distribution of the amplitudes may be prepared. We examine trade-off relations between measures of quantum coherence and the success probability in amplitude amplification processes. As measures of coherence, the geometric coherence and the relative entropy of coherence are considered. In terms of the relative entropy of coherence, complementarity relations with the success probability seem to be the most expository. The general relations presented are illustrated within several model scenarios of amplitude amplification processes.

Work Measurement as a Generalized Quantum Measurement

NASA Astrophysics Data System (ADS)

Roncaglia, Augusto J.; Cerisola, Federico; Paz, Juan Pablo

2014-12-01

We present a new method to measure the work w performed on a driven quantum system and to sample its probability distribution P (w ). The method is based on a simple fact that remained unnoticed until now: Work on a quantum system can be measured by performing a generalized quantum measurement at a single time. Such measurement, which technically speaking is denoted as a positive operator valued measure reduces to an ordinary projective measurement on an enlarged system. This observation not only demystifies work measurement but also suggests a new quantum algorithm to efficiently sample the distribution P (w ). This can be used, in combination with fluctuation theorems, to estimate free energies of quantum states on a quantum computer.

Physical realization of topological quantum walks on IBM-Q and beyond

NASA Astrophysics Data System (ADS)

Balu, Radhakrishnan; Castillo, Daniel; Siopsis, George

2018-07-01

We discuss an efficient physical realization of topological quantum walks on a one-dimensional finite lattice with periodic boundary conditions (circle). The N-point lattice is realized with {log}}2N qubits, and the quantum circuit utilizes a number of quantum gates that are polynomial in the number of qubits. In a certain scaling limit, we show that a large number of steps are implemented with a number of quantum gates which are independent of the number of steps. We ran the quantum algorithm on the IBM-Q five-qubit quantum computer, thus experimentally demonstrating topological features, such as boundary bound states, on a one-dimensional lattice with N = 4 points.

Quantum neural network-based EEG filtering for a brain-computer interface.

PubMed

Gandhi, Vaibhav; Prasad, Girijesh; Coyle, Damien; Behera, Laxmidhar; McGinnity, Thomas Martin

2014-02-01

A novel neural information processing architecture inspired by quantum mechanics and incorporating the well-known Schrodinger wave equation is proposed in this paper. The proposed architecture referred to as recurrent quantum neural network (RQNN) can characterize a nonstationary stochastic signal as time-varying wave packets. A robust unsupervised learning algorithm enables the RQNN to effectively capture the statistical behavior of the input signal and facilitates the estimation of signal embedded in noise with unknown characteristics. The results from a number of benchmark tests show that simple signals such as dc, staircase dc, and sinusoidal signals embedded within high noise can be accurately filtered and particle swarm optimization can be employed to select model parameters. The RQNN filtering procedure is applied in a two-class motor imagery-based brain-computer interface where the objective was to filter electroencephalogram (EEG) signals before feature extraction and classification to increase signal separability. A two-step inner-outer fivefold cross-validation approach is utilized to select the algorithm parameters subject-specifically for nine subjects. It is shown that the subject-specific RQNN EEG filtering significantly improves brain-computer interface performance compared to using only the raw EEG or Savitzky-Golay filtered EEG across multiple sessions.

The full spectrum of AdS5/CFT4 I: representation theory and one-loop Q-system

NASA Astrophysics Data System (ADS)

Marboe, Christian; Volin, Dmytro

2018-04-01

With the formulation of the quantum spectral curve for the AdS5/CFT4 integrable system, it became potentially possible to compute its full spectrum with high efficiency. This is the first paper in a series devoted to the explicit design of such computations, with no restrictions to particular subsectors being imposed. We revisit the representation theoretical classification of possible states in the spectrum and map the symmetry multiplets to solutions of the quantum spectral curve at zero coupling. To this end it is practical to introduce a generalisation of Young diagrams to the case of non-compact representations and define algebraic Q-systems directly on these diagrams. Furthermore, we propose an algorithm to explicitly solve such Q-systems that circumvents the traditional usage of Bethe equations and simplifies the computation effort. For example, our algorithm quickly obtains explicit analytic results for all 495 multiplets that accommodate single-trace operators in N=4 SYM with classical conformal dimension up to \\frac{13}{2} . We plan to use these results as the seed for solving the quantum spectral curve perturbatively to high loop orders in the next paper of the series.

Do quantum strategies always win?

NASA Astrophysics Data System (ADS)

Anand, Namit; Benjamin, Colin

2015-11-01

In a seminal paper, Meyer (Phys Rev Lett 82:1052, 1999) described the advantages of quantum game theory by looking at the classical penny flip game. A player using a quantum strategy can win against a classical player almost 100 % of the time. Here we make a slight modification to the quantum game, with the two players sharing an entangled state to begin with. We then analyze two different scenarios: First in which quantum player makes unitary transformations to his qubit, while the classical player uses a pure strategy of either flipping or not flipping the state of his qubit. In this case, the quantum player always wins against the classical player. In the second scenario, we have the quantum player making similar unitary transformations, while the classical player makes use of a mixed strategy wherein he either flips or not with some probability " p." We show that in the second scenario, 100 % win record of a quantum player is drastically reduced and for a particular probability " p" the classical player can even win against the quantum player. This is of possible relevance to the field of quantum computation as we show that in this quantum game of preserving versus destroying entanglement a particular classical algorithm can beat the quantum algorithm.

Non-stoquastic Hamiltonians in quantum annealing via geometric phases

NASA Astrophysics Data System (ADS)

Vinci, Walter; Lidar, Daniel A.

2017-09-01

We argue that a complete description of quantum annealing implemented with continuous variables must take into account the non-adiabatic Aharonov-Anandan geometric phase that arises when the system Hamiltonian changes during the anneal. We show that this geometric effect leads to the appearance of non-stoquasticity in the effective quantum Ising Hamiltonians that are typically used to describe quantum annealing with flux qubits. We explicitly demonstrate the effect of this geometric non-stoquasticity when quantum annealing is performed with a system of one and two coupled flux qubits. The realization of non-stoquastic Hamiltonians has important implications from a computational complexity perspective, since it is believed that in many cases quantum annealing with stoquastic Hamiltonians can be efficiently simulated via classical algorithms such as Quantum Monte Carlo. It is well known that the direct implementation of non-stoquastic Hamiltonians with flux qubits is particularly challenging. Our results suggest an alternative path for the implementation of non-stoquasticity via geometric phases that can be exploited for computational purposes.

A quantum Fredkin gate

PubMed Central

Patel, Raj B.; Ho, Joseph; Ferreyrol, Franck; Ralph, Timothy C.; Pryde, Geoff J.

2016-01-01

Minimizing the resources required to build logic gates into useful processing circuits is key to realizing quantum computers. Although the salient features of a quantum computer have been shown in proof-of-principle experiments, difficulties in scaling quantum systems have made more complex operations intractable. This is exemplified in the classical Fredkin (controlled-SWAP) gate for which, despite theoretical proposals, no quantum analog has been realized. By adding control to the SWAP unitary, we use photonic qubit logic to demonstrate the first quantum Fredkin gate, which promises many applications in quantum information and measurement. We implement example algorithms and generate the highest-fidelity three-photon Greenberger-Horne-Zeilinger states to date. The technique we use allows one to add a control operation to a black-box unitary, something that is impossible in the standard circuit model. Our experiment represents the first use of this technique to control a two-qubit operation and paves the way for larger controlled circuits to be realized efficiently. PMID:27051868

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

Ising Processing Units: Potential and Challenges for Discrete Optimization

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

Coffrin, Carleton James; Nagarajan, Harsha; Bent, Russell Whitford

The recent emergence of novel computational devices, such as adiabatic quantum computers, CMOS annealers, and optical parametric oscillators, presents new opportunities for hybrid-optimization algorithms that leverage these kinds of specialized hardware. In this work, we propose the idea of an Ising processing unit as a computational abstraction for these emerging tools. Challenges involved in using and bench- marking these devices are presented, and open-source software tools are proposed to address some of these challenges. The proposed benchmarking tools and methodology are demonstrated by conducting a baseline study of established solution methods to a D-Wave 2X adiabatic quantum computer, one examplemore » of a commercially available Ising processing unit.« less

Nanofabrication of Gate-defined GaAs/AlGaAs Lateral Quantum Dots

PubMed Central

Bureau-Oxton, Chloé; Camirand Lemyre, Julien; Pioro-Ladrière, Michel

2013-01-01

A quantum computer is a computer composed of quantum bits (qubits) that takes advantage of quantum effects, such as superposition of states and entanglement, to solve certain problems exponentially faster than with the best known algorithms on a classical computer. Gate-defined lateral quantum dots on GaAs/AlGaAs are one of many avenues explored for the implementation of a qubit. When properly fabricated, such a device is able to trap a small number of electrons in a certain region of space. The spin states of these electrons can then be used to implement the logical 0 and 1 of the quantum bit. Given the nanometer scale of these quantum dots, cleanroom facilities offering specialized equipment- such as scanning electron microscopes and e-beam evaporators- are required for their fabrication. Great care must be taken throughout the fabrication process to maintain cleanliness of the sample surface and to avoid damaging the fragile gates of the structure. This paper presents the detailed fabrication protocol of gate-defined lateral quantum dots from the wafer to a working device. Characterization methods and representative results are also briefly discussed. Although this paper concentrates on double quantum dots, the fabrication process remains the same for single or triple dots or even arrays of quantum dots. Moreover, the protocol can be adapted to fabricate lateral quantum dots on other substrates, such as Si/SiGe. PMID:24300661

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.

Photonic quantum digital signatures operating over kilometer ranges in installed optical fiber

NASA Astrophysics Data System (ADS)

Collins, Robert J.; Fujiwara, Mikio; Amiri, Ryan; Honjo, Toshimori; Shimizu, Kaoru; Tamaki, Kiyoshi; Takeoka, Masahiro; Andersson, Erika; Buller, Gerald S.; Sasaki, Masahide

2016-10-01

The security of electronic communications is a topic that has gained noteworthy public interest in recent years. As a result, there is an increasing public recognition of the existence and importance of mathematically based approaches to digital security. Many of these implement digital signatures to ensure that a malicious party has not tampered with the message in transit, that a legitimate receiver can validate the identity of the signer and that messages are transferable. The security of most digital signature schemes relies on the assumed computational difficulty of solving certain mathematical problems. However, reports in the media have shown that certain implementations of such signature schemes are vulnerable to algorithmic breakthroughs and emerging quantum processing technologies. Indeed, even without quantum processors, the possibility remains that classical algorithmic breakthroughs will render these schemes insecure. There is ongoing research into information-theoretically secure signature schemes, where the security is guaranteed against an attacker with arbitrary computational resources. One such approach is quantum digital signatures. Quantum signature schemes can be made information-theoretically secure based on the laws of quantum mechanics while comparable classical protocols require additional resources such as anonymous broadcast and/or a trusted authority. Previously, most early demonstrations of quantum digital signatures required dedicated single-purpose hardware and operated over restricted ranges in a laboratory environment. Here, for the first time, we present a demonstration of quantum digital signatures conducted over several kilometers of installed optical fiber. The system reported here operates at a higher signature generation rate than previous fiber systems.

Path-integral Monte Carlo method for Rényi entanglement entropies.

PubMed

Herdman, C M; Inglis, Stephen; Roy, P-N; Melko, R G; Del Maestro, A

2014-07-01

We introduce a quantum Monte Carlo algorithm to measure the Rényi entanglement entropies in systems of interacting bosons in the continuum. This approach is based on a path-integral ground state method that can be applied to interacting itinerant bosons in any spatial dimension with direct relevance to experimental systems of quantum fluids. We demonstrate how it may be used to compute spatial mode entanglement, particle partitioned entanglement, and the entanglement of particles, providing insights into quantum correlations generated by fluctuations, indistinguishability, and interactions. We present proof-of-principle calculations and benchmark against an exactly soluble model of interacting bosons in one spatial dimension. As this algorithm retains the fundamental polynomial scaling of quantum Monte Carlo when applied to sign-problem-free models, future applications should allow for the study of entanglement entropy in large-scale many-body systems of interacting bosons.

Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians

NASA Astrophysics Data System (ADS)

Bringewatt, Jacob; Dorland, William; Jordan, Stephen P.; Mink, Alan

2018-02-01

Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k -SAT problems, use k -local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n -body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

A Weak Quantum Blind Signature with Entanglement Permutation

NASA Astrophysics Data System (ADS)

Lou, Xiaoping; Chen, Zhigang; Guo, Ying

2015-09-01

Motivated by the permutation encryption algorithm, a weak quantum blind signature (QBS) scheme is proposed. It involves three participants, including the sender Alice, the signatory Bob and the trusted entity Charlie, in four phases, i.e., initializing phase, blinding phase, signing phase and verifying phase. In a small-scale quantum computation network, Alice blinds the message based on a quantum entanglement permutation encryption algorithm that embraces the chaotic position string. Bob signs the blinded message with private parameters shared beforehand while Charlie verifies the signature's validity and recovers the original message. Analysis shows that the proposed scheme achieves the secure blindness for the signer and traceability for the message owner with the aid of the authentic arbitrator who plays a crucial role when a dispute arises. In addition, the signature can neither be forged nor disavowed by the malicious attackers. It has a wide application to E-voting and E-payment system, etc.

Quantum Algorithms for Computational Physics: Volume 3 of Lattice Gas Dynamics

DTIC Science & Technology

2007-01-03

time- dependent state |q(t)〉 of a two- energy level quantum mechanical system, which is a fermionic qubit and is governed by the Schroedinger wave...on-site ket of size 2B |Ψ〉 total system ket of size 2Q 2.2 The quantum state in the number representation From the previous section, a time- dependent ...duration depend on the particular experimental realization, so that the natural coupling along with the program of externally applied pulses together

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.

What Can Quantum Optics Say about Computational Complexity Theory?

NASA Astrophysics Data System (ADS)

Rahimi-Keshari, Saleh; Lund, Austin P.; Ralph, Timothy C.

2015-02-01

Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational complexity theory point of view. We derive a general formula for calculating the output probabilities, and by considering input thermal states, we show that the output probabilities are proportional to permanents of positive-semidefinite Hermitian matrices. It is believed that approximating permanents of complex matrices in general is a #P-hard problem. However, we show that these permanents can be approximated with an algorithm in the BPPNP complexity class, as there exists an efficient classical algorithm for sampling from the output probability distribution. We further consider input squeezed-vacuum states and discuss the complexity of sampling from the probability distribution at the output.

Efficient and Adaptive Methods for Computing Accurate Potential Surfaces for Quantum Nuclear Effects: Applications to Hydrogen-Transfer Reactions.

PubMed

DeGregorio, Nicole; Iyengar, Srinivasan S

2018-01-09

We present two sampling measures to gauge critical regions of potential energy surfaces. These sampling measures employ (a) the instantaneous quantum wavepacket density, an approximation to the (b) potential surface, its (c) gradients, and (d) a Shannon information theory based expression that estimates the local entropy associated with the quantum wavepacket. These four criteria together enable a directed sampling of potential surfaces that appears to correctly describe the local oscillation frequencies, or the local Nyquist frequency, of a potential surface. The sampling functions are then utilized to derive a tessellation scheme that discretizes the multidimensional space to enable efficient sampling of potential surfaces. The sampled potential surface is then combined with four different interpolation procedures, namely, (a) local Hermite curve interpolation, (b) low-pass filtered Lagrange interpolation, (c) the monomial symmetrization approximation (MSA) developed by Bowman and co-workers, and (d) a modified Shepard algorithm. The sampling procedure and the fitting schemes are used to compute (a) potential surfaces in highly anharmonic hydrogen-bonded systems and (b) study hydrogen-transfer reactions in biogenic volatile organic compounds (isoprene) where the transferring hydrogen atom is found to demonstrate critical quantum nuclear effects. In the case of isoprene, the algorithm discussed here is used to derive multidimensional potential surfaces along a hydrogen-transfer reaction path to gauge the effect of quantum-nuclear degrees of freedom on the hydrogen-transfer process. Based on the decreased computational effort, facilitated by the optimal sampling of the potential surfaces through the use of sampling functions discussed here, and the accuracy of the associated potential surfaces, we believe the method will find great utility in the study of quantum nuclear dynamics problems, of which application to hydrogen-transfer reactions and hydrogen-bonded systems is demonstrated here.

Research on Palmprint Identification Method Based on Quantum Algorithms

PubMed Central

Zhang, Zhanzhan

2014-01-01

Quantum image recognition is a technology by using quantum algorithm to process the image information. It can obtain better effect than classical algorithm. In this paper, four different quantum algorithms are used in the three stages of palmprint recognition. First, quantum adaptive median filtering algorithm is presented in palmprint filtering processing. Quantum filtering algorithm can get a better filtering result than classical algorithm through the comparison. Next, quantum Fourier transform (QFT) is used to extract pattern features by only one operation due to quantum parallelism. The proposed algorithm exhibits an exponential speed-up compared with discrete Fourier transform in the feature extraction. Finally, quantum set operations and Grover algorithm are used in palmprint matching. According to the experimental results, quantum algorithm only needs to apply square of N operations to find out the target palmprint, but the traditional method needs N times of calculation. At the same time, the matching accuracy of quantum algorithm is almost 100%. PMID:25105165

Maximal violation of a bipartite three-setting, two-outcome Bell inequality using infinite-dimensional quantum systems

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

Pal, Karoly F.; Vertesi, Tamas

2010-08-15

The I{sub 3322} inequality is the simplest bipartite two-outcome Bell inequality beyond the Clauser-Horne-Shimony-Holt (CHSH) inequality, consisting of three two-outcome measurements per party. In the case of the CHSH inequality the maximal quantum violation can already be attained with local two-dimensional quantum systems; however, there is no such evidence for the I{sub 3322} inequality. In this paper a family of measurement operators and states is given which enables us to attain the maximum quantum value in an infinite-dimensional Hilbert space. Further, it is conjectured that our construction is optimal in the sense that measuring finite-dimensional quantum systems is not enoughmore » to achieve the true quantum maximum. We also describe an efficient iterative algorithm for computing quantum maximum of an arbitrary two-outcome Bell inequality in any given Hilbert space dimension. This algorithm played a key role in obtaining our results for the I{sub 3322} inequality, and we also applied it to improve on our previous results concerning the maximum quantum violation of several bipartite two-outcome Bell inequalities with up to five settings per party.« less

Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm

NASA Astrophysics Data System (ADS)

Nakatani, Naoki; Chan, Garnet Kin-Lic

2013-04-01

We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and π-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an illustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.

Superfast maximum-likelihood reconstruction for quantum tomography

NASA Astrophysics Data System (ADS)

Shang, Jiangwei; Zhang, Zhengyun; Ng, Hui Khoon

2017-06-01

Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we provide a fast and reliable algorithm for maximum-likelihood reconstruction that avoids this slow convergence. Our method utilizes the state-of-the-art convex optimization scheme, an accelerated projected-gradient method, that allows one to accommodate the quantum nature of the problem in a different way than in the standard methods. We demonstrate the power of our approach by comparing its performance with other algorithms for n -qubit state tomography. In particular, an eight-qubit situation that purportedly took weeks of computation time in 2005 can now be completed in under a minute for a single set of data, with far higher accuracy than previously possible. This refutes the common claim that MLE reconstruction is slow and reduces the need for alternative methods that often come with difficult-to-verify assumptions. In fact, recent methods assuming Gaussian statistics or relying on compressed sensing ideas are demonstrably inapplicable for the situation under consideration here. Our algorithm can be applied to general optimization problems over the quantum state space; the philosophy of projected gradients can further be utilized for optimization contexts with general constraints.

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.

Optical studies of current-induced magnetization switching and photonic quantum states

NASA Astrophysics Data System (ADS)

Lorenz, Virginia

2017-04-01

The ever-decreasing size of electronic components is leading to a fundamental change in the way computers operate, as at the few-nanometer scale, resistive heating and quantum mechanics prohibit efficient and stable operation. One of the most promising next-generation computing paradigms is Spintronics, which uses the spin of the electron to manipulate and store information in the form of magnetic thin films. I will present our optical studies of the fundamental mechanisms by which we can efficiently manipulate magnetization using electrical current. Although electron spin is a quantum-mechanical property, Spintronics relies on macroscopic magnetization and thus does not take advantage of quantum mechanics in the algorithms used to encode and transmit information. For the second part of my talk, I will present our work under the umbrella of new computing and communication technologies based on the quantum mechanical properties of photons. Quantum technologies often require the carriers of information, or qubits, to have specific properties. Photonic quantum states are good information carriers because they travel fast and are robust to environmental fluctuations, but characterizing and controlling photonic sources so the photons have just the right properties is still a challenge. I will describe our work towards enabling quantum-physics-based secure long-distance communication using photons.

Novel systems and methods for quantum communication, quantum computation, and quantum simulation

NASA Astrophysics Data System (ADS)

Gorshkov, Alexey Vyacheslavovich

Precise control over quantum systems can enable the realization of fascinating applications such as powerful computers, secure communication devices, and simulators that can elucidate the physics of complex condensed matter systems. However, the fragility of quantum effects makes it very difficult to harness the power of quantum mechanics. In this thesis, we present novel systems and tools for gaining fundamental insights into the complex quantum world and for bringing practical applications of quantum mechanics closer to reality. We first optimize and show equivalence between a wide range of techniques for storage of photons in atomic ensembles. We describe experiments demonstrating the potential of our optimization algorithms for quantum communication and computation applications. Next, we combine the technique of photon storage with strong atom-atom interactions to propose a robust protocol for implementing the two-qubit photonic phase gate, which is an important ingredient in many quantum computation and communication tasks. In contrast to photon storage, many quantum computation and simulation applications require individual addressing of closely-spaced atoms, ions, quantum dots, or solid state defects. To meet this requirement, we propose a method for coherent optical far-field manipulation of quantum systems with a resolution that is not limited by the wavelength of radiation. While alkali atoms are currently the system of choice for photon storage and many other applications, we develop new methods for quantum information processing and quantum simulation with ultracold alkaline-earth atoms in optical lattices. We show how multiple qubits can be encoded in individual alkaline-earth atoms and harnessed for quantum computing and precision measurements applications. We also demonstrate that alkaline-earth atoms can be used to simulate highly symmetric systems exhibiting spin-orbital interactions and capable of providing valuable insights into strongly correlated physics of transition metal oxides, heavy fermion materials, and spin liquid phases. While ultracold atoms typically exhibit only short-range interactions, numerous exotic phenomena and practical applications require long-range interactions, which can be achieved with ultracold polar molecules. We demonstrate the possibility to engineer a repulsive interaction between polar molecules, which allows for the suppression of inelastic collisions, efficient evaporative cooling, and the creation of novel phases of polar molecules.

Novel pseudo-random number generator based on quantum random walks.

PubMed

Yang, Yu-Guang; Zhao, Qian-Qian

2016-02-04

In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation.

Novel pseudo-random number generator based on quantum random walks

PubMed Central

Yang, Yu-Guang; Zhao, Qian-Qian

2016-01-01

In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation. PMID:26842402

The Quantum Socket: Wiring for Superconducting Qubits - Part 2

NASA Astrophysics Data System (ADS)

Bejanin, J. H.; McConkey, T. G.; Rinehart, J. R.; Bateman, J. D.; Earnest, C. T.; McRae, C. H.; Rohanizadegan, Y.; Shiri, D.; Mariantoni, M.; Penava, B.; Breul, P.; Royak, S.; Zapatka, M.; Fowler, A. G.

Quantum computing research has reached a level of maturity where quantum error correction (QEC) codes can be executed on linear arrays of superconducting quantum bits (qubits). A truly scalable quantum computing architecture, however, based on practical QEC algorithms, requires nearest neighbor interaction between qubits on a two-dimensional array. Such an arrangement is not possible with techniques that rely on wire bonding. To address this issue, we have developed the quantum socket, a device based on three-dimensional wires that enables the control of superconducting qubits on a two-dimensional grid. In this talk, we present experimental results characterizing this type of wiring. We will show that the quantum socket performs exceptionally well for the transmission and reflection of microwave signals up to 10 GHz, while minimizing crosstalk between adjacent wires. Under realistic conditions, we measured an S21 of -5 dB at 6 GHz and an average crosstalk of -60 dB. We also describe time domain reflectometry results and arbitrary pulse transmission tests, showing that the quantum socket can be used to control superconducting qubits.

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.

A two-qubit photonic quantum processor and its application to solving systems of linear equations

PubMed Central

Barz, Stefanie; Kassal, Ivan; Ringbauer, Martin; Lipp, Yannick Ole; Dakić, Borivoje; Aspuru-Guzik, Alán; Walther, Philip

2014-01-01

Large-scale quantum computers will require the ability to apply long sequences of entangling gates to many qubits. In a photonic architecture, where single-qubit gates can be performed easily and precisely, the application of consecutive two-qubit entangling gates has been a significant obstacle. Here, we demonstrate a two-qubit photonic quantum processor that implements two consecutive CNOT gates on the same pair of polarisation-encoded qubits. To demonstrate the flexibility of our system, we implement various instances of the quantum algorithm for solving of systems of linear equations. PMID:25135432

A quantum algorithm for obtaining the lowest eigenstate of a Hamiltonian assisted with an ancillary qubit system

NASA Astrophysics Data System (ADS)

Bang, Jeongho; Lee, Seung-Woo; Lee, Chang-Woo; Jeong, Hyunseok

2015-01-01

We propose a quantum algorithm to obtain the lowest eigenstate of any Hamiltonian simulated by a quantum computer. The proposed algorithm begins with an arbitrary initial state of the simulated system. A finite series of transforms is iteratively applied to the initial state assisted with an ancillary qubit. The fraction of the lowest eigenstate in the initial state is then amplified up to 1. We prove that our algorithm can faithfully work for any arbitrary Hamiltonian in the theoretical analysis. Numerical analyses are also carried out. We firstly provide a numerical proof-of-principle demonstration with a simple Hamiltonian in order to compare our scheme with the so-called "Demon-like algorithmic cooling (DLAC)", recently proposed in Xu (Nat Photonics 8:113, 2014). The result shows a good agreement with our theoretical analysis, exhibiting the comparable behavior to the best `cooling' with the DLAC method. We then consider a random Hamiltonian model for further analysis of our algorithm. By numerical simulations, we show that the total number of iterations is proportional to , where is the difference between the two lowest eigenvalues and is an error defined as the probability that the finally obtained system state is in an unexpected (i.e., not the lowest) eigenstate.

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.

Qubit lattice coherence induced by electromagnetic pulses in superconducting metamaterials.

PubMed

Ivić, Z; Lazarides, N; Tsironis, G P

2016-07-12

Quantum bits (qubits) are at the heart of quantum information processing schemes. Currently, solid-state qubits, and in particular the superconducting ones, seem to satisfy the requirements for being the building blocks of viable quantum computers, since they exhibit relatively long coherence times, extremely low dissipation, and scalability. The possibility of achieving quantum coherence in macroscopic circuits comprising Josephson junctions, envisioned by Legett in the 1980's, was demonstrated for the first time in a charge qubit; since then, the exploitation of macroscopic quantum effects in low-capacitance Josephson junction circuits allowed for the realization of several kinds of superconducting qubits. Furthermore, coupling between qubits has been successfully achieved that was followed by the construction of multiple-qubit logic gates and the implementation of several algorithms. Here it is demonstrated that induced qubit lattice coherence as well as two remarkable quantum coherent optical phenomena, i.e., self-induced transparency and Dicke-type superradiance, may occur during light-pulse propagation in quantum metamaterials comprising superconducting charge qubits. The generated qubit lattice pulse forms a compound "quantum breather" that propagates in synchrony with the electromagnetic pulse. The experimental confirmation of such effects in superconducting quantum metamaterials may open a new pathway to potentially powerful quantum computing.

Enhanced factoring with a bose-einstein condensate.

PubMed

Sadgrove, Mark; Kumar, Sanjay; Nakagawa, Ken'ichi

2008-10-31

We present a novel method to realize analog sum computation with a Bose-Einstein condensate in an optical lattice potential subject to controlled phase jumps. We use the method to implement the Gauss sum algorithm for factoring numbers. By exploiting higher order quantum momentum states, we are able to improve the algorithm's accuracy beyond the limits of the usual classical implementation.

Properties of the numerical algorithms for problems of quantum information technologies: Benefits of deep analysis

NASA Astrophysics Data System (ADS)

Chernyavskiy, Andrey; Khamitov, Kamil; Teplov, Alexey; Voevodin, Vadim; Voevodin, Vladimir

2016-10-01

In recent years, quantum information technologies (QIT) showed great development, although, the way of the implementation of QIT faces the serious difficulties, some of which are challenging computational tasks. This work is devoted to the deep and broad analysis of the parallel algorithmic properties of such tasks. As an example we take one- and two-qubit transformations of a many-qubit quantum state, which are the most critical kernels of many important QIT applications. The analysis of the algorithms uses the methodology of the AlgoWiki project (algowiki-project.org) and consists of two parts: theoretical and experimental. Theoretical part includes features like sequential and parallel complexity, macro structure, and visual information graph. Experimental part was made by using the petascale Lomonosov supercomputer (Moscow State University, Russia) and includes the analysis of locality and memory access, scalability and the set of more specific dynamic characteristics of realization. This approach allowed us to obtain bottlenecks and generate ideas of efficiency improvement.

Parallelizing quantum circuit synthesis

NASA Astrophysics Data System (ADS)

Di Matteo, Olivia; Mosca, Michele

2016-03-01

Quantum circuit synthesis is the process in which an arbitrary unitary operation is decomposed into a sequence of gates from a universal set, typically one which a quantum computer can implement both efficiently and fault-tolerantly. As physical implementations of quantum computers improve, the need is growing for tools that can effectively synthesize components of the circuits and algorithms they will run. Existing algorithms for exact, multi-qubit circuit synthesis scale exponentially in the number of qubits and circuit depth, leaving synthesis intractable for circuits on more than a handful of qubits. Even modest improvements in circuit synthesis procedures may lead to significant advances, pushing forward the boundaries of not only the size of solvable circuit synthesis problems, but also in what can be realized physically as a result of having more efficient circuits. We present a method for quantum circuit synthesis using deterministic walks. Also termed pseudorandom walks, these are walks in which once a starting point is chosen, its path is completely determined. We apply our method to construct a parallel framework for circuit synthesis, and implement one such version performing optimal T-count synthesis over the Clifford+T gate set. We use our software to present examples where parallelization offers a significant speedup on the runtime, as well as directly confirm that the 4-qubit 1-bit full adder has optimal T-count 7 and T-depth 3.

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.

Experimental determination of Ramsey numbers.

PubMed

Bian, Zhengbing; Chudak, Fabian; Macready, William G; Clark, Lane; Gaitan, Frank

2013-09-27

Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has been proposed that calculates the two-color Ramsey numbers R(m,n). Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(m,2) for 4≤m≤8. The R(8,2) computation used 84 qubits of which 28 were computational qubits. This computation is the largest experimental implementation of a scientifically meaningful adiabatic evolution algorithm that has been done to date.

Experimental Determination of Ramsey Numbers

NASA Astrophysics Data System (ADS)

Bian, Zhengbing; Chudak, Fabian; Macready, William G.; Clark, Lane; Gaitan, Frank

2013-09-01

Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has been proposed that calculates the two-color Ramsey numbers R(m,n). Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(m,2) for 4≤m≤8. The R(8,2) computation used 84 qubits of which 28 were computational qubits. This computation is the largest experimental implementation of a scientifically meaningful adiabatic evolution algorithm that has been done to date.

Optimizing Teleportation Cost in Distributed Quantum Circuits

NASA Astrophysics Data System (ADS)

Zomorodi-Moghadam, Mariam; Houshmand, Mahboobeh; Houshmand, Monireh

2018-03-01

The presented work provides a procedure for optimizing the communication cost of a distributed quantum circuit (DQC) in terms of the number of qubit teleportations. Because of technology limitations which do not allow large quantum computers to work as a single processing element, distributed quantum computation is an appropriate solution to overcome this difficulty. Previous studies have applied ad-hoc solutions to distribute a quantum system for special cases and applications. In this study, a general approach is proposed to optimize the number of teleportations for a DQC consisting of two spatially separated and long-distance quantum subsystems. To this end, different configurations of locations for executing gates whose qubits are in distinct subsystems are considered and for each of these configurations, the proposed algorithm is run to find the minimum number of required teleportations. Finally, the configuration which leads to the minimum number of teleportations is reported. The proposed method can be used as an automated procedure to find the configuration with the optimal communication cost for the DQC. This cost can be used as a basic measure of the communication cost for future works in the distributed quantum circuits.

Error regions in quantum state tomography: computational complexity caused by geometry of quantum states

NASA Astrophysics Data System (ADS)

Suess, Daniel; Rudnicki, Łukasz; maciel, Thiago O.; Gross, David

2017-09-01

The outcomes of quantum mechanical measurements are inherently random. It is therefore necessary to develop stringent methods for quantifying the degree of statistical uncertainty about the results of quantum experiments. For the particularly relevant task of quantum state tomography, it has been shown that a significant reduction in uncertainty can be achieved by taking the positivity of quantum states into account. However—the large number of partial results and heuristics notwithstanding—no efficient general algorithm is known that produces an optimal uncertainty region from experimental data, while making use of the prior constraint of positivity. Here, we provide a precise formulation of this problem and show that the general case is NP-hard. Our result leaves room for the existence of efficient approximate solutions, and therefore does not in itself imply that the practical task of quantum uncertainty quantification is intractable. However, it does show that there exists a non-trivial trade-off between optimality and computational efficiency for error regions. We prove two versions of the result: one for frequentist and one for Bayesian statistics.

Coherent feedback control of a single qubit in diamond

NASA Astrophysics Data System (ADS)

Hirose, Masashi; Cappellaro, Paola

2016-04-01

Engineering desired operations on qubits subjected to the deleterious effects of their environment is a critical task in quantum information processing, quantum simulation and sensing. The most common approach relies on open-loop quantum control techniques, including optimal-control algorithms based on analytical or numerical solutions, Lyapunov design and Hamiltonian engineering. An alternative strategy, inspired by the success of classical control, is feedback control. Because of the complications introduced by quantum measurement, closed-loop control is less pervasive in the quantum setting and, with exceptions, its experimental implementations have been mainly limited to quantum optics experiments. Here we implement a feedback-control algorithm using a solid-state spin qubit system associated with the nitrogen vacancy centre in diamond, using coherent feedback to overcome the limitations of measurement-based feedback, and show that it can protect the qubit against intrinsic dephasing noise for milliseconds. In coherent feedback, the quantum system is connected to an auxiliary quantum controller (ancilla) that acquires information about the output state of the system (by an entangling operation) and performs an appropriate feedback action (by a conditional gate). In contrast to open-loop dynamical decoupling techniques, feedback control can protect the qubit even against Markovian noise and for an arbitrary period of time (limited only by the coherence time of the ancilla), while allowing gate operations. It is thus more closely related to quantum error-correction schemes, although these require larger and increasing qubit overheads. Increasing the number of fresh ancillas enables protection beyond their coherence time. We further evaluate the robustness of the feedback protocol, which could be applied to quantum computation and sensing, by exploring a trade-off between information gain and decoherence protection, as measurement of the ancilla-qubit correlation after the feedback algorithm voids the protection, even if the rest of the dynamics is unchanged.

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.

Quantum Engineering of Dynamical Gauge Fields on Optical Lattices

DTIC Science & Technology

2016-07-08

opens the door for exciting new research directions, such as quantum simulation of the Schwinger model and of non-Abelian models. (a) Papers...exact blocking formulas from the TRG formulation of the transfer matrix. The second is a worm algorithm. The particle number distributions obtained...a fact that can be explained by an approximate particle- hole symmetry. We have also developed a computer code suite for simulating the Abelian

Algorithmic cooling in liquid-state nuclear magnetic resonance

NASA Astrophysics Data System (ADS)

Atia, Yosi; Elias, Yuval; Mor, Tal; Weinstein, Yossi

2016-01-01

Algorithmic cooling is a method that employs thermalization to increase qubit purification level; namely, it reduces the qubit system's entropy. We utilized gradient ascent pulse engineering, an optimal control algorithm, to implement algorithmic cooling in liquid-state nuclear magnetic resonance. Various cooling algorithms were applied onto the three qubits of C132-trichloroethylene, cooling the system beyond Shannon's entropy bound in several different ways. In particular, in one experiment a carbon qubit was cooled by a factor of 4.61. This work is a step towards potentially integrating tools of NMR quantum computing into in vivo magnetic-resonance spectroscopy.

Universal programmable quantum circuit schemes to emulate an operator

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

Daskin, Anmer; Grama, Ananth; Kollias, Giorgos

Unlike fixed designs, programmable circuit designs support an infinite number of operators. The functionality of a programmable circuit can be altered by simply changing the angle values of the rotation gates in the circuit. Here, we present a new quantum circuit design technique resulting in two general programmable circuit schemes. The circuit schemes can be used to simulate any given operator by setting the angle values in the circuit. This provides a fixed circuit design whose angles are determined from the elements of the given matrix-which can be non-unitary-in an efficient way. We also give both the classical and quantummore » complexity analysis for these circuits and show that the circuits require a few classical computations. For the electronic structure simulation on a quantum computer, one has to perform the following steps: prepare the initial wave function of the system; present the evolution operator U=e{sup -iHt} for a given atomic and molecular Hamiltonian H in terms of quantum gates array and apply the phase estimation algorithm to find the energy eigenvalues. Thus, in the circuit model of quantum computing for quantum chemistry, a crucial step is presenting the evolution operator for the atomic and molecular Hamiltonians in terms of quantum gate arrays. Since the presented circuit designs are independent from the matrix decomposition techniques and the global optimization processes used to find quantum circuits for a given operator, high accuracy simulations can be done for the unitary propagators of molecular Hamiltonians on quantum computers. As an example, we show how to build the circuit design for the hydrogen molecule.« less

Rigorous RG Algorithms and Area Laws for Low Energy Eigenstates in 1D

NASA Astrophysics Data System (ADS)

Arad, Itai; Landau, Zeph; Vazirani, Umesh; Vidick, Thomas

2017-11-01

One of the central challenges in the study of quantum many-body systems is the complexity of simulating them on a classical computer. A recent advance (Landau et al. in Nat Phys, 2015) gave a polynomial time algorithm to compute a succinct classical description for unique ground states of gapped 1D quantum systems. Despite this progress many questions remained unsolved, including whether there exist efficient algorithms when the ground space is degenerate (and of polynomial dimension in the system size), or for the polynomially many lowest energy states, or even whether such states admit succinct classical descriptions or area laws. In this paper we give a new algorithm, based on a rigorously justified RG type transformation, for finding low energy states for 1D Hamiltonians acting on a chain of n particles. In the process we resolve some of the aforementioned open questions, including giving a polynomial time algorithm for poly( n) degenerate ground spaces and an n O(log n) algorithm for the poly( n) lowest energy states (under a mild density condition). For these classes of systems the existence of a succinct classical description and area laws were not rigorously proved before this work. The algorithms are natural and efficient, and for the case of finding unique ground states for frustration-free Hamiltonians the running time is {\\tilde{O}(nM(n))} , where M( n) is the time required to multiply two n × n matrices.

Simulating and assessing boson sampling experiments with phase-space representations

NASA Astrophysics Data System (ADS)

Opanchuk, Bogdan; Rosales-Zárate, Laura; Reid, Margaret D.; Drummond, Peter D.

2018-04-01

The search for new, application-specific quantum computers designed to outperform any classical computer is driven by the ending of Moore's law and the quantum advantages potentially obtainable. Photonic networks are promising examples, with experimental demonstrations and potential for obtaining a quantum computer to solve problems believed classically impossible. This introduces a challenge: how does one design or understand such photonic networks? One must be able to calculate observables using general methods capable of treating arbitrary inputs, dissipation, and noise. We develop complex phase-space software for simulating these photonic networks, and apply this to boson sampling experiments. Our techniques give sampling errors orders of magnitude lower than experimental correlation measurements for the same number of samples. We show that these techniques remove systematic errors in previous algorithms for estimating correlations, with large improvements in errors in some cases. In addition, we obtain a scalable channel-combination strategy for assessment of boson sampling devices.

Perspective: Ring-polymer instanton theory

NASA Astrophysics Data System (ADS)

Richardson, Jeremy O.

2018-05-01

Since the earliest explorations of quantum mechanics, it has been a topic of great interest that quantum tunneling allows particles to penetrate classically insurmountable barriers. Instanton theory provides a simple description of these processes in terms of dominant tunneling pathways. Using a ring-polymer discretization, an efficient computational method is obtained for applying this theory to compute reaction rates and tunneling splittings in molecular systems. Unlike other quantum-dynamics approaches, the method scales well with the number of degrees of freedom, and for many polyatomic systems, the method may provide the most accurate predictions which can be practically computed. Instanton theory thus has the capability to produce useful data for many fields of low-temperature chemistry including spectroscopy, atmospheric and astrochemistry, as well as surface science. There is however still room for improvement in the efficiency of the numerical algorithms, and new theories are under development for describing tunneling in nonadiabatic transitions.

Occam’s Quantum Strop: Synchronizing and Compressing Classical Cryptic Processes via a Quantum Channel

NASA Astrophysics Data System (ADS)

Mahoney, John R.; Aghamohammadi, Cina; Crutchfield, James P.

2016-02-01

A stochastic process’ statistical complexity stands out as a fundamental property: the minimum information required to synchronize one process generator to another. How much information is required, though, when synchronizing over a quantum channel? Recent work demonstrated that representing causal similarity as quantum state-indistinguishability provides a quantum advantage. We generalize this to synchronization and offer a sequence of constructions that exploit extended causal structures, finding substantial increase of the quantum advantage. We demonstrate that maximum compression is determined by the process’ cryptic order-a classical, topological property closely allied to Markov order, itself a measure of historical dependence. We introduce an efficient algorithm that computes the quantum advantage and close noting that the advantage comes at a cost-one trades off prediction for generation complexity.

Occam's Quantum Strop: Synchronizing and Compressing Classical Cryptic Processes via a Quantum Channel.

PubMed

Mahoney, John R; Aghamohammadi, Cina; Crutchfield, James P

2016-02-15

A stochastic process' statistical complexity stands out as a fundamental property: the minimum information required to synchronize one process generator to another. How much information is required, though, when synchronizing over a quantum channel? Recent work demonstrated that representing causal similarity as quantum state-indistinguishability provides a quantum advantage. We generalize this to synchronization and offer a sequence of constructions that exploit extended causal structures, finding substantial increase of the quantum advantage. We demonstrate that maximum compression is determined by the process' cryptic order--a classical, topological property closely allied to Markov order, itself a measure of historical dependence. We introduce an efficient algorithm that computes the quantum advantage and close noting that the advantage comes at a cost-one trades off prediction for generation complexity.

A new algorithm to handle finite nuclear mass effects in electronic calculations: the ISOTOPE program.

PubMed

Gonçalves, Cristina P; Mohallem, José R

2004-11-15

We report the development of a simple algorithm to modify quantum chemistry codes based on the LCAO procedure, to account for the isotope problem in electronic structure calculations. No extra computations are required compared to standard Born-Oppenheimer calculations. An upgrade of the Gamess package called ISOTOPE is presented, and its applicability is demonstrated in some examples.

Quantum realization of the nearest neighbor value interpolation method for INEQR

NASA Astrophysics Data System (ADS)

Zhou, RiGui; Hu, WenWen; Luo, GaoFeng; Liu, XingAo; Fan, Ping

2018-07-01

This paper presents the nearest neighbor value (NNV) interpolation algorithm for the improved novel enhanced quantum representation of digital images (INEQR). It is necessary to use interpolation in image scaling because there is an increase or a decrease in the number of pixels. The difference between the proposed scheme and nearest neighbor interpolation is that the concept applied, to estimate the missing pixel value, is guided by the nearest value rather than the distance. Firstly, a sequence of quantum operations is predefined, such as cyclic shift transformations and the basic arithmetic operations. Then, the feasibility of the nearest neighbor value interpolation method for quantum image of INEQR is proven using the previously designed quantum operations. Furthermore, quantum image scaling algorithm in the form of circuits of the NNV interpolation for INEQR is constructed for the first time. The merit of the proposed INEQR circuit lies in their low complexity, which is achieved by utilizing the unique properties of quantum superposition and entanglement. Finally, simulation-based experimental results involving different classical images and ratios (i.e., conventional or non-quantum) are simulated based on the classical computer's MATLAB 2014b software, which demonstrates that the proposed interpolation method has higher performances in terms of high resolution compared to the nearest neighbor and bilinear interpolation.

Efficient Classical Algorithm for Boson Sampling with Partially Distinguishable Photons

NASA Astrophysics Data System (ADS)

Renema, J. J.; Menssen, A.; Clements, W. R.; Triginer, G.; Kolthammer, W. S.; Walmsley, I. A.

2018-06-01

We demonstrate how boson sampling with photons of partial distinguishability can be expressed in terms of interference of fewer photons. We use this observation to propose a classical algorithm to simulate the output of a boson sampler fed with photons of partial distinguishability. We find conditions for which this algorithm is efficient, which gives a lower limit on the required indistinguishability to demonstrate a quantum advantage. Under these conditions, adding more photons only polynomially increases the computational cost to simulate a boson sampling experiment.

Quantum machine learning for quantum anomaly detection

NASA Astrophysics Data System (ADS)

Liu, Nana; Rebentrost, Patrick

2018-04-01

Anomaly detection is used for identifying data that deviate from "normal" data patterns. Its usage on classical data finds diverse applications in many important areas such as finance, fraud detection, medical diagnoses, data cleaning, and surveillance. With the advent of quantum technologies, anomaly detection of quantum data, in the form of quantum states, may become an important component of quantum applications. Machine-learning algorithms are playing pivotal roles in anomaly detection using classical data. Two widely used algorithms are the kernel principal component analysis and the one-class support vector machine. We find corresponding quantum algorithms to detect anomalies in quantum states. We show that these two quantum algorithms can be performed using resources that are logarithmic in the dimensionality of quantum states. For pure quantum states, these resources can also be logarithmic in the number of quantum states used for training the machine-learning algorithm. This makes these algorithms potentially applicable to big quantum data applications.

Excited states from quantum Monte Carlo in the basis of Slater determinants

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

Humeniuk, Alexander; Mitrić, Roland, E-mail: roland.mitric@uni-wuerzburg.de

2014-11-21

Building on the full configuration interaction quantum Monte Carlo (FCIQMC) algorithm introduced recently by Booth et al. [J. Chem. Phys. 131, 054106 (2009)] to compute the ground state of correlated many-electron systems, an extension to the computation of excited states (exFCIQMC) is presented. The Hilbert space is divided into a large part consisting of pure Slater determinants and a much smaller orthogonal part (the size of which is controlled by a cut-off threshold), from which the lowest eigenstates can be removed efficiently. In this way, the quantum Monte Carlo algorithm is restricted to the orthogonal complement of the lower excitedmore » states and projects out the next highest excited state. Starting from the ground state, higher excited states can be found one after the other. The Schrödinger equation in imaginary time is solved by the same population dynamics as in the ground state algorithm with modified probabilities and matrix elements, for which working formulae are provided. As a proof of principle, the method is applied to lithium hydride in the 3-21G basis set and to the helium dimer in the aug-cc-pVDZ basis set. It is shown to give the correct electronic structure for all bond lengths. Much more testing will be required before the applicability of this method to electron correlation problems of interesting size can be assessed.« less

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.

Measurement-induced nonlocality in arbitrary dimensions in terms of the inverse approximate joint diagonalization

NASA Astrophysics Data System (ADS)

Zhang, Li-qiang; Ma, Ting-ting; Yu, Chang-shui

2018-03-01

The computability of the quantifier of a given quantum resource is the essential challenge in the resource theory and the inevitable bottleneck for its application. Here we focus on the measurement-induced nonlocality and present a redefinition in terms of the skew information subject to a broken observable. It is shown that the obtained quantity possesses an obvious operational meaning, can tackle the noncontractivity of the measurement-induced nonlocality and has analytic expressions for pure states, (2 ⊗d )-dimensional quantum states, and some particular high-dimensional quantum states. Most importantly, an inverse approximate joint diagonalization algorithm, due to its simplicity, high efficiency, stability, and state independence, is presented to provide almost-analytic expressions for any quantum state, which can also shed light on other aspects in physics. To illustrate applications as well as demonstrate the validity of the algorithm, we compare the analytic and numerical expressions of various examples and show their perfect consistency.

Qubit lattice coherence induced by electromagnetic pulses in superconducting metamaterials

PubMed Central

Ivić, Z.; Lazarides, N.; Tsironis, G. P.

2016-01-01

Quantum bits (qubits) are at the heart of quantum information processing schemes. Currently, solid-state qubits, and in particular the superconducting ones, seem to satisfy the requirements for being the building blocks of viable quantum computers, since they exhibit relatively long coherence times, extremely low dissipation, and scalability. The possibility of achieving quantum coherence in macroscopic circuits comprising Josephson junctions, envisioned by Legett in the 1980’s, was demonstrated for the first time in a charge qubit; since then, the exploitation of macroscopic quantum effects in low-capacitance Josephson junction circuits allowed for the realization of several kinds of superconducting qubits. Furthermore, coupling between qubits has been successfully achieved that was followed by the construction of multiple-qubit logic gates and the implementation of several algorithms. Here it is demonstrated that induced qubit lattice coherence as well as two remarkable quantum coherent optical phenomena, i.e., self-induced transparency and Dicke-type superradiance, may occur during light-pulse propagation in quantum metamaterials comprising superconducting charge qubits. The generated qubit lattice pulse forms a compound ”quantum breather” that propagates in synchrony with the electromagnetic pulse. The experimental confirmation of such effects in superconducting quantum metamaterials may open a new pathway to potentially powerful quantum computing. PMID:27403780

Qubit lattice coherence induced by electromagnetic pulses in superconducting metamaterials

NASA Astrophysics Data System (ADS)

Ivić, Z.; Lazarides, N.; Tsironis, G. P.

2016-07-01

Quantum bits (qubits) are at the heart of quantum information processing schemes. Currently, solid-state qubits, and in particular the superconducting ones, seem to satisfy the requirements for being the building blocks of viable quantum computers, since they exhibit relatively long coherence times, extremely low dissipation, and scalability. The possibility of achieving quantum coherence in macroscopic circuits comprising Josephson junctions, envisioned by Legett in the 1980’s, was demonstrated for the first time in a charge qubit; since then, the exploitation of macroscopic quantum effects in low-capacitance Josephson junction circuits allowed for the realization of several kinds of superconducting qubits. Furthermore, coupling between qubits has been successfully achieved that was followed by the construction of multiple-qubit logic gates and the implementation of several algorithms. Here it is demonstrated that induced qubit lattice coherence as well as two remarkable quantum coherent optical phenomena, i.e., self-induced transparency and Dicke-type superradiance, may occur during light-pulse propagation in quantum metamaterials comprising superconducting charge qubits. The generated qubit lattice pulse forms a compound ”quantum breather” that propagates in synchrony with the electromagnetic pulse. The experimental confirmation of such effects in superconducting quantum metamaterials may open a new pathway to potentially powerful quantum computing.

Quantum Testbeds Stakeholder Workshop (QTSW) Report meeting purpose and agenda.

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

Hebner, Gregory A.

Quantum computing (QC) is a promising early-stage technology with the potential to provide scientific computing capabilities far beyond what is possible with even an Exascale computer in specific problems of relevance to the Office of Science. These include (but are not limited to) materials modeling, molecular dynamics, and quantum chromodynamics. However, commercial QC systems are not yet available and the technical maturity of current QC hardware, software, algorithms, and systems integration is woefully incomplete. Thus, there is a significant opportunity for DOE to define the technology building blocks, and solve the system integration issues to enable a revolutionary tool. Oncemore » realized, QC will have world changing impact on economic competitiveness, the scientific enterprise, and citizen well-being. Prior to this workshop, DOE / Office of Advanced Scientific Computing Research (ASCR) hosted a workshop in 2015 to explore QC scientific applications. The goal of that workshop was to assess the viability of QC technologies to meet the computational requirements in support of DOE’s science and energy mission and to identify the potential impact of these technologies.« less

Coherent controlization using superconducting qubits

PubMed Central

Friis, Nicolai; Melnikov, Alexey A.; Kirchmair, Gerhard; Briegel, Hans J.

2015-01-01

Coherent controlization, i.e., coherent conditioning of arbitrary single- or multi-qubit operations on the state of one or more control qubits, is an important ingredient for the flexible implementation of many algorithms in quantum computation. This is of particular significance when certain subroutines are changing over time or when they are frequently modified, such as in decision-making algorithms for learning agents. We propose a scheme to realize coherent controlization for any number of superconducting qubits coupled to a microwave resonator. For two and three qubits, we present an explicit construction that is of high relevance for quantum learning agents. We demonstrate the feasibility of our proposal, taking into account loss, dephasing, and the cavity self-Kerr effect. PMID:26667893

Parallel simulations of Grover's algorithm for closest match search in neutron monitor data

NASA Astrophysics Data System (ADS)

Kussainov, Arman; White, Yelena

We are studying the parallel implementations of Grover's closest match search algorithm for neutron monitor data analysis. This includes data formatting, and matching quantum parameters to a conventional structure of a chosen programming language and selected experimental data type. We have employed several workload distribution models based on acquired data and search parameters. As a result of these simulations, we have an understanding of potential problems that may arise during configuration of real quantum computational devices and the way they could run tasks in parallel. The work was supported by the Science Committee of the Ministry of Science and Education of the Republic of Kazakhstan Grant #2532/GF3.

Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo

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

Filippi, Claudia, E-mail: c.filippi@utwente.nl; Assaraf, Roland, E-mail: assaraf@lct.jussieu.fr; Moroni, Saverio, E-mail: moroni@democritos.it

2016-05-21

We present a simple and general formalism to compute efficiently the derivatives of a multi-determinant Jastrow-Slater wave function, the local energy, the interatomic forces, and similar quantities needed in quantum Monte Carlo. Through a straightforward manipulation of matrices evaluated on the occupied and virtual orbitals, we obtain an efficiency equivalent to algorithmic differentiation in the computation of the interatomic forces and the optimization of the orbital parameters. Furthermore, for a large multi-determinant expansion, the significant computational gain afforded by a recently introduced table method is here extended to the local value of any one-body operator and to its derivatives, inmore » both all-electron and pseudopotential calculations.« less

Quantum computation with classical light: Implementation of the Deutsch-Jozsa algorithm

NASA Astrophysics Data System (ADS)

Perez-Garcia, Benjamin; McLaren, Melanie; Goyal, Sandeep K.; Hernandez-Aranda, Raul I.; Forbes, Andrew; Konrad, Thomas

2016-05-01

We propose an optical implementation of the Deutsch-Jozsa Algorithm using classical light in a binary decision-tree scheme. Our approach uses a ring cavity and linear optical devices in order to efficiently query the oracle functional values. In addition, we take advantage of the intrinsic Fourier transforming properties of a lens to read out whether the function given by the oracle is balanced or constant.

Nicholas Metropolis Award for Outstanding Doctoral Thesis Work in Computational Physics: Quantum many-body physics of ultracold molecules in optical lattices: models and simulation methods

NASA Astrophysics Data System (ADS)

Wall, Michael

2014-03-01

Experimental progress in generating and manipulating synthetic quantum systems, such as ultracold atoms and molecules in optical lattices, has revolutionized our understanding of quantum many-body phenomena and posed new challenges for modern numerical techniques. Ultracold molecules, in particular, feature long-range dipole-dipole interactions and a complex and selectively accessible internal structure of rotational and hyperfine states, leading to many-body models with long range interactions and many internal degrees of freedom. Additionally, the many-body physics of ultracold molecules is often probed far from equilibrium, and so algorithms which simulate quantum many-body dynamics are essential. Numerical methods which are to have significant impact in the design and understanding of such synthetic quantum materials must be able to adapt to a variety of different interactions, physical degrees of freedom, and out-of-equilibrium dynamical protocols. Matrix product state (MPS)-based methods, such as the density-matrix renormalization group (DMRG), have become the de facto standard for strongly interacting low-dimensional systems. Moreover, the flexibility of MPS-based methods makes them ideally suited both to generic, open source implementation as well as to studies of the quantum many-body dynamics of ultracold molecules. After introducing MPSs and variational algorithms using MPSs generally, I will discuss my own research using MPSs for many-body dynamics of long-range interacting systems. In addition, I will describe two open source implementations of MPS-based algorithms in which I was involved, as well as educational materials designed to help undergraduates and graduates perform research in computational quantum many-body physics using a variety of numerical methods including exact diagonalization and static and dynamic variational MPS methods. Finally, I will mention present research on ultracold molecules in optical lattices, such as the exploration of many-body physics with polyatomic molecules, and the next generation of open source matrix product state codes. This work was performed in the research group of Prof. Lincoln D. Carr.

Quantum image pseudocolor coding based on the density-stratified method

NASA Astrophysics Data System (ADS)

Jiang, Nan; Wu, Wenya; Wang, Luo; Zhao, Na

2015-05-01

Pseudocolor processing is a branch of image enhancement. It dyes grayscale images to color images to make the images more beautiful or to highlight some parts on the images. This paper proposes a quantum image pseudocolor coding scheme based on the density-stratified method which defines a colormap and changes the density value from gray to color parallel according to the colormap. Firstly, two data structures: quantum image GQIR and quantum colormap QCR are reviewed or proposed. Then, the quantum density-stratified algorithm is presented. Based on them, the quantum realization in the form of circuits is given. The main advantages of the quantum version for pseudocolor processing over the classical approach are that it needs less memory and can speed up the computation. Two kinds of examples help us to describe the scheme further. Finally, the future work are analyzed.

Quantum State Tomography via Linear Regression Estimation

PubMed Central

Qi, Bo; Hou, Zhibo; Li, Li; Dong, Daoyi; Xiang, Guoyong; Guo, Guangcan

2013-01-01

A simple yet efficient state reconstruction algorithm of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. An asymptotic mean squared error (MSE) upper bound for all possible states to be estimated is given analytically, which depends explicitly upon the involved measurement bases. This analytical MSE upper bound can guide one to choose optimal measurement sets. The computational complexity of LRE is O(d4) where d is the dimension of the quantum state. Numerical examples show that LRE is much faster than maximum-likelihood estimation for quantum state tomography. PMID:24336519

Open source Matrix Product States: Opening ways to simulate entangled many-body quantum systems in one dimension

NASA Astrophysics Data System (ADS)

Jaschke, Daniel; Wall, Michael L.; Carr, Lincoln D.

2018-04-01

Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States (MPSs), have attracted interest from different fields of quantum physics ranging from solid state systems to quantum simulators and quantum computing. Our open source MPS code provides the community with a toolset to analyze the statics and dynamics of one-dimensional quantum systems. Here, we present our open source library, Open Source Matrix Product States (OSMPS), of MPS methods implemented in Python and Fortran2003. The library includes tools for ground state calculation and excited states via the variational ansatz. We also support ground states for infinite systems with translational invariance. Dynamics are simulated with different algorithms, including three algorithms with support for long-range interactions. Convenient features include built-in support for fermionic systems and number conservation with rotational U(1) and discrete Z2 symmetries for finite systems, as well as data parallelism with MPI. We explain the principles and techniques used in this library along with examples of how to efficiently use the general interfaces to analyze the Ising and Bose-Hubbard models. This description includes the preparation of simulations as well as dispatching and post-processing of them.

Open-Source Software for Modeling of Nanoelectronic Devices

NASA Technical Reports Server (NTRS)

Oyafuso, Fabiano; Hua, Hook; Tisdale, Edwin; Hart, Don

2004-01-01

The Nanoelectronic Modeling 3-D (NEMO 3-D) computer program has been upgraded to open-source status through elimination of license-restricted components. The present version functions equivalently to the version reported in "Software for Numerical Modeling of Nanoelectronic Devices" (NPO-30520), NASA Tech Briefs, Vol. 27, No. 11 (November 2003), page 37. To recapitulate: NEMO 3-D performs numerical modeling of the electronic transport and structural properties of a semiconductor device that has overall dimensions of the order of tens of nanometers. The underlying mathematical model represents the quantum-mechanical behavior of the device resolved to the atomistic level of granularity. NEMO 3-D solves the applicable quantum matrix equation on a Beowulf-class cluster computer by use of a parallel-processing matrix vector multiplication algorithm coupled to a Lanczos and/or Rayleigh-Ritz algorithm that solves for eigenvalues. A prior upgrade of NEMO 3-D incorporated a capability for a strain treatment, parameterized for bulk material properties of GaAs and InAs, for two tight-binding submodels. NEMO 3-D has been demonstrated in atomistic analyses of effects of disorder in alloys and, in particular, in bulk In(x)Ga(1-x)As and in In(0.6)Ga(0.4)As quantum dots.

Sanibel Symposium in the Petascale-Exascale Computational Era

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

Cheng, Hai-Ping

The 56 th Sanibel Symposium was held February 14-19 2016 at the King and Prince Hotel, St. Simons Island, GA. It successfully brought quantum chemists and chemical and condensed matter physicists together in presentations, posters, and informal discussions bridging those two communities. The Symposium has had a significant role in preparing generations of quantum theorists. As computational potency and algorithmic sophistication have grown, the Symposium has evolved to emphasize more heavily computationally oriented method development in chemistry and materials physics, including nanoscience, complex molecular phenomena, and even bio-molecular methods and problems. Given this context, the 56 th Sanibel meeting systematicallymore » and deliberately had sessions focused on exascale computation. A selection of outstanding theoretical problems that need serious attention was included. Five invited sessions, two contributed sessions (hot topics), and a poster session were organized with the exascale theme. This was a historic milestone in the evolution of the Symposia. Just as years ago linear algebra, perturbation theory, density matrices, and band-structure methods dominated early Sanibel Symposia, the exascale sessions of the 56 thmeeting contributed a transformative influence to add structure and strength to the computational physical science community in an unprecedented way. A copy of the full program of the 56 th Symposium is attached. The exascale sessions were Linear Scaling, Non-Adabatic Dynamics, Interpretive Theory and Models, Computation, Software, and Algorithms, and Quantum Monte Carlo. The Symposium Proceedings will be published in Molecular Physics (2017). Note that the Sanibel proceedings from 2015 and 2014 were published as Molecular Physics vol. 114, issue 3-4 (2016) and vol. 113, issue 3-4 (2015) respectively.« less

Quantum control via a genetic algorithm of the field ionization pathway of a Rydberg electron

NASA Astrophysics Data System (ADS)

Gregoric, Vincent C.; Kang, Xinyue; Liu, Zhimin Cheryl; Rowley, Zoe A.; Carroll, Thomas J.; Noel, Michael W.

2017-08-01

Quantum control of the pathway along which a Rydberg electron field ionizes is experimentally and computationally demonstrated. Selective field ionization is typically done with a slowly rising electric field pulse. The (1/n*)4 scaling of the classical ionization threshold leads to a rough mapping between arrival time of the electron signal and principal quantum number of the Rydberg electron. This is complicated by the many avoided level crossings that the electron must traverse on the way to ionization, which in general leads to broadening of the time-resolved field ionization signal. In order to control the ionization pathway, thus directing the signal to the desired arrival time, a perturbing electric field produced by an arbitrary wave-form generator is added to a slowly rising electric field. A genetic algorithm evolves the perturbing field in an effort to achieve the target time-resolved field ionization signal.

Simulation of n-qubit quantum systems. I. Quantum registers and quantum gates

NASA Astrophysics Data System (ADS)

Radtke, T.; Fritzsche, S.

2005-12-01

During recent years, quantum computations and the study of n-qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing quantum computations, however, these investigations also revealed a great deal of difficulties which still need to be solved in practice. In quantum computing, unitary and non-unitary quantum operations act on a given set of qubits to form (entangled) states, in which the information is encoded by the overall system often referred to as quantum registers. To facilitate the simulation of such n-qubit quantum systems, we present the FEYNMAN program to provide all necessary tools in order to define and to deal with quantum registers and quantum operations. Although the present version of the program is restricted to unitary transformations, it equally supports—whenever possible—the representation of the quantum registers both, in terms of their state vectors and density matrices. In addition to the composition of two or more quantum registers, moreover, the program also supports their decomposition into various parts by applying the partial trace operation and the concept of the reduced density matrix. Using an interactive design within the framework of MAPLE, therefore, we expect the FEYNMAN program to be helpful not only for teaching the basic elements of quantum computing but also for studying their physical realization in the future. Program summaryTitle of program:FEYNMAN Catalogue number:ADWE Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:None Computers for which the program is designed:All computers with a license of the computer algebra system MAPLE [Maple is a registered trademark of Waterlo Maple Inc.] Operating systems or monitors under which the program has been tested:Linux, MS Windows XP Programming language used:MAPLE 9.5 (but should be compatible with 9.0 and 8.0, too) Memory and time required to execute with typical data:Storage and time requirements critically depend on the number of qubits, n, in the quantum registers due to the exponential increase of the associated Hilbert space. In particular, complex algebraic operations may require large amounts of memory even for small qubit numbers. However, most of the standard commands (see Section 4 for simple examples) react promptly for up to five qubits on a normal single-processor machine ( ⩾1GHz with 512 MB memory) and use less than 10 MB memory. No. of lines in distributed program, including test data, etc.: 8864 No. of bytes in distributed program, including test data, etc.: 493 182 Distribution format: tar.gz Nature of the physical problem:During the last decade, quantum computing has been found to provide a revolutionary new form of computation. The algorithms by Shor [P.W. Shor, SIAM J. Sci. Statist. Comput. 26 (1997) 1484] and Grover [L.K. Grover, Phys. Rev. Lett. 79 (1997) 325. [2

Algorithmes et architectures pour ordinateurs quantiques supraconducteurs

NASA Astrophysics Data System (ADS)

Blais, A.

2003-09-01

Algorithms and architectures for superconducting quantum computers Since its formulation, information theory was based, implicitly, on the laws of classical physics. Such a formulation is however incomplete because it does not take into account quantum reality. During the last twenty years, expansion of theory information to include quantum effects has known growing interest. The practical realization of a system for quantum data processing system, a quantum computer, presents however many challenges. In this book, we are interested in various aspects of these challenges. We start by presenting algorithmic concepts like optimization of quantum computations and geometric quantum computation. We then consider various designs and aspects of qubits based on Josephson junctions. In particular, an original approach to the interaction between superconducting qubits is presented. This approach is very general since it can be applied to various designs of qubits. Finally, we are interested in read-out of the superconductic flux qubits. The detector suggested here has the advantage that it is possible to uncouple it from the qubit when no measurement is in progress. Depuis sa formulation, la théorie de l'information a été basée, implicitement, sur les lois de la physique classique. Une telle formulation est toutefois incomplète puisqu'elle ne tient pas compte de la réalité quantique. Au cours des vingt dernières années, l'expansion de la théorie de l'information, de façon à englober les effets purement quantiques, a connu un intérêt grandissant. La réalisation d'un système de traitement de l'information quantique, un ordinateur quantique, présente toutefois de nombreux défis. Dans cet ouvrage, on s'intéresse à différents aspects concernant ces défis. On commence par présenter des concepts algorithmiques comme l'optimisation de calculs quantiques et le calcul quantique géométrique. Par la suite, on s'intéresse à différents designs et aspects de l'utilisation de qubits basés sur les jonctions Josephson. On présente entre autres une approche originale pour l'interaction entre qubits. Cette approche est très générale puisqu'elle peut être appliquée à différents designs de qubits. Finalement, on s'intéresse à la lecture des qubits supraconducteurs de flux. Le détecteur suggéré ici a l'avantage de pouvoir être découplé du qubit lorsqu'il n'y a pas de mesure en cours.

Machine Learning and Quantum Mechanics

NASA Astrophysics Data System (ADS)

Chapline, George

The author has previously pointed out some similarities between selforganizing neural networks and quantum mechanics. These types of neural networks were originally conceived of as away of emulating the cognitive capabilities of the human brain. Recently extensions of these networks, collectively referred to as deep learning networks, have strengthened the connection between self-organizing neural networks and human cognitive capabilities. In this note we consider whether hardware quantum devices might be useful for emulating neural networks with human-like cognitive capabilities, or alternatively whether implementations of deep learning neural networks using conventional computers might lead to better algorithms for solving the many body Schrodinger equation.

Distinguishing computable mixtures of quantum states

NASA Astrophysics Data System (ADS)

Grande, Ignacio H. López; Senno, Gabriel; de la Torre, Gonzalo; Larotonda, Miguel A.; Bendersky, Ariel; Figueira, Santiago; Acín, Antonio

2018-05-01

In this article we extend results from our previous work [Bendersky et al., Phys. Rev. Lett. 116, 230402 (2016), 10.1103/PhysRevLett.116.230402] by providing a protocol to distinguish in finite time and with arbitrarily high success probability any algorithmic mixture of pure states from the maximally mixed state. Moreover, we include an experimental realization, using a modified quantum key distribution setup, where two different random sequences of pure states are prepared; these sequences are indistinguishable according to quantum mechanics, but they become distinguishable when randomness is replaced with pseudorandomness within the experimental preparation process.

Hybrid glowworm swarm optimization for task scheduling in the cloud environment

NASA Astrophysics Data System (ADS)

Zhou, Jing; Dong, Shoubin

2018-06-01

In recent years many heuristic algorithms have been proposed to solve task scheduling problems in the cloud environment owing to their optimization capability. This article proposes a hybrid glowworm swarm optimization (HGSO) based on glowworm swarm optimization (GSO), which uses a technique of evolutionary computation, a strategy of quantum behaviour based on the principle of neighbourhood, offspring production and random walk, to achieve more efficient scheduling with reasonable scheduling costs. The proposed HGSO reduces the redundant computation and the dependence on the initialization of GSO, accelerates the convergence and more easily escapes from local optima. The conducted experiments and statistical analysis showed that in most cases the proposed HGSO algorithm outperformed previous heuristic algorithms to deal with independent tasks.

Demonstration of Qubit Operations Below a Rigorous Fault Tolerance Threshold With Gate Set Tomography (Open Access, Publisher’s Version)

DTIC Science & Technology

2017-02-15

Maunz2 Quantum information processors promise fast algorithms for problems inaccessible to classical computers. But since qubits are noisy and error-prone...information processors have been demonstrated experimentally using superconducting circuits1–3, electrons in semiconductors4–6, trapped atoms and...qubit quantum information processor has been realized14, and single- qubit gates have demonstrated randomized benchmarking (RB) infidelities as low as 10

Human body motion tracking based on quantum-inspired immune cloning algorithm

NASA Astrophysics Data System (ADS)

Han, Hong; Yue, Lichuan; Jiao, Licheng; Wu, Xing

2009-10-01

In a static monocular camera system, to gain a perfect 3D human body posture is a great challenge for Computer Vision technology now. This paper presented human postures recognition from video sequences using the Quantum-Inspired Immune Cloning Algorithm (QICA). The algorithm included three parts. Firstly, prior knowledge of human beings was used, the key joint points of human could be detected automatically from the human contours and skeletons which could be thinning from the contours; And due to the complexity of human movement, a forecasting mechanism of occlusion joint points was addressed to get optimum 2D key joint points of human body; And then pose estimation recovered by optimizing between the 2D projection of 3D human key joint points and 2D detection key joint points using QICA, which recovered the movement of human body perfectly, because this algorithm could acquire not only the global optimal solution, but the local optimal solution.

Surface hopping with a manifold of electronic states. I. Incorporating surface-leaking to capture lifetimes

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

Ouyang, Wenjun; Dou, Wenjie; Subotnik, Joseph E., E-mail: subotnik@sas.upenn.edu

2015-02-28

We investigate the incorporation of the surface-leaking (SL) algorithm into Tully’s fewest-switches surface hopping (FSSH) algorithm to simulate some electronic relaxation induced by an electronic bath in conjunction with some electronic transitions between discrete states. The resulting SL-FSSH algorithm is benchmarked against exact quantum scattering calculations for three one-dimensional model problems. The results show excellent agreement between SL-FSSH and exact quantum dynamics in the wide band limit, suggesting the potential for a SL-FSSH algorithm. Discrepancies and failures are investigated in detail to understand the factors that will limit the reliability of SL-FSSH, especially the wide band approximation. Considering the easinessmore » of implementation and the low computational cost, we expect this method to be useful in studying processes involving both a continuum of electronic states (where electronic dynamics are probabilistic) and processes involving only a few electronic states (where non-adiabatic processes cannot ignore short-time coherence)« 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.

Polynomial complexity despite the fermionic sign

NASA Astrophysics Data System (ADS)

Rossi, R.; Prokof'ev, N.; Svistunov, B.; Van Houcke, K.; Werner, F.

2017-04-01

It is commonly believed that in unbiased quantum Monte Carlo approaches to fermionic many-body problems, the infamous sign problem generically implies prohibitively large computational times for obtaining thermodynamic-limit quantities. We point out that for convergent Feynman diagrammatic series evaluated with a recently introduced Monte Carlo algorithm (see Rossi R., arXiv:1612.05184), the computational time increases only polynomially with the inverse error on thermodynamic-limit quantities.

Applications of quantum measurement techniques: Counterfactual quantum computation, spin hall effect of light, and atomic-vapor-based photon detectors

NASA Astrophysics Data System (ADS)

Hosten, Onur

This dissertation investigates several physical phenomena in atomic and optical physics, and quantum information science, by utilizing various types and techniques of quantum measurements. It is the deeper concepts of these measurements, and the way they are integrated into the seemingly unrelated topics investigated, which binds together the research presented here. The research comprises three different topics: Counterfactual quantum computation, the spin Hall effect of light, and ultra-high-efficiency photon detectors based on atomic vapors. Counterfactual computation entails obtaining answers from a quantum computer without actually running it, and is accomplished by preparing the computer as a whole into a superposition of being activated and not activated. The first experimental demonstration is presented, including the best performing implementation of Grover's quantum search algorithm to date. In addition, we develop new counterfactual computation protocols that enable unconditional and completely deterministic operation. These methods stimulated a debate in the literature, on the meaning of counterfactuality in quantum processes, which we also discuss. The spin Hall effect of light entails tiny spin-dependent displacements, unsuspected until 2004, of a beam of light when it changes propagation direction. The first experimental demonstration of the effect during refraction at an air-glass interface is presented, together with a novel enabling metrological tool relying on the concepts of quantum weak measurements. Extensions of the effect to smoothly varying media are also presented, along with utilization of a time-varying version of the weak measurement techniques. Our approach to ultra-high-efficiency photon detection develops and extends a recent novel non-solid-state scheme for photo-detection based on atomic vapors. This approach is in principle capable of resolving the number of photons in a pulse, can be extended to non-destructive detection of photons, and most importantly is proposed to operate with single-photon detection efficiencies exceeding 99%, ideally without dark counts. Such a detector would have tremendous implications, e.g., for optical quantum information processing. The feasibility of operation of this approach at the desired level is studied theoretically and several promising physical systems are investigated.

Accelerating atomistic calculations of quantum energy eigenstates on graphic cards

NASA Astrophysics Data System (ADS)

Rodrigues, Walter; Pecchia, A.; Lopez, M.; Auf der Maur, M.; Di Carlo, A.

2014-10-01

Electronic properties of nanoscale materials require the calculation of eigenvalues and eigenvectors of large matrices. This bottleneck can be overcome by parallel computing techniques or the introduction of faster algorithms. In this paper we report a custom implementation of the Lanczos algorithm with simple restart, optimized for graphical processing units (GPUs). The whole algorithm has been developed using CUDA and runs entirely on the GPU, with a specialized implementation that spares memory and reduces at most machine-to-device data transfers. Furthermore parallel distribution over several GPUs has been attained using the standard message passing interface (MPI). Benchmark calculations performed on a GaN/AlGaN wurtzite quantum dot with up to 600,000 atoms are presented. The empirical tight-binding (ETB) model with an sp3d5s∗+spin-orbit parametrization has been used to build the system Hamiltonian (H).

Transforming graph states using single-qubit operations.

PubMed

Dahlberg, Axel; Wehner, Stephanie

2018-07-13

Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from another stabilizer (source) state by single-qubit Clifford operations (LC), single-qubit Pauli measurements (LPM) and classical communication (CC) between sites holding the individual qubits. What is more, we provide a recipe to obtain the sequence of LC+LPM+CC operations which prepare the desired target state from the source state, and show how these operations can be applied in parallel to reach the target state in constant time. Our algorithm has applications in quantum networks, quantum computing, and can also serve as a design tool-for example, to find transformations between quantum error correcting codes. We provide a software implementation of our algorithm that makes this tool easier to apply. A key insight leading to our algorithm is to show that the problem is equivalent to one in graph theory, which is to decide whether some graph G ' is a vertex-minor of another graph G The vertex-minor problem is, in general, [Formula: see text]-Complete, but can be solved efficiently on graphs which are not too complex. A measure of the complexity of a graph is the rank-width which equals the Schmidt-rank width of a subclass of stabilizer states called graph states, and thus intuitively is a measure of entanglement. Here, we show that the vertex-minor problem can be solved in time O (| G | 3 ), where | G | is the size of the graph G , whenever the rank-width of G and the size of G ' are bounded. Our algorithm is based on techniques by Courcelle for solving fixed parameter tractable problems, where here the relevant fixed parameter is the rank width. The second half of this paper serves as an accessible but far from exhausting introduction to these concepts, that could be useful for many other problems in quantum information.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Numerical stabilization of entanglement computation in auxiliary-field quantum Monte Carlo simulations of interacting many-fermion systems.

PubMed

Broecker, Peter; Trebst, Simon

2016-12-01

In the absence of a fermion sign problem, auxiliary-field (or determinantal) quantum Monte Carlo (DQMC) approaches have long been the numerical method of choice for unbiased, large-scale simulations of interacting many-fermion systems. More recently, the conceptual scope of this approach has been expanded by introducing ingenious schemes to compute entanglement entropies within its framework. On a practical level, these approaches, however, suffer from a variety of numerical instabilities that have largely impeded their applicability. Here we report on a number of algorithmic advances to overcome many of these numerical instabilities and significantly improve the calculation of entanglement measures in the zero-temperature projective DQMC approach, ultimately allowing us to reach similar system sizes as for the computation of conventional observables. We demonstrate the applicability of this improved DQMC approach by providing an entanglement perspective on the quantum phase transition from a magnetically ordered Mott insulator to a band insulator in the bilayer square lattice Hubbard model at half filling.

Momentum Distribution as a Fingerprint of Quantum Delocalization in Enzymatic Reactions: Open-Chain Path-Integral Simulations of Model Systems and the Hydride Transfer in Dihydrofolate Reductase.

PubMed

Engel, Hamutal; Doron, Dvir; Kohen, Amnon; Major, Dan Thomas

2012-04-10

The inclusion of nuclear quantum effects such as zero-point energy and tunneling is of great importance in studying condensed phase chemical reactions involving the transfer of protons, hydrogen atoms, and hydride ions. In the current work, we derive an efficient quantum simulation approach for the computation of the momentum distribution in condensed phase chemical reactions. The method is based on a quantum-classical approach wherein quantum and classical simulations are performed separately. The classical simulations use standard sampling techniques, whereas the quantum simulations employ an open polymer chain path integral formulation which is computed using an efficient Monte Carlo staging algorithm. The approach is validated by applying it to a one-dimensional harmonic oscillator and symmetric double-well potential. Subsequently, the method is applied to the dihydrofolate reductase (DHFR) catalyzed reduction of 7,8-dihydrofolate by nicotinamide adenine dinucleotide phosphate hydride (NADPH) to yield S-5,6,7,8-tetrahydrofolate and NADP(+). The key chemical step in the catalytic cycle of DHFR involves a stereospecific hydride transfer. In order to estimate the amount of quantum delocalization, we compute the position and momentum distributions for the transferring hydride ion in the reactant state (RS) and transition state (TS) using a recently developed hybrid semiempirical quantum mechanics-molecular mechanics potential energy surface. Additionally, we examine the effect of compression of the donor-acceptor distance (DAD) in the TS on the momentum distribution. The present results suggest differential quantum delocalization in the RS and TS, as well as reduced tunneling upon DAD compression.

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.

Quantum Image Steganography and Steganalysis Based On LSQu-Blocks Image Information Concealing Algorithm

NASA Astrophysics Data System (ADS)

A. AL-Salhi, Yahya E.; Lu, Songfeng

2016-08-01

Quantum steganography can solve some problems that are considered inefficient in image information concealing. It researches on Quantum image information concealing to have been widely exploited in recent years. Quantum image information concealing can be categorized into quantum image digital blocking, quantum image stereography, anonymity and other branches. Least significant bit (LSB) information concealing plays vital roles in the classical world because many image information concealing algorithms are designed based on it. Firstly, based on the novel enhanced quantum representation (NEQR), image uniform blocks clustering around the concrete the least significant Qu-block (LSQB) information concealing algorithm for quantum image steganography is presented. Secondly, a clustering algorithm is proposed to optimize the concealment of important data. Finally, we used Con-Steg algorithm to conceal the clustered image blocks. Information concealing located on the Fourier domain of an image can achieve the security of image information, thus we further discuss the Fourier domain LSQu-block information concealing algorithm for quantum image based on Quantum Fourier Transforms. In our algorithms, the corresponding unitary Transformations are designed to realize the aim of concealing the secret information to the least significant Qu-block representing color of the quantum cover image. Finally, the procedures of extracting the secret information are illustrated. Quantum image LSQu-block image information concealing algorithm can be applied in many fields according to different needs.

Fast and simple high-capacity quantum cryptography with error detection

PubMed Central

Lai, Hong; Luo, Ming-Xing; Pieprzyk, Josef; Zhang, Jun; Pan, Lei; Li, Shudong; Orgun, Mehmet A.

2017-01-01

Quantum cryptography is commonly used to generate fresh secure keys with quantum signal transmission for instant use between two parties. However, research shows that the relatively low key generation rate hinders its practical use where a symmetric cryptography component consumes the shared key. That is, the security of the symmetric cryptography demands frequent rate of key updates, which leads to a higher consumption of the internal one-time-pad communication bandwidth, since it requires the length of the key to be as long as that of the secret. In order to alleviate these issues, we develop a matrix algorithm for fast and simple high-capacity quantum cryptography. Our scheme can achieve secure private communication with fresh keys generated from Fibonacci- and Lucas- valued orbital angular momentum (OAM) states for the seed to construct recursive Fibonacci and Lucas matrices. Moreover, the proposed matrix algorithm for quantum cryptography can ultimately be simplified to matrix multiplication, which is implemented and optimized in modern computers. Most importantly, considerably information capacity can be improved effectively and efficiently by the recursive property of Fibonacci and Lucas matrices, thereby avoiding the restriction of physical conditions, such as the communication bandwidth. PMID:28406240

Fast and simple high-capacity quantum cryptography with error detection.

PubMed

Lai, Hong; Luo, Ming-Xing; Pieprzyk, Josef; Zhang, Jun; Pan, Lei; Li, Shudong; Orgun, Mehmet A

2017-04-13

Quantum cryptography is commonly used to generate fresh secure keys with quantum signal transmission for instant use between two parties. However, research shows that the relatively low key generation rate hinders its practical use where a symmetric cryptography component consumes the shared key. That is, the security of the symmetric cryptography demands frequent rate of key updates, which leads to a higher consumption of the internal one-time-pad communication bandwidth, since it requires the length of the key to be as long as that of the secret. In order to alleviate these issues, we develop a matrix algorithm for fast and simple high-capacity quantum cryptography. Our scheme can achieve secure private communication with fresh keys generated from Fibonacci- and Lucas- valued orbital angular momentum (OAM) states for the seed to construct recursive Fibonacci and Lucas matrices. Moreover, the proposed matrix algorithm for quantum cryptography can ultimately be simplified to matrix multiplication, which is implemented and optimized in modern computers. Most importantly, considerably information capacity can be improved effectively and efficiently by the recursive property of Fibonacci and Lucas matrices, thereby avoiding the restriction of physical conditions, such as the communication bandwidth.

Fast and simple high-capacity quantum cryptography with error detection

NASA Astrophysics Data System (ADS)

Lai, Hong; Luo, Ming-Xing; Pieprzyk, Josef; Zhang, Jun; Pan, Lei; Li, Shudong; Orgun, Mehmet A.

2017-04-01

Quantum cryptography is commonly used to generate fresh secure keys with quantum signal transmission for instant use between two parties. However, research shows that the relatively low key generation rate hinders its practical use where a symmetric cryptography component consumes the shared key. That is, the security of the symmetric cryptography demands frequent rate of key updates, which leads to a higher consumption of the internal one-time-pad communication bandwidth, since it requires the length of the key to be as long as that of the secret. In order to alleviate these issues, we develop a matrix algorithm for fast and simple high-capacity quantum cryptography. Our scheme can achieve secure private communication with fresh keys generated from Fibonacci- and Lucas- valued orbital angular momentum (OAM) states for the seed to construct recursive Fibonacci and Lucas matrices. Moreover, the proposed matrix algorithm for quantum cryptography can ultimately be simplified to matrix multiplication, which is implemented and optimized in modern computers. Most importantly, considerably information capacity can be improved effectively and efficiently by the recursive property of Fibonacci and Lucas matrices, thereby avoiding the restriction of physical conditions, such as the communication bandwidth.

Topological quantum computation of the Dold-Thom functor

NASA Astrophysics Data System (ADS)

Ospina, Juan

2014-05-01

A possible topological quantum computation of the Dold-Thom functor is presented. The method that will be used is the following: a) Certain 1+1-topological quantum field theories valued in symmetric bimonoidal categories are converted into stable homotopical data, using a machinery recently introduced by Elmendorf and Mandell; b) we exploit, in this framework, two recent results (independent of each other) on refinements of Khovanov homology: our refinement into a module over the connective k-theory spectrum and a stronger result by Lipshitz and Sarkar refining Khovanov homology into a stable homotopy type; c) starting from the Khovanov homotopy the Dold-Thom functor is constructed; d) the full construction is formulated as a topological quantum algorithm. It is conjectured that the Jones polynomial can be described as the analytical index of certain Dirac operator defined in the context of the Khovanov homotopy using the Dold-Thom functor. As a line for future research is interesting to study the corresponding supersymmetric model for which the Khovanov-Dirac operator plays the role of a supercharge.

Proceedings of the Quantum Computation for Physical Modeling Workshop Held in North Falmouth, Massachusetts on October 18-19, 2000

DTIC Science & Technology

2002-01-01

1-3], a task that is exponen- algorithms to model quantum mechanical systems. tially complex in the number of particles treated and A starting point ...cell size approaches zero). There- tion were presented by Succi and Benzi [10,11] and fore, from the point -of-view of the modeler, there ex- by... point regarding this particular In both cases, the model behaves as expected. gate is that when measurements are periodically made Third, in Section 4

Quantum Engineering of Dynamical Gauge Fields on Optical Lattices

DTIC Science & Technology

2016-07-08

exact blocking formulas from the TRG formulation of the transfer matrix. The second is a worm algorithm. The particle number distributions obtained...a fact that can be explained by an approximate particle- hole symmetry. We have also developed a computer code suite for simulating the Abelian

Making Classical Ground State Spin Computing Fault-Tolerant

DTIC Science & Technology

2010-06-24

approaches to perebor (brute-force searches) algorithms,” IEEE Annals of the History of Computing, 6, 384–400 (1984). [24] D. Bacon and S . T. Flammia ...Adiabatic gate teleportation,” Phys. Rev. Lett., 103, 120504 (2009). [25] D. Bacon and S . T. Flammia , “Adiabatic cluster state quantum computing...v1 [ co nd -m at . s ta t- m ec h] 2 2 Ju n 20 10 Report Documentation Page Form ApprovedOMB No. 0704-0188 Public reporting burden for the

Linear Scaling Density Functional Calculations with Gaussian Orbitals

NASA Technical Reports Server (NTRS)

Scuseria, Gustavo E.

1999-01-01

Recent advances in linear scaling algorithms that circumvent the computational bottlenecks of large-scale electronic structure simulations make it possible to carry out density functional calculations with Gaussian orbitals on molecules containing more than 1000 atoms and 15000 basis functions using current workstations and personal computers. This paper discusses the recent theoretical developments that have led to these advances and demonstrates in a series of benchmark calculations the present capabilities of state-of-the-art computational quantum chemistry programs for the prediction of molecular structure and properties.

Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation.

PubMed

Sawaya, Nicolas P D; Smelyanskiy, Mikhail; McClean, Jarrod R; Aspuru-Guzik, Alán

2016-07-12

Calculating molecular energies is likely to be one of the first useful applications to achieve quantum supremacy, performing faster on a quantum than a classical computer. However, if future quantum devices are to produce accurate calculations, errors due to environmental noise and algorithmic approximations need to be characterized and reduced. In this study, we use the high performance qHiPSTER software to investigate the effects of environmental noise on the preparation of quantum chemistry states. We simulated 18 16-qubit quantum circuits under environmental noise, each corresponding to a unitary coupled cluster state preparation of a different molecule or molecular configuration. Additionally, we analyze the nature of simple gate errors in noise-free circuits of up to 40 qubits. We find that, in most cases, the Jordan-Wigner (JW) encoding produces smaller errors under a noisy environment as compared to the Bravyi-Kitaev (BK) encoding. For the JW encoding, pure dephasing noise is shown to produce substantially smaller errors than pure relaxation noise of the same magnitude. We report error trends in both molecular energy and electron particle number within a unitary coupled cluster state preparation scheme, against changes in nuclear charge, bond length, number of electrons, noise types, and noise magnitude. These trends may prove to be useful in making algorithmic and hardware-related choices for quantum simulation of molecular energies.

Extending Strong Scaling of Quantum Monte Carlo to the Exascale

NASA Astrophysics Data System (ADS)

Shulenburger, Luke; Baczewski, Andrew; Luo, Ye; Romero, Nichols; Kent, Paul

Quantum Monte Carlo is one of the most accurate and most computationally expensive methods for solving the electronic structure problem. In spite of its significant computational expense, its massively parallel nature is ideally suited to petascale computers which have enabled a wide range of applications to relatively large molecular and extended systems. Exascale capabilities have the potential to enable the application of QMC to significantly larger systems, capturing much of the complexity of real materials such as defects and impurities. However, both memory and computational demands will require significant changes to current algorithms to realize this possibility. This talk will detail both the causes of the problem and potential solutions. Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corp, a wholly owned subsidiary of Lockheed Martin Corp, for the US Department of Energys National Nuclear Security Administration under contract DE-AC04-94AL85000.

Ab initio quantum chemistry: methodology and applications.

PubMed

Friesner, Richard A

2005-05-10

This Perspective provides an overview of state-of-the-art ab initio quantum chemical methodology and applications. The methods that are discussed include coupled cluster theory, localized second-order Moller-Plesset perturbation theory, multireference perturbation approaches, and density functional theory. The accuracy of each approach for key chemical properties is summarized, and the computational performance is analyzed, emphasizing significant advances in algorithms and implementation over the past decade. Incorporation of a condensed-phase environment by means of mixed quantum mechanical/molecular mechanics or self-consistent reaction field techniques, is presented. A wide range of illustrative applications, focusing on materials science and biology, are discussed briefly.

Gouy Phase Radial Mode Sorter for Light: Concepts and Experiments.

PubMed

Gu, Xuemei; Krenn, Mario; Erhard, Manuel; Zeilinger, Anton

2018-03-09

We present an in principle lossless sorter for radial modes of light, using accumulated Gouy phases. The experimental setups have been found by a computer algorithm, and can be intuitively understood in a geometric way. Together with the ability to sort angular-momentum modes, we now have access to the complete two-dimensional transverse plane of light. The device can readily be used in multiplexing classical information. On a quantum level, it is an analog of the Stern-Gerlach experiment-significant for the discussion of fundamental concepts in quantum physics. As such, it can be applied in high-dimensional and multiphotonic quantum experiments.

Gouy Phase Radial Mode Sorter for Light: Concepts and Experiments

NASA Astrophysics Data System (ADS)

Gu, Xuemei; Krenn, Mario; Erhard, Manuel; Zeilinger, Anton

2018-03-01

We present an in principle lossless sorter for radial modes of light, using accumulated Gouy phases. The experimental setups have been found by a computer algorithm, and can be intuitively understood in a geometric way. Together with the ability to sort angular-momentum modes, we now have access to the complete two-dimensional transverse plane of light. The device can readily be used in multiplexing classical information. On a quantum level, it is an analog of the Stern-Gerlach experiment—significant for the discussion of fundamental concepts in quantum physics. As such, it can be applied in high-dimensional and multiphotonic quantum experiments.

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.

Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo

DOE PAGES

McDaniel, Tyler; D’Azevedo, Ed F.; Li, Ying Wai; ...

2017-11-07

Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is therefore formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with applicationmore » of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. Here this procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi- core CPUs and GPUs.« less

Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo

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

McDaniel, Tyler; D’Azevedo, Ed F.; Li, Ying Wai

Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is therefore formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with applicationmore » of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. Here this procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi- core CPUs and GPUs.« less

Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo.

PubMed

McDaniel, T; D'Azevedo, E F; Li, Y W; Wong, K; Kent, P R C

2017-11-07

Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is, therefore, formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with an application of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. This procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo, where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi-core central processing units and graphical processing units.

Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo

NASA Astrophysics Data System (ADS)

McDaniel, T.; D'Azevedo, E. F.; Li, Y. W.; Wong, K.; Kent, P. R. C.

2017-11-01

Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is, therefore, formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with an application of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. This procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo, where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi-core central processing units and graphical processing units.

High-efficiency wavefunction updates for large scale Quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Kent, Paul; McDaniel, Tyler; Li, Ying Wai; D'Azevedo, Ed

Within ab intio Quantum Monte Carlo (QMC) simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunctions. The evaluation of each Monte Carlo move requires finding the determinant of a dense matrix, which is traditionally iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. For calculations with thousands of electrons, this operation dominates the execution profile. We propose a novel rank- k delayed update scheme. This strategy enables probability evaluation for multiple successive Monte Carlo moves, with application of accepted moves to the matrices delayed until after a predetermined number of moves, k. Accepted events grouped in this manner are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency. This procedure does not change the underlying Monte Carlo sampling or the sampling efficiency. For large systems and algorithms such as diffusion Monte Carlo where the acceptance ratio is high, order of magnitude speedups can be obtained on both multi-core CPU and on GPUs, making this algorithm highly advantageous for current petascale and future exascale computations.

Off-diagonal expansion quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Albash, Tameem; Wagenbreth, Gene; Hen, Itay

2017-12-01

We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a decomposition of the quantum partition function that can be viewed as a series expansion about its classical part. We argue that the algorithm not only provides a theoretical advancement in the field of quantum Monte Carlo simulations, but is optimally suited to tackle quantum many-body systems that exhibit a range of behaviors from "fully quantum" to "fully classical," in contrast to many existing methods. We demonstrate the advantages, sometimes by orders of magnitude, of the technique by comparing it against existing state-of-the-art schemes such as path integral quantum Monte Carlo and stochastic series expansion. We also illustrate how our method allows for the unification of quantum and classical thermal parallel tempering techniques into a single algorithm and discuss its practical significance.

Off-diagonal expansion quantum Monte Carlo.

PubMed

Albash, Tameem; Wagenbreth, Gene; Hen, Itay

2017-12-01

We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a decomposition of the quantum partition function that can be viewed as a series expansion about its classical part. We argue that the algorithm not only provides a theoretical advancement in the field of quantum Monte Carlo simulations, but is optimally suited to tackle quantum many-body systems that exhibit a range of behaviors from "fully quantum" to "fully classical," in contrast to many existing methods. We demonstrate the advantages, sometimes by orders of magnitude, of the technique by comparing it against existing state-of-the-art schemes such as path integral quantum Monte Carlo and stochastic series expansion. We also illustrate how our method allows for the unification of quantum and classical thermal parallel tempering techniques into a single algorithm and discuss its practical significance.

Multiparty Quantum Key Agreement Based on Quantum Search Algorithm

PubMed Central

Cao, Hao; Ma, Wenping

2017-01-01

Quantum key agreement is an important topic that the shared key must be negotiated equally by all participants, and any nontrivial subset of participants cannot fully determine the shared key. To date, the embed modes of subkey in all the previously proposed quantum key agreement protocols are based on either BB84 or entangled states. The research of the quantum key agreement protocol based on quantum search algorithms is still blank. In this paper, on the basis of investigating the properties of quantum search algorithms, we propose the first quantum key agreement protocol whose embed mode of subkey is based on a quantum search algorithm known as Grover’s algorithm. A novel example of protocols with 5 – party is presented. The efficiency analysis shows that our protocol is prior to existing MQKA protocols. Furthermore it is secure against both external attack and internal attacks. PMID:28332610

Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography

DOE PAGES

Blume-Kohout, Robin; Gamble, John King; Nielsen, Erik; ...

2017-02-15

Quantum information processors promise fast algorithms for problems inaccessible to classical computers. But since qubits are noisy and error-prone, they will depend on fault-tolerant quantum error correction (FTQEC) to compute reliably. Quantum error correction can protect against general noise if—and only if—the error in each physical qubit operation is smaller than a certain threshold. The threshold for general errors is quantified by their diamond norm. Until now, qubits have been assessed primarily by randomized benchmarking, which reports a different error rate that is not sensitive to all errors, and cannot be compared directly to diamond norm thresholds. Finally, we usemore » gate set tomography to completely characterize operations on a trapped-Yb +-ion qubit and demonstrate with greater than 95% confidence that they satisfy a rigorous threshold for FTQEC (diamond norm ≤6.7 × 10 -4).« less

Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography

PubMed Central

Blume-Kohout, Robin; Gamble, John King; Nielsen, Erik; Rudinger, Kenneth; Mizrahi, Jonathan; Fortier, Kevin; Maunz, Peter

2017-01-01

Quantum information processors promise fast algorithms for problems inaccessible to classical computers. But since qubits are noisy and error-prone, they will depend on fault-tolerant quantum error correction (FTQEC) to compute reliably. Quantum error correction can protect against general noise if—and only if—the error in each physical qubit operation is smaller than a certain threshold. The threshold for general errors is quantified by their diamond norm. Until now, qubits have been assessed primarily by randomized benchmarking, which reports a different error rate that is not sensitive to all errors, and cannot be compared directly to diamond norm thresholds. Here we use gate set tomography to completely characterize operations on a trapped-Yb+-ion qubit and demonstrate with greater than 95% confidence that they satisfy a rigorous threshold for FTQEC (diamond norm ≤6.7 × 10−4). PMID:28198466

Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography

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

Blume-Kohout, Robin; Gamble, John King; Nielsen, Erik

Quantum information processors promise fast algorithms for problems inaccessible to classical computers. But since qubits are noisy and error-prone, they will depend on fault-tolerant quantum error correction (FTQEC) to compute reliably. Quantum error correction can protect against general noise if—and only if—the error in each physical qubit operation is smaller than a certain threshold. The threshold for general errors is quantified by their diamond norm. Until now, qubits have been assessed primarily by randomized benchmarking, which reports a different error rate that is not sensitive to all errors, and cannot be compared directly to diamond norm thresholds. Finally, we usemore » gate set tomography to completely characterize operations on a trapped-Yb +-ion qubit and demonstrate with greater than 95% confidence that they satisfy a rigorous threshold for FTQEC (diamond norm ≤6.7 × 10 -4).« less

Quantum-Inspired Multidirectional Associative Memory With a Self-Convergent Iterative Learning.

PubMed

Masuyama, Naoki; Loo, Chu Kiong; Seera, Manjeevan; Kubota, Naoyuki

2018-04-01

Quantum-inspired computing is an emerging research area, which has significantly improved the capabilities of conventional algorithms. In general, quantum-inspired hopfield associative memory (QHAM) has demonstrated quantum information processing in neural structures. This has resulted in an exponential increase in storage capacity while explaining the extensive memory, and it has the potential to illustrate the dynamics of neurons in the human brain when viewed from quantum mechanics perspective although the application of QHAM is limited as an autoassociation. We introduce a quantum-inspired multidirectional associative memory (QMAM) with a one-shot learning model, and QMAM with a self-convergent iterative learning model (IQMAM) based on QHAM in this paper. The self-convergent iterative learning enables the network to progressively develop a resonance state, from inputs to outputs. The simulation experiments demonstrate the advantages of QMAM and IQMAM, especially the stability to recall reliability.

Quantum Monte Carlo with very large multideterminant wavefunctions.

PubMed

Scemama, Anthony; Applencourt, Thomas; Giner, Emmanuel; Caffarel, Michel

2016-07-01

An algorithm to compute efficiently the first two derivatives of (very) large multideterminant wavefunctions for quantum Monte Carlo calculations is presented. The calculation of determinants and their derivatives is performed using the Sherman-Morrison formula for updating the inverse Slater matrix. An improved implementation based on the reduction of the number of column substitutions and on a very efficient implementation of the calculation of the scalar products involved is presented. It is emphasized that multideterminant expansions contain in general a large number of identical spin-specific determinants: for typical configuration interaction-type wavefunctions the number of unique spin-specific determinants Ndetσ ( σ=↑,↓) with a non-negligible weight in the expansion is of order O(Ndet). We show that a careful implementation of the calculation of the Ndet -dependent contributions can make this step negligible enough so that in practice the algorithm scales as the total number of unique spin-specific determinants,  Ndet↑+Ndet↓, over a wide range of total number of determinants (here, Ndet up to about one million), thus greatly reducing the total computational cost. Finally, a new truncation scheme for the multideterminant expansion is proposed so that larger expansions can be considered without increasing the computational time. The algorithm is illustrated with all-electron fixed-node diffusion Monte Carlo calculations of the total energy of the chlorine atom. Calculations using a trial wavefunction including about 750,000 determinants with a computational increase of ∼400 compared to a single-determinant calculation are shown to be feasible. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Random Walk Quantum Clustering Algorithm Based on Space

NASA Astrophysics Data System (ADS)

Xiao, Shufen; Dong, Yumin; Ma, Hongyang

2018-01-01

In the random quantum walk, which is a quantum simulation of the classical walk, data points interacted when selecting the appropriate walk strategy by taking advantage of quantum-entanglement features; thus, the results obtained when the quantum walk is used are different from those when the classical walk is adopted. A new quantum walk clustering algorithm based on space is proposed by applying the quantum walk to clustering analysis. In this algorithm, data points are viewed as walking participants, and similar data points are clustered using the walk function in the pay-off matrix according to a certain rule. The walk process is simplified by implementing a space-combining rule. The proposed algorithm is validated by a simulation test and is proved superior to existing clustering algorithms, namely, Kmeans, PCA + Kmeans, and LDA-Km. The effects of some of the parameters in the proposed algorithm on its performance are also analyzed and discussed. Specific suggestions are provided.

The Quantum Socket: Wiring for Superconducting Qubits - Part 1

NASA Astrophysics Data System (ADS)

McConkey, T. G.; Bejanin, J. H.; Rinehart, J. R.; Bateman, J. D.; Earnest, C. T.; McRae, C. H.; Rohanizadegan, Y.; Shiri, D.; Mariantoni, M.; Penava, B.; Breul, P.; Royak, S.; Zapatka, M.; Fowler, A. G.

Quantum systems with ten superconducting quantum bits (qubits) have been realized, making it possible to show basic quantum error correction (QEC) algorithms. However, a truly scalable architecture has not been developed yet. QEC requires a two-dimensional array of qubits, restricting any interconnection to external classical systems to the third axis. In this talk, we introduce an interconnect solution for solid-state qubits: The quantum socket. The quantum socket employs three-dimensional wires and makes it possible to connect classical electronics with quantum circuits more densely and accurately than methods based on wire bonding. The three-dimensional wires are based on spring-loaded pins engineered to insure compatibility with quantum computing applications. Extensive design work and machining was required, with focus on material quality to prevent magnetic impurities. Microwave simulations were undertaken to optimize the design, focusing on the interface between the micro-connector and an on-chip coplanar waveguide pad. Simulations revealed good performance from DC to 10 GHz and were later confirmed against experimental measurements.

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

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.

Adaptive recurrence quantum entanglement distillation for two-Kraus-operator channels

NASA Astrophysics Data System (ADS)

Ruan, Liangzhong; Dai, Wenhan; Win, Moe Z.

2018-05-01

Quantum entanglement serves as a valuable resource for many important quantum operations. A pair of entangled qubits can be shared between two agents by first preparing a maximally entangled qubit pair at one agent, and then sending one of the qubits to the other agent through a quantum channel. In this process, the deterioration of entanglement is inevitable since the noise inherent in the channel contaminates the qubit. To address this challenge, various quantum entanglement distillation (QED) algorithms have been developed. Among them, recurrence algorithms have advantages in terms of implementability and robustness. However, the efficiency of recurrence QED algorithms has not been investigated thoroughly in the literature. This paper puts forth two recurrence QED algorithms that adapt to the quantum channel to tackle the efficiency issue. The proposed algorithms have guaranteed convergence for quantum channels with two Kraus operators, which include phase-damping and amplitude-damping channels. Analytical results show that the convergence speed of these algorithms is improved from linear to quadratic and one of the algorithms achieves the optimal speed. Numerical results confirm that the proposed algorithms significantly improve the efficiency of QED.

Complex Rotation Quantum Dynamic Neural Networks (CRQDNN) using Complex Quantum Neuron (CQN): Applications to time series prediction.

PubMed

Cui, Yiqian; Shi, Junyou; Wang, Zili

2015-11-01

Quantum Neural Networks (QNN) models have attracted great attention since it innovates a new neural computing manner based on quantum entanglement. However, the existing QNN models are mainly based on the real quantum operations, and the potential of quantum entanglement is not fully exploited. In this paper, we proposes a novel quantum neuron model called Complex Quantum Neuron (CQN) that realizes a deep quantum entanglement. Also, a novel hybrid networks model Complex Rotation Quantum Dynamic Neural Networks (CRQDNN) is proposed based on Complex Quantum Neuron (CQN). CRQDNN is a three layer model with both CQN and classical neurons. An infinite impulse response (IIR) filter is embedded in the Networks model to enable the memory function to process time series inputs. The Levenberg-Marquardt (LM) algorithm is used for fast parameter learning. The networks model is developed to conduct time series predictions. Two application studies are done in this paper, including the chaotic time series prediction and electronic remaining useful life (RUL) prediction. Copyright © 2015 Elsevier Ltd. All rights reserved.

Extremal Optimization for estimation of the error threshold in topological subsystem codes at T = 0

NASA Astrophysics Data System (ADS)

Millán-Otoya, Jorge E.; Boettcher, Stefan

2014-03-01

Quantum decoherence is a problem that arises in implementations of quantum computing proposals. Topological subsystem codes (TSC) have been suggested as a way to overcome decoherence. These offer a higher optimal error tolerance when compared to typical error-correcting algorithms. A TSC has been translated into a planar Ising spin-glass with constrained bimodal three-spin couplings. This spin-glass has been considered at finite temperature to determine the phase boundary between the unstable phase and the stable phase, where error recovery is possible.[1] We approach the study of the error threshold problem by exploring ground states of this spin-glass with the Extremal Optimization algorithm (EO).[2] EO has proven to be a effective heuristic to explore ground state configurations of glassy spin-systems.[3

Lattice surgery on the Raussendorf lattice

NASA Astrophysics Data System (ADS)

Herr, Daniel; Paler, Alexandru; Devitt, Simon J.; Nori, Franco

2018-07-01

Lattice surgery is a method to perform quantum computation fault-tolerantly by using operations on boundary qubits between different patches of the planar code. This technique allows for universal planar code computation without eliminating the intrinsic two-dimensional nearest-neighbor properties of the surface code that eases physical hardware implementations. Lattice surgery approaches to algorithmic compilation and optimization have been demonstrated to be more resource efficient for resource-intensive components of a fault-tolerant algorithm, and consequently may be preferable over braid-based logic. Lattice surgery can be extended to the Raussendorf lattice, providing a measurement-based approach to the surface code. In this paper we describe how lattice surgery can be performed on the Raussendorf lattice and therefore give a viable alternative to computation using braiding in measurement-based implementations of topological codes.

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.

Dynamic load balancing for petascale quantum Monte Carlo applications: The Alias method

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

Sudheer, C. D.; Krishnan, S.; Srinivasan, A.

Diffusion Monte Carlo is the most accurate widely used Quantum Monte Carlo method for the electronic structure of materials, but it requires frequent load balancing or population redistribution steps to maintain efficiency and avoid accumulation of systematic errors on parallel machines. The load balancing step can be a significant factor affecting performance, and will become more important as the number of processing elements increases. We propose a new dynamic load balancing algorithm, the Alias Method, and evaluate it theoretically and empirically. An important feature of the new algorithm is that the load can be perfectly balanced with each process receivingmore » at most one message. It is also optimal in the maximum size of messages received by any process. We also optimize its implementation to reduce network contention, a process facilitated by the low messaging requirement of the algorithm. Empirical results on the petaflop Cray XT Jaguar supercomputer at ORNL showing up to 30% improvement in performance on 120,000 cores. The load balancing algorithm may be straightforwardly implemented in existing codes. The algorithm may also be employed by any method with many near identical computational tasks that requires load balancing.« less

Highly Parallel Computing Architectures by using Arrays of Quantum-dot Cellular Automata (QCA): Opportunities, Challenges, and Recent Results

NASA Technical Reports Server (NTRS)

Fijany, Amir; Toomarian, Benny N.

2000-01-01

There has been significant improvement in the performance of VLSI devices, in terms of size, power consumption, and speed, in recent years and this trend may also continue for some near future. However, it is a well known fact that there are major obstacles, i.e., physical limitation of feature size reduction and ever increasing cost of foundry, that would prevent the long term continuation of this trend. This has motivated the exploration of some fundamentally new technologies that are not dependent on the conventional feature size approach. Such technologies are expected to enable scaling to continue to the ultimate level, i.e., molecular and atomistic size. Quantum computing, quantum dot-based computing, DNA based computing, biologically inspired computing, etc., are examples of such new technologies. In particular, quantum-dots based computing by using Quantum-dot Cellular Automata (QCA) has recently been intensely investigated as a promising new technology capable of offering significant improvement over conventional VLSI in terms of reduction of feature size (and hence increase in integration level), reduction of power consumption, and increase of switching speed. Quantum dot-based computing and memory in general and QCA specifically, are intriguing to NASA due to their high packing density (10(exp 11) - 10(exp 12) per square cm ) and low power consumption (no transfer of current) and potentially higher radiation tolerant. Under Revolutionary Computing Technology (RTC) Program at the NASA/JPL Center for Integrated Space Microelectronics (CISM), we have been investigating the potential applications of QCA for the space program. To this end, exploiting the intrinsic features of QCA, we have designed novel QCA-based circuits for co-planner (i.e., single layer) and compact implementation of a class of data permutation matrices, a class of interconnection networks, and a bit-serial processor. Building upon these circuits, we have developed novel algorithms and QCA-based architectures for highly parallel and systolic computation of signal/image processing applications, such as FFT and Wavelet and Wlash-Hadamard Transforms.

Complexity of Quantum Impurity Problems

NASA Astrophysics Data System (ADS)

Bravyi, Sergey; Gosset, David

2017-12-01

We give a quasi-polynomial time classical algorithm for estimating the ground state energy and for computing low energy states of quantum impurity models. Such models describe a bath of free fermions coupled to a small interacting subsystem called an impurity. The full system consists of n fermionic modes and has a Hamiltonian {H=H_0+H_{imp}}, where H 0 is quadratic in creation-annihilation operators and H imp is an arbitrary Hamiltonian acting on a subset of O(1) modes. We show that the ground energy of H can be approximated with an additive error {2^{-b}} in time {n^3 \\exp{[O(b^3)]}}. Our algorithm also finds a low energy state that achieves this approximation. The low energy state is represented as a superposition of {\\exp{[O(b^3)]}} fermionic Gaussian states. To arrive at this result we prove several theorems concerning exact ground states of impurity models. In particular, we show that eigenvalues of the ground state covariance matrix decay exponentially with the exponent depending very mildly on the spectral gap of H 0. A key ingredient of our proof is Zolotarev's rational approximation to the {√{x}} function. We anticipate that our algorithms may be used in hybrid quantum-classical simulations of strongly correlated materials based on dynamical mean field theory. We implemented a simplified practical version of our algorithm and benchmarked it using the single impurity Anderson model.

Scheme for Quantum Computing Immune to Decoherence

NASA Technical Reports Server (NTRS)

Williams, Colin; Vatan, Farrokh

2008-01-01

A constructive scheme has been devised to enable mapping of any quantum computation into a spintronic circuit in which the computation is encoded in a basis that is, in principle, immune to quantum decoherence. The scheme is implemented by an algorithm that utilizes multiple physical spins to encode each logical bit in such a way that collective errors affecting all the physical spins do not disturb the logical bit. The scheme is expected to be of use to experimenters working on spintronic implementations of quantum logic. Spintronic computing devices use quantum-mechanical spins (typically, electron spins) to encode logical bits. Bits thus encoded (denoted qubits) are potentially susceptible to errors caused by noise and decoherence. The traditional model of quantum computation is based partly on the assumption that each qubit is implemented by use of a single two-state quantum system, such as an electron or other spin-1.2 particle. It can be surprisingly difficult to achieve certain gate operations . most notably, those of arbitrary 1-qubit gates . in spintronic hardware according to this model. However, ironically, certain 2-qubit interactions (in particular, spin-spin exchange interactions) can be achieved relatively easily in spintronic hardware. Therefore, it would be fortunate if it were possible to implement any 1-qubit gate by use of a spin-spin exchange interaction. While such a direct representation is not possible, it is possible to achieve an arbitrary 1-qubit gate indirectly by means of a sequence of four spin-spin exchange interactions, which could be implemented by use of four exchange gates. Accordingly, the present scheme provides for mapping any 1-qubit gate in the logical basis into an equivalent sequence of at most four spin-spin exchange interactions in the physical (encoded) basis. The complexity of the mathematical derivation of the scheme from basic quantum principles precludes a description within this article; it must suffice to report that the derivation provides explicit constructions for finding the exchange couplings in the physical basis needed to implement any arbitrary 1-qubit gate. These constructions lead to spintronic encodings of quantum logic that are more efficient than those of a previously published scheme that utilizes a universal but fixed set of gates.