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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Quantum Hall effect in graphene with interface-induced spin-orbit coupling

NASA Astrophysics Data System (ADS)

Cysne, Tarik P.; Garcia, Jose H.; Rocha, Alexandre R.; Rappoport, Tatiana G.

2018-02-01

We consider an effective model for graphene with interface-induced spin-orbit coupling and calculate the quantum Hall effect in the low-energy limit. We perform a systematic analysis of the contribution of the different terms of the effective Hamiltonian to the quantum Hall effect (QHE). By analyzing the spin splitting of the quantum Hall states as a function of magnetic field and gate voltage, we obtain different scaling laws that can be used to characterize the spin-orbit coupling in experiments. Furthermore, we employ a real-space quantum transport approach to calculate the quantum Hall conductivity and investigate the robustness of the QHE to disorder introduced by hydrogen impurities. For that purpose, we combine first-principles calculations and a genetic algorithm strategy to obtain a graphene-only Hamiltonian that models the impurity.

Duality quantum algorithm efficiently simulates open quantum systems

PubMed Central

Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu

2016-01-01

Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d3) in contrast to O(d4) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm. PMID:27464855

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

A review on quantum search algorithms

NASA Astrophysics Data System (ADS)

Giri, Pulak Ranjan; Korepin, Vladimir E.

2017-12-01

The use of superposition of states in quantum computation, known as quantum parallelism, has significant advantage in terms of speed over the classical computation. It is evident from the early invented quantum algorithms such as Deutsch's algorithm, Deutsch-Jozsa algorithm and its variation as Bernstein-Vazirani algorithm, Simon algorithm, Shor's algorithms, etc. Quantum parallelism also significantly speeds up the database search algorithm, which is important in computer science because it comes as a subroutine in many important algorithms. Quantum database search of Grover achieves the task of finding the target element in an unsorted database in a time quadratically faster than the classical computer. We review Grover's quantum search algorithms for a singe and multiple target elements in a database. The partial search algorithm of Grover and Radhakrishnan and its optimization by Korepin called GRK algorithm are also discussed.

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.

Genetic design of enhanced valley splitting towards a spin qubit in silicon

PubMed Central

Zhang, Lijun; Luo, Jun-Wei; Saraiva, Andre; Koiller, Belita; Zunger, Alex

2013-01-01

The long spin coherence time and microelectronics compatibility of Si makes it an attractive material for realizing solid-state qubits. Unfortunately, the orbital (valley) degeneracy of the conduction band of bulk Si makes it difficult to isolate individual two-level spin-1/2 states, limiting their development. This degeneracy is lifted within Si quantum wells clad between Ge-Si alloy barrier layers, but the magnitude of the valley splittings achieved so far is small—of the order of 1 meV or less—degrading the fidelity of information stored within such a qubit. Here we combine an atomistic pseudopotential theory with a genetic search algorithm to optimize the structure of layered-Ge/Si-clad Si quantum wells to improve this splitting. We identify an optimal sequence of multiple Ge/Si barrier layers that more effectively isolates the electron ground state of a Si quantum well and increases the valley splitting by an order of magnitude, to ∼9 meV. PMID:24013452

Algorithmic complexity of quantum capacity

NASA Astrophysics Data System (ADS)

Oskouei, Samad Khabbazi; Mancini, Stefano

2018-04-01

We analyze the notion of quantum capacity from the perspective of algorithmic (descriptive) complexity. To this end, we resort to the concept of semi-computability in order to describe quantum states and quantum channel maps. We introduce algorithmic entropies (like algorithmic quantum coherent information) and derive relevant properties for them. Then we show that quantum capacity based on semi-computable concept equals the entropy rate of algorithmic coherent information, which in turn equals the standard quantum capacity. Thanks to this, we finally prove that the quantum capacity, for a given semi-computable channel, is limit computable.

QCE: A Simulator for Quantum Computer Hardware

NASA Astrophysics Data System (ADS)

Michielsen, Kristel; de Raedt, Hans

2003-09-01

The Quantum Computer Emulator (QCE) described in this paper consists of a simulator of a generic, general purpose quantum computer and a graphical user interface. The latter is used to control the simulator, to define the hardware of the quantum computer and to debug and execute quantum algorithms. QCE runs in a Windows 98/NT/2000/ME/XP environment. It can be used to validate designs of physically realizable quantum processors and as an interactive educational tool to learn about quantum computers and quantum algorithms. A detailed exposition is given of the implementation of the CNOT and the Toffoli gate, the quantum Fourier transform, Grover's database search algorithm, an order finding algorithm, Shor's algorithm, a three-input adder and a number partitioning algorithm. We also review the results of simulations of an NMR-like quantum computer.

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.

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.

QCCM Center for Quantum Algorithms

DTIC Science & Technology

2008-10-17

algorithms (e.g., quantum walks and adiabatic computing ), as well as theoretical advances relating algorithms to physical implementations (e.g...Park, NC 27709-2211 15. SUBJECT TERMS Quantum algorithms, quantum computing , fault-tolerant error correction Richard Cleve MITACS East Academic...0511200 Algebraic results on quantum automata A. Ambainis, M. Beaudry, M. Golovkins, A. Kikusts, M. Mercer, D. Thrien Theory of Computing Systems 39(2006

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 cross-disciplinary introduction to quantum annealing-based algorithms

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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.

Quantum dot ternary-valued full-adder: Logic synthesis by a multiobjective design optimization based on a genetic algorithm

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

Klymenko, M. V.; Remacle, F., E-mail: fremacle@ulg.ac.be

2014-10-28

A methodology is proposed for designing a low-energy consuming ternary-valued full adder based on a quantum dot (QD) electrostatically coupled with a single electron transistor operating as a charge sensor. The methodology is based on design optimization: the values of the physical parameters of the system required for implementing the logic operations are optimized using a multiobjective genetic algorithm. The searching space is determined by elements of the capacitance matrix describing the electrostatic couplings in the entire device. The objective functions are defined as the maximal absolute error over actual device logic outputs relative to the ideal truth tables formore » the sum and the carry-out in base 3. The logic units are implemented on the same device: a single dual-gate quantum dot and a charge sensor. Their physical parameters are optimized to compute either the sum or the carry out outputs and are compatible with current experimental capabilities. The outputs are encoded in the value of the electric current passing through the charge sensor, while the logic inputs are supplied by the voltage levels on the two gate electrodes attached to the QD. The complex logic ternary operations are directly implemented on an extremely simple device, characterized by small sizes and low-energy consumption compared to devices based on switching single-electron transistors. The design methodology is general and provides a rational approach for realizing non-switching logic operations on QD devices.« less

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.

Quantum-behaved particle swarm optimization for the synthesis of fibre Bragg gratings filter

NASA Astrophysics Data System (ADS)

Yu, Xuelian; Sun, Yunxu; Yao, Yong; Tian, Jiajun; Cong, Shan

2011-12-01

A method based on the quantum-behaved particle swarm optimization algorithm is presented to design a bandpass filter of the fibre Bragg gratings. In contrast to the other optimization algorithms such as the genetic algorithm and particle swarm optimization algorithm, this method is simpler and easier to implement. To demonstrate the effectiveness of the QPSO algorithm, we consider a bandpass filter. With the parameters the half the bandwidth of the filter 0.05 nm, the Bragg wavelength 1550 nm, the grating length with 2cm is divided into 40 uniform sections and its index modulation is what should be optimized and whole feasible solution space is searched for the index modulation. After the index modulation profile is known for all the sections, the transfer matrix method is used to verify the final optimal index modulation by calculating the refection spectrum. The results show the group delay is less than 12ps in band and the calculated dispersion is relatively flat inside the passband. It is further found that the reflective spectrum has sidelobes around -30dB and the worst in-band dispersion value is less than 200ps/nm . In addition, for this design, it takes approximately several minutes to find the acceptable index modulation values with a notebook computer.

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.

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 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.

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

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.

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.

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

SASS: A symmetry adapted stochastic search algorithm exploiting site symmetry

NASA Astrophysics Data System (ADS)

Wheeler, Steven E.; Schleyer, Paul v. R.; Schaefer, Henry F.

2007-03-01

A simple symmetry adapted search algorithm (SASS) exploiting point group symmetry increases the efficiency of systematic explorations of complex quantum mechanical potential energy surfaces. In contrast to previously described stochastic approaches, which do not employ symmetry, candidate structures are generated within simple point groups, such as C2, Cs, and C2v. This facilitates efficient sampling of the 3N-6 Pople's dimensional configuration space and increases the speed and effectiveness of quantum chemical geometry optimizations. Pople's concept of framework groups [J. Am. Chem. Soc. 102, 4615 (1980)] is used to partition the configuration space into structures spanning all possible distributions of sets of symmetry equivalent atoms. This provides an efficient means of computing all structures of a given symmetry with minimum redundancy. This approach also is advantageous for generating initial structures for global optimizations via genetic algorithm and other stochastic global search techniques. Application of the SASS method is illustrated by locating 14 low-lying stationary points on the cc-pwCVDZ ROCCSD(T) potential energy surface of Li5H2. The global minimum structure is identified, along with many unique, nonintuitive, energetically favorable isomers.

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.

Interfacing External Quantum Devices to a Universal Quantum Computer

PubMed Central

Lagana, Antonio A.; Lohe, Max A.; von Smekal, Lorenz

2011-01-01

We present a scheme to use external quantum devices using the universal quantum computer previously constructed. We thereby show how the universal quantum computer can utilize networked quantum information resources to carry out local computations. Such information may come from specialized quantum devices or even from remote universal quantum computers. We show how to accomplish this by devising universal quantum computer programs that implement well known oracle based quantum algorithms, namely the Deutsch, Deutsch-Jozsa, and the Grover algorithms using external black-box quantum oracle devices. In the process, we demonstrate a method to map existing quantum algorithms onto the universal quantum computer. PMID:22216276

Interfacing external quantum devices to a universal quantum computer.

PubMed

Lagana, Antonio A; Lohe, Max A; von Smekal, Lorenz

2011-01-01

We present a scheme to use external quantum devices using the universal quantum computer previously constructed. We thereby show how the universal quantum computer can utilize networked quantum information resources to carry out local computations. Such information may come from specialized quantum devices or even from remote universal quantum computers. We show how to accomplish this by devising universal quantum computer programs that implement well known oracle based quantum algorithms, namely the Deutsch, Deutsch-Jozsa, and the Grover algorithms using external black-box quantum oracle devices. In the process, we demonstrate a method to map existing quantum algorithms onto the universal quantum computer. © 2011 Lagana et al.

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

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.

Quantum speedup of Monte Carlo methods.

PubMed

Montanaro, Ashley

2015-09-08

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.

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

Quantum speedup of Monte Carlo methods

PubMed Central

Montanaro, Ashley

2015-01-01

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently. PMID:26528079

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.

Closed-loop and robust control of quantum systems.

PubMed

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

2013-01-01

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

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.

CNOT sequences for heterogeneous spin qubit architectures in a noisy environment

NASA Astrophysics Data System (ADS)

Ferraro, Elena; Fanciulli, Marco; de Michielis, Marco

Explicit CNOT gate sequences for two-qubits mixed architectures are presented in view of applications for large-scale quantum computation. Different kinds of coded spin qubits are combined allowing indeed the favorable physical properties of each to be employed. The building blocks for such composite systems are qubit architectures based on the electronic spin in electrostatically defined semiconductor quantum dots. They are the single quantum dot spin qubit, the double quantum dot singlet-triplet qubit and the double quantum dot hybrid qubit. The effective Hamiltonian models expressed by only exchange interactions between pair of electrons are exploited in different geometrical configurations. A numerical genetic algorithm that takes into account the realistic physical parameters involved is adopted. Gate operations are addressed by modulating the tunneling barriers and the energy offsets between different couple of quantum dots. Gate infidelities are calculated considering limitations due to unideal control of gate sequence pulses, hyperfine interaction and unwanted charge coupling. Second affiliation: Dipartimento di Scienza dei Materiali, University of Milano Bicocca, Via R. Cozzi, 55, 20126 Milano, Italy.

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.

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.

Demonstration of a small programmable quantum computer with atomic qubits.

PubMed

Debnath, S; Linke, N M; Figgatt, C; Landsman, K A; Wright, K; Monroe, C

2016-08-04

Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully connected set of gate operations that are native to the hardware and have a mean fidelity of 98 per cent. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms with average success rates of 95 and 90 per cent, respectively. We also perform a coherent quantum Fourier transform on five trapped-ion qubits for phase estimation and period finding with average fidelities of 62 and 84 per cent, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.

Demonstration of a small programmable quantum computer with atomic qubits

NASA Astrophysics Data System (ADS)

Debnath, S.; Linke, N. M.; Figgatt, C.; Landsman, K. A.; Wright, K.; Monroe, C.

2016-08-01

Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully connected set of gate operations that are native to the hardware and have a mean fidelity of 98 per cent. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms with average success rates of 95 and 90 per cent, respectively. We also perform a coherent quantum Fourier transform on five trapped-ion qubits for phase estimation and period finding with average fidelities of 62 and 84 per cent, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.

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.

A strategy for quantum algorithm design assisted by machine learning

NASA Astrophysics Data System (ADS)

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

2014-07-01

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

Quantum annealing for combinatorial clustering

NASA Astrophysics Data System (ADS)

Kumar, Vaibhaw; Bass, Gideon; Tomlin, Casey; Dulny, Joseph

2018-02-01

Clustering is a powerful machine learning technique that groups "similar" data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of within-the-cluster distances between points. The straightforward approach involves examining all the possible assignments of points to each of the clusters. This approach guarantees the solution will be a global minimum; however, the number of possible assignments scales quickly with the number of data points and becomes computationally intractable even for very small datasets. In order to circumvent this issue, cost function minima are found using popular local search-based heuristic approaches such as k-means and hierarchical clustering. Due to their greedy nature, such techniques do not guarantee that a global minimum will be found and can lead to sub-optimal clustering assignments. Other classes of global search-based techniques, such as simulated annealing, tabu search, and genetic algorithms, may offer better quality results but can be too time-consuming to implement. In this work, we describe how quantum annealing can be used to carry out clustering. We map the clustering objective to a quadratic binary optimization problem and discuss two clustering algorithms which are then implemented on commercially available quantum annealing hardware, as well as on a purely classical solver "qbsolv." The first algorithm assigns N data points to K clusters, and the second one can be used to perform binary clustering in a hierarchical manner. We present our results in the form of benchmarks against well-known k-means clustering and discuss the advantages and disadvantages of the proposed techniques.

Investigations of quantum heuristics for optimization

NASA Astrophysics Data System (ADS)

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

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

Quantum digital-to-analog conversion algorithm using decoherence

NASA Astrophysics Data System (ADS)

SaiToh, Akira

2015-08-01

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

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.

Complexity of the Quantum Adiabatic Algorithm

NASA Technical Reports Server (NTRS)

Hen, Itay

2013-01-01

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 algorithms.

Genetic algorithms and genetic programming for multiscale modeling: Applications in materials science and chemistry and advances in scalability

NASA Astrophysics Data System (ADS)

Sastry, Kumara Narasimha

2007-03-01

Effective and efficient rnultiscale modeling is essential to advance both the science and synthesis in a, wide array of fields such as physics, chemistry, materials science; biology, biotechnology and pharmacology. This study investigates the efficacy and potential of rising genetic algorithms for rnultiscale materials modeling and addresses some of the challenges involved in designing competent algorithms that solve hard problems quickly, reliably and accurately. In particular, this thesis demonstrates the use of genetic algorithms (GAs) and genetic programming (GP) in multiscale modeling with the help of two non-trivial case studies in materials science and chemistry. The first case study explores the utility of genetic programming (GP) in multi-timescaling alloy kinetics simulations. In essence, GP is used to bridge molecular dynamics and kinetic Monte Carlo methods to span orders-of-magnitude in simulation time. Specifically, GP is used to regress symbolically an inline barrier function from a limited set of molecular dynamics simulations to enable kinetic Monte Carlo that simulate seconds of real time. Results on a non-trivial example of vacancy-assisted migration on a surface of a face-centered cubic (fcc) Copper-Cobalt (CuxCo 1-x) alloy show that GP predicts all barriers with 0.1% error from calculations for less than 3% of active configurations, independent of type of potentials used to obtain the learning set of barriers via molecular dynamics. The resulting method enables 2--9 orders-of-magnitude increase in real-time dynamics simulations taking 4--7 orders-of-magnitude less CPU time. The second case study presents the application of multiobjective genetic algorithms (MOGAs) in multiscaling quantum chemistry simulations. Specifically, MOGAs are used to bridge high-level quantum chemistry and semiempirical methods to provide accurate representation of complex molecular excited-state and ground-state behavior. Results on ethylene and benzene---two common building blocks in organic chemistry---indicate that MOGAs produce High-quality semiempirical methods that (1) are stable to small perturbations, (2) yield accurate configuration energies on untested and critical excited states, and (3) yield ab initio quality excited-state dynamics. The proposed method enables simulations of more complex systems to realistic, multi-picosecond timescales, well beyond previous attempts or expectation of human experts, and 2--3 orders-of-magnitude reduction in computational cost. While the two applications use simple evolutionary operators, in order to tackle more complex systems, their scalability and limitations have to be investigated. The second part of the thesis addresses some of the challenges involved with a successful design of genetic algorithms and genetic programming for multiscale modeling. The first issue addressed is the scalability of genetic programming, where facetwise models are built to assess the population size required by GP to ensure adequate supply of raw building blocks and also to ensure accurate decision-making between competing building blocks. This study also presents a design of competent genetic programming, where traditional fixed recombination operators are replaced by building and sampling probabilistic models of promising candidate programs. The proposed scalable GP, called extended compact GP (eCGP), combines the ideas from extended compact genetic algorithm (eCGA) and probabilistic incremental program evolution (PIPE) and adaptively identifies, propagates and exchanges important subsolutions of a search problem. Results show that eCGP scales cubically with problem size on both GP-easy and GP-hard problems. Finally, facetwise models are developed to explore limitations of scalability of MOGAs, where the scalability of multiobjective algorithms in reliably maintaining Pareto-optimal solutions is addressed. The results show that even when the building blocks are accurately identified, massive multimodality of the search problems can easily overwhelm the nicher (diversity preserving operator) and lead to exponential scale-up. Facetwise models are developed, which incorporate the combined effects of model accuracy, decision making, and sub-structure supply, as well as the effect of niching on the population sizing, to predict a limit on the growth rate of a maximum number of sub-structures that can compete in the two objectives to circumvent the failure of the niching method. The results show that if the number of competing building blocks between multiple objectives is less than the proposed limit, multiobjective GAs scale-up polynomially with the problem size on boundedly-difficult problems.

An efficient quantum algorithm for spectral estimation

NASA Astrophysics Data System (ADS)

Steffens, Adrian; Rebentrost, Patrick; Marvian, Iman; Eisert, Jens; Lloyd, Seth

2017-03-01

We develop an efficient quantum implementation of an important signal processing algorithm for line spectral estimation: the matrix pencil method, which determines the frequencies and damping factors of signals consisting of finite sums of exponentially damped sinusoids. Our algorithm provides a quantum speedup in a natural regime where the sampling rate is much higher than the number of sinusoid components. Along the way, we develop techniques that are expected to be useful for other quantum algorithms as well—consecutive phase estimations to efficiently make products of asymmetric low rank matrices classically accessible and an alternative method to efficiently exponentiate non-Hermitian matrices. Our algorithm features an efficient quantum-classical division of labor: the time-critical steps are implemented in quantum superposition, while an interjacent step, requiring much fewer parameters, can operate classically. We show that frequencies and damping factors can be obtained in time logarithmic in the number of sampling points, exponentially faster than known classical algorithms.

A quantum causal discovery algorithm

NASA Astrophysics Data System (ADS)

Giarmatzi, Christina; Costa, Fabio

2018-03-01

Finding a causal model for a set of classical variables is now a well-established task—but what about the quantum equivalent? Even the notion of a quantum causal model is controversial. Here, we present a causal discovery algorithm for quantum systems. The input to the algorithm is a process matrix describing correlations between quantum events. Its output consists of different levels of information about the underlying causal model. Our algorithm determines whether the process is causally ordered by grouping the events into causally ordered non-signaling sets. It detects if all relevant common causes are included in the process, which we label Markovian, or alternatively if some causal relations are mediated through some external memory. For a Markovian process, it outputs a causal model, namely the causal relations and the corresponding mechanisms, represented as quantum states and channels. Our algorithm opens the route to more general quantum causal discovery methods.

Enhanced round robin CPU scheduling with burst time based time quantum

NASA Astrophysics Data System (ADS)

Indusree, J. R.; Prabadevi, B.

2017-11-01

Process scheduling is a very important functionality of Operating system. The main-known process-scheduling algorithms are First Come First Serve (FCFS) algorithm, Round Robin (RR) algorithm, Priority scheduling algorithm and Shortest Job First (SJF) algorithm. Compared to its peers, Round Robin (RR) algorithm has the advantage that it gives fair share of CPU to the processes which are already in the ready-queue. The effectiveness of the RR algorithm greatly depends on chosen time quantum value. Through this research paper, we are proposing an enhanced algorithm called Enhanced Round Robin with Burst-time based Time Quantum (ERRBTQ) process scheduling algorithm which calculates time quantum as per the burst-time of processes already in ready queue. The experimental results and analysis of ERRBTQ algorithm clearly indicates the improved performance when compared with conventional RR and its variants.

Harmony Search as a Powerful Tool for Feature Selection in QSPR Study of the Drugs Lipophilicity.

PubMed

Bahadori, Behnoosh; Atabati, Morteza

2017-01-01

Aims & Scope: Lipophilicity represents one of the most studied and most frequently used fundamental physicochemical properties. In the present work, harmony search (HS) algorithm is suggested to feature selection in quantitative structure-property relationship (QSPR) modeling to predict lipophilicity of neutral, acidic, basic and amphotheric drugs that were determined by UHPLC. Harmony search is a music-based metaheuristic optimization algorithm. It was affected by the observation that the aim of music is to search for a perfect state of harmony. Semi-empirical quantum-chemical calculations at AM1 level were used to find the optimum 3D geometry of the studied molecules and variant descriptors (1497 descriptors) were calculated by the Dragon software. The selected descriptors by harmony search algorithm (9 descriptors) were applied for model development using multiple linear regression (MLR). In comparison with other feature selection methods such as genetic algorithm and simulated annealing, harmony search algorithm has better results. The root mean square error (RMSE) with and without leave-one out cross validation (LOOCV) were obtained 0.417 and 0.302, respectively. The results were compared with those obtained from the genetic algorithm and simulated annealing methods and it showed that the HS is a helpful tool for feature selection with fine performance. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.

Quantum algorithms for Gibbs sampling and hitting-time estimation

DOE PAGES

Chowdhury, Anirban Narayan; Somma, Rolando D.

2017-02-01

In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. Formore » a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ 3/2), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.« less

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.

Algorithms Bridging Quantum Computation and Chemistry

NASA Astrophysics Data System (ADS)

McClean, Jarrod Ryan

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

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.

Quantum Computation: Entangling with the Future

NASA Technical Reports Server (NTRS)

Jiang, Zhang

2017-01-01

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

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

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

Parametric Quantum Search Algorithm as Quantum Walk: A Quantum Simulation

NASA Astrophysics Data System (ADS)

Ellinas, Demosthenes; Konstandakis, Christos

2016-02-01

Parametric quantum search algorithm (PQSA) is a form of quantum search that results by relaxing the unitarity of the original algorithm. PQSA can naturally be cast in the form of quantum walk, by means of the formalism of oracle algebra. This is due to the fact that the completely positive trace preserving search map used by PQSA, admits a unitarization (unitary dilation) a la quantum walk, at the expense of introducing auxiliary quantum coin-qubit space. The ensuing QW describes a process of spiral motion, chosen to be driven by two unitary Kraus generators, generating planar rotations of Bloch vector around an axis. The quadratic acceleration of quantum search translates into an equivalent quadratic saving of the number of coin qubits in the QW analogue. The associated to QW model Hamiltonian operator is obtained and is shown to represent a multi-particle long-range interacting quantum system that simulates parametric search. Finally, the relation of PQSA-QW simulator to the QW search algorithm is elucidated.

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

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

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.

One-way quantum computing in superconducting circuits

NASA Astrophysics Data System (ADS)

Albarrán-Arriagada, F.; Alvarado Barrios, G.; Sanz, M.; Romero, G.; Lamata, L.; Retamal, J. C.; Solano, E.

2018-03-01

We propose a method for the implementation of one-way quantum computing in superconducting circuits. Measurement-based quantum computing is a universal quantum computation paradigm in which an initial cluster state provides the quantum resource, while the iteration of sequential measurements and local rotations encodes the quantum algorithm. Up to now, technical constraints have limited a scalable approach to this quantum computing alternative. The initial cluster state can be generated with available controlled-phase gates, while the quantum algorithm makes use of high-fidelity readout and coherent feedforward. With current technology, we estimate that quantum algorithms with above 20 qubits may be implemented in the path toward quantum supremacy. Moreover, we propose an alternative initial state with properties of maximal persistence and maximal connectedness, reducing the required resources of one-way quantum computing protocols.

Closed-Loop and Robust Control of Quantum Systems

PubMed Central

Wang, Lin-Cheng

2013-01-01

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

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.

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.

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.

Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip.

PubMed

Paesani, S; Gentile, A A; Santagati, R; Wang, J; Wiebe, N; Tew, D P; O'Brien, J L; Thompson, M G

2017-03-10

Quantum phase estimation is a fundamental subroutine in many quantum algorithms, including Shor's factorization algorithm and quantum simulation. However, so far results have cast doubt on its practicability for near-term, nonfault tolerant, quantum devices. Here we report experimental results demonstrating that this intuition need not be true. We implement a recently proposed adaptive Bayesian approach to quantum phase estimation and use it to simulate molecular energies on a silicon quantum photonic device. The approach is verified to be well suited for prethreshold quantum processors by investigating its superior robustness to noise and decoherence compared to the iterative phase estimation algorithm. This shows a promising route to unlock the power of quantum phase estimation much sooner than previously believed.

Quantum Statistical Mechanics on a Quantum Computer

NASA Astrophysics Data System (ADS)

Raedt, H. D.; Hams, A. H.; Michielsen, K.; Miyashita, S.; Saito, K.

We describe a quantum algorithm to compute the density of states and thermal equilibrium properties of quantum many-body systems. We present results obtained by running this algorithm on a software implementation of a 21-qubit quantum computer for the case of an antiferromagnetic Heisenberg model on triangular lattices of different size.

Gossip algorithms in quantum networks

NASA Astrophysics Data System (ADS)

Siomau, Michael

2017-01-01

Gossip algorithms is a common term to describe protocols for unreliable information dissemination in natural networks, which are not optimally designed for efficient communication between network entities. We consider application of gossip algorithms to quantum networks and show that any quantum network can be updated to optimal configuration with local operations and classical communication. This allows to speed-up - in the best case exponentially - the quantum information dissemination. Irrespective of the initial configuration of the quantum network, the update requiters at most polynomial number of local operations and classical communication.

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.

Coherent Operations, Entanglement, and Progress Toward Quantum Search in a Large 2D Array of Neutral Atom Qubits

DTIC Science & Technology

2015-08-18

by Benjamin Bederson and Herbert Walther, pp. 95 –170. issn: 1049-250X. doi: 10.1016/S1049-250X(08)60186-X. [49] Nicolas Schlosser, Georges Reymond...144 9.5.1.2 Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 145 9.5.1.3 Nelder- Mead Simplex...from 2013-11-14-15-18-54. 90 Nelder- Mead optimizing readout frequency, power and time Readout frequency Iterations Python Controller Arroyo TEC and

Self-consistent optimization of [111]-AlGaInAs/InP MQWs structures lasing at 1.55 μm by a genetic algorithm

NASA Astrophysics Data System (ADS)

Saidi, Hosni; Msahli, Melek; Ben Dhafer, Rania; Ridene, Said

2017-12-01

Band structure and optical gain properties of [111]-oriented AlGaInAs/AlGaInAs-delta-InGaAs multi-quantum wells, subjected to piezoelectric field, for the near-infrared lasers diodes applications was proposed and investigated in this paper. By using genetic algorithm based on optimization technique we demonstrate that the structural parameters can be conveniently optimized to achieve high-efficiency laser diode performance at room temperature. In this work, significant optical gain for the wished emission wavelength at 1.55 μm and low threshold injection current are the optimization target. The end result of this optimization is a laser diode based on InP substrate using quaternary compound material of AlGaInAs in both quantum wells and barriers with different composition. It has been shown that the transverse electric polarized optical gain which reaches 3500 cm-1 may be acquired for λ = 1.55 μm with a threshold carrier density Nth≈1.31018cm-3, which is very promising to serve as an alternative active region for high-efficiency near-infrared lasers. Finally, from the design presented here, we show that it is possible to apply this technique to a different III-V compound semiconductors and wavelength ranging from deep-ultra-violet to far infrared.

Gacs quantum algorithmic entropy in infinite dimensional Hilbert spaces

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

Benatti, Fabio, E-mail: benatti@ts.infn.it; Oskouei, Samad Khabbazi, E-mail: kh.oskuei@ut.ac.ir; Deh Abad, Ahmad Shafiei, E-mail: shafiei@khayam.ut.ac.ir

We extend the notion of Gacs quantum algorithmic entropy, originally formulated for finitely many qubits, to infinite dimensional quantum spin chains and investigate the relation of this extension with two quantum dynamical entropies that have been proposed in recent years.

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.

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

Experimental quantum computing to solve systems of linear equations.

PubMed

Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei

2013-06-07

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

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.

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.

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.

Combining DCQGMP-Based Sparse Decomposition and MPDR Beamformer for Multi-Type Interferences Mitigation for GNSS Receivers.

PubMed

Guo, Qiang; Qi, Liangang

2017-04-10

In the coexistence of multiple types of interfering signals, the performance of interference suppression methods based on time and frequency domains is degraded seriously, and the technique using an antenna array requires a large enough size and huge hardware costs. To combat multi-type interferences better for GNSS receivers, this paper proposes a cascaded multi-type interferences mitigation method combining improved double chain quantum genetic matching pursuit (DCQGMP)-based sparse decomposition and an MPDR beamformer. The key idea behind the proposed method is that the multiple types of interfering signals can be excised by taking advantage of their sparse features in different domains. In the first stage, the single-tone (multi-tone) and linear chirp interfering signals are canceled by sparse decomposition according to their sparsity in the over-complete dictionary. In order to improve the timeliness of matching pursuit (MP)-based sparse decomposition, a DCQGMP is introduced by combining an improved double chain quantum genetic algorithm (DCQGA) and the MP algorithm, and the DCQGMP algorithm is extended to handle the multi-channel signals according to the correlation among the signals in different channels. In the second stage, the minimum power distortionless response (MPDR) beamformer is utilized to nullify the residuary interferences (e.g., wideband Gaussian noise interferences). Several simulation results show that the proposed method can not only improve the interference mitigation degree of freedom (DoF) of the array antenna, but also effectively deal with the interference arriving from the same direction with the GNSS signal, which can be sparse represented in the over-complete dictionary. Moreover, it does not bring serious distortions into the navigation signal.

Combining DCQGMP-Based Sparse Decomposition and MPDR Beamformer for Multi-Type Interferences Mitigation for GNSS Receivers

PubMed Central

Guo, Qiang; Qi, Liangang

2017-01-01

In the coexistence of multiple types of interfering signals, the performance of interference suppression methods based on time and frequency domains is degraded seriously, and the technique using an antenna array requires a large enough size and huge hardware costs. To combat multi-type interferences better for GNSS receivers, this paper proposes a cascaded multi-type interferences mitigation method combining improved double chain quantum genetic matching pursuit (DCQGMP)-based sparse decomposition and an MPDR beamformer. The key idea behind the proposed method is that the multiple types of interfering signals can be excised by taking advantage of their sparse features in different domains. In the first stage, the single-tone (multi-tone) and linear chirp interfering signals are canceled by sparse decomposition according to their sparsity in the over-complete dictionary. In order to improve the timeliness of matching pursuit (MP)-based sparse decomposition, a DCQGMP is introduced by combining an improved double chain quantum genetic algorithm (DCQGA) and the MP algorithm, and the DCQGMP algorithm is extended to handle the multi-channel signals according to the correlation among the signals in different channels. In the second stage, the minimum power distortionless response (MPDR) beamformer is utilized to nullify the residuary interferences (e.g., wideband Gaussian noise interferences). Several simulation results show that the proposed method can not only improve the interference mitigation degree of freedom (DoF) of the array antenna, but also effectively deal with the interference arriving from the same direction with the GNSS signal, which can be sparse represented in the over-complete dictionary. Moreover, it does not bring serious distortions into the navigation signal. PMID:28394290

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.

Generalized Jaynes-Cummings model as a quantum search algorithm

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

Romanelli, A.

2009-07-15

We propose a continuous time quantum search algorithm using a generalization of the Jaynes-Cummings model. In this model the states of the atom are the elements among which the algorithm realizes the search, exciting resonances between the initial and the searched states. This algorithm behaves like Grover's algorithm; the optimal search time is proportional to the square root of the size of the search set and the probability to find the searched state oscillates periodically in time. In this frame, it is possible to reinterpret the usual Jaynes-Cummings model as a trivial case of the quantum search algorithm.

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.

4D-Qsar Study of Some Pyrazole Pyridine Carboxylic Acid Derivatives by Electron Conformational-Genetic Algorithm Method.

PubMed

Tuzun, Burak; Yavuz, Sevtap Caglar; Sabanci, Nazmiye; Saripinar, Emin

2018-05-13

In the present work, pharmacophore identification and biological activity prediction for 86 pyrazole pyridine carboxylic acid derivatives were made using the electron conformational genetic algorithm approach which was introduced as a 4D-QSAR analysis by us in recent years. In the light of the data obtained from quantum chemical calculations at HF/6-311 G** level, the electron conformational matrices of congruity (ECMC) were constructed by EMRE software. Comparing the matrices, electron conformational submatrix of activity (ECSA, Pha) was revealed that are common for these compounds within a minimum tolerance. A parameter pool was generated considering the obtained pharmacophore. To determine the theoretical biological activity of molecules and identify the best subset of variables affecting bioactivities, we used the nonlinear least square regression method and genetic algorithm. The results obtained in this study are in good agreement with the experimental data presented in the literature. The model for training and test sets attained by the optimum 12 parameters gave highly satisfactory results with R2training= 0.889, q2=0.839 and SEtraining=0.066, q2ext1 = 0.770, q2ext2 = 0.750, q2ext3=0.824, ccctr = 0.941, ccctest = 0.869 and cccall = 0.927. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.

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 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.

Quantum Color Image Encryption Algorithm Based on A Hyper-Chaotic System and Quantum Fourier Transform

NASA Astrophysics Data System (ADS)

Tan, Ru-Chao; Lei, Tong; Zhao, Qing-Min; Gong, Li-Hua; Zhou, Zhi-Hong

2016-12-01

To improve the slow processing speed of the classical image encryption algorithms and enhance the security of the private color images, a new quantum color image encryption algorithm based on a hyper-chaotic system is proposed, in which the sequences generated by the Chen's hyper-chaotic system are scrambled and diffused with three components of the original color image. Sequentially, the quantum Fourier transform is exploited to fulfill the encryption. Numerical simulations show that the presented quantum color image encryption algorithm possesses large key space to resist illegal attacks, sensitive dependence on initial keys, uniform distribution of gray values for the encrypted image and weak correlation between two adjacent pixels in the cipher-image.

LSB Based Quantum Image Steganography Algorithm

NASA Astrophysics Data System (ADS)

Jiang, Nan; Zhao, Na; Wang, Luo

2016-01-01

Quantum steganography is the technique which hides a secret message into quantum covers such as quantum images. In this paper, two blind LSB steganography algorithms in the form of quantum circuits are proposed based on the novel enhanced quantum representation (NEQR) for quantum images. One algorithm is plain LSB which uses the message bits to substitute for the pixels' LSB directly. The other is block LSB which embeds a message bit into a number of pixels that belong to one image block. The extracting circuits can regain the secret message only according to the stego cover. Analysis and simulation-based experimental results demonstrate that the invisibility is good, and the balance between the capacity and the robustness can be adjusted according to the needs of applications.

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

NASA Astrophysics Data System (ADS)

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

2009-02-01

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

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.

Near-optimal quantum circuit for Grover's unstructured search using a transverse field

NASA Astrophysics Data System (ADS)

Jiang, Zhang; Rieffel, Eleanor G.; Wang, Zhihui

2017-06-01

Inspired by a class of algorithms proposed by Farhi et al. (arXiv:1411.4028), namely, the quantum approximate optimization algorithm (QAOA), we present a circuit-based quantum algorithm to search for a needle in a haystack, obtaining the same quadratic speedup achieved by Grover's original algorithm. In our algorithm, the problem Hamiltonian (oracle) and a transverse field are applied alternately to the system in a periodic manner. We introduce a technique, based on spin-coherent states, to analyze the composite unitary in a single period. This composite unitary drives a closed transition between two states that have high degrees of overlap with the initial state and the target state, respectively. The transition rate in our algorithm is of order Θ (1 /√{N }) , and the overlaps are of order Θ (1 ) , yielding a nearly optimal query complexity of T ≃√{N }(π /2 √{2 }) . Our algorithm is a QAOA circuit that demonstrates a quantum advantage with a large number of iterations that is not derived from Trotterization of an adiabatic quantum optimization (AQO) algorithm. It also suggests that the analysis required to understand QAOA circuits involves a very different process from estimating the energy gap of a Hamiltonian in AQO.

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.

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.

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.

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.

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.

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.

Equivalence of Szegedy's and coined quantum walks

NASA Astrophysics Data System (ADS)

Wong, Thomas G.

2017-09-01

Szegedy's quantum walk is a quantization of a classical random walk or Markov chain, where the walk occurs on the edges of the bipartite double cover of the original graph. To search, one can simply quantize a Markov chain with absorbing vertices. Recently, Santos proposed two alternative search algorithms that instead utilize the sign-flip oracle in Grover's algorithm rather than absorbing vertices. In this paper, we show that these two algorithms are exactly equivalent to two algorithms involving coined quantum walks, which are walks on the vertices of the original graph with an internal degree of freedom. The first scheme is equivalent to a coined quantum walk with one walk step per query of Grover's oracle, and the second is equivalent to a coined quantum walk with two walk steps per query of Grover's oracle. These equivalences lie outside the previously known equivalence of Szegedy's quantum walk with absorbing vertices and the coined quantum walk with the negative identity operator as the coin for marked vertices, whose precise relationships we also investigate.

Quantum computation for solving linear systems

NASA Astrophysics Data System (ADS)

Cao, Yudong

Quantum computation is a subject born out of the combination between physics and computer science. It studies how the laws of quantum mechanics can be exploited to perform computations much more efficiently than current computers (termed classical computers as oppose to quantum computers). The thesis starts by introducing ideas from quantum physics and theoretical computer science and based on these ideas, introducing the basic concepts in quantum computing. These introductory discussions are intended for non-specialists to obtain the essential knowledge needed for understanding the new results presented in the subsequent chapters. After introducing the basics of quantum computing, we focus on the recently proposed quantum algorithm for linear systems. The new results include i) special instances of quantum circuits that can be implemented using current experimental resources; ii) detailed quantum algorithms that are suitable for a broader class of linear systems. We show that for some particular problems the quantum algorithm is able to achieve exponential speedup over their classical counterparts.

Quantum partial search for uneven distribution of multiple target items

NASA Astrophysics Data System (ADS)

Zhang, Kun; Korepin, Vladimir

2018-06-01

Quantum partial search algorithm is an approximate search. It aims to find a target block (which has the target items). It runs a little faster than full Grover search. In this paper, we consider quantum partial search algorithm for multiple target items unevenly distributed in a database (target blocks have different number of target items). The algorithm we describe can locate one of the target blocks. Efficiency of the algorithm is measured by number of queries to the oracle. We optimize the algorithm in order to improve efficiency. By perturbation method, we find that the algorithm runs the fastest when target items are evenly distributed in database.

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.

Resource-aware system architecture model for implementation of quantum aided Byzantine agreement on quantum repeater networks

NASA Astrophysics Data System (ADS)

Taherkhani, Mohammand Amin; Navi, Keivan; Van Meter, Rodney

2018-01-01

Quantum aided Byzantine agreement is an important distributed quantum algorithm with unique features in comparison to classical deterministic and randomized algorithms, requiring only a constant expected number of rounds in addition to giving a higher level of security. In this paper, we analyze details of the high level multi-party algorithm, and propose elements of the design for the quantum architecture and circuits required at each node to run the algorithm on a quantum repeater network (QRN). Our optimization techniques have reduced the quantum circuit depth by 44% and the number of qubits in each node by 20% for a minimum five-node setup compared to the design based on the standard arithmetic circuits. These improvements lead to a quantum system architecture with 160 qubits per node, space-time product (an estimate of the required fidelity) {KQ}≈ 1.3× {10}5 per node and error threshold 1.1× {10}-6 for the total nodes in the network. The evaluation of the designed architecture shows that to execute the algorithm once on the minimum setup, we need to successfully distribute a total of 648 Bell pairs across the network, spread evenly between all pairs of nodes. This framework can be considered a starting point for establishing a road-map for light-weight demonstration of a distributed quantum application on QRNs.

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.

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.

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.

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.

Optical simulation of quantum algorithms using programmable liquid-crystal displays

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

Puentes, Graciana; La Mela, Cecilia; Ledesma, Silvia

2004-04-01

We present a scheme to perform an all optical simulation of quantum algorithms and maps. The main components are lenses to efficiently implement the Fourier transform and programmable liquid-crystal displays to introduce space dependent phase changes on a classical optical beam. We show how to simulate Deutsch-Jozsa and Grover's quantum algorithms using essentially the same optical array programmed in two different ways.

Quantum Google in a Complex Network

PubMed Central

Paparo, Giuseppe Davide; Müller, Markus; Comellas, Francesc; Martin-Delgado, Miguel Angel

2013-01-01

We investigate the behaviour of the recently proposed Quantum PageRank algorithm, in large complex networks. We find that the algorithm is able to univocally reveal the underlying topology of the network and to identify and order the most relevant nodes. Furthermore, it is capable to clearly highlight the structure of secondary hubs and to resolve the degeneracy in importance of the low lying part of the list of rankings. The quantum algorithm displays an increased stability with respect to a variation of the damping parameter, present in the Google algorithm, and a more clearly pronounced power-law behaviour in the distribution of importance, as compared to the classical algorithm. We test the performance and confirm the listed features by applying it to real world examples from the WWW. Finally, we raise and partially address whether the increased sensitivity of the quantum algorithm persists under coordinated attacks in scale-free and random networks. PMID:24091980

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.

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.

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.

First-Order Phase Transition in the Quantum Adiabatic Algorithm

DTIC Science & Technology

2010-01-14

London) 400, 133 (1999). [19] T. Jörg, F. Krzakala, G . Semerjian, and F. Zamponi, arXiv:0911.3438. PRL 104, 020502 (2010) P HY S I CA L R EV I EW LE T T E R S week ending 15 JANUARY 2010 020502-4 ...Box 12211 Research Triangle Park, NC 27709-2211 15. SUBJECT TERMS Quantum Adiabatic Algorithm, Monte Carlo, Quantum Phase Transition A. P . Young, V...documentation. Approved for public release; distribution is unlimited. ... 56290.2-PH-QC First-Order Phase Transition in the Quantum Adiabatic Algorithm A. P

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.

Quantum red-green-blue image steganography

NASA Astrophysics Data System (ADS)

Heidari, Shahrokh; Pourarian, Mohammad Rasoul; Gheibi, Reza; Naseri, Mosayeb; Houshmand, Monireh

One of the most considering matters in the field of quantum information processing is quantum data hiding including quantum steganography and quantum watermarking. This field is an efficient tool for protecting any kind of digital data. In this paper, three quantum color images steganography algorithms are investigated based on Least Significant Bit (LSB). The first algorithm employs only one of the image’s channels to cover secret data. The second procedure is based on LSB XORing technique, and the last algorithm utilizes two channels to cover the color image for hiding secret quantum data. The performances of the proposed schemes are analyzed by using software simulations in MATLAB environment. The analysis of PSNR, BER and Histogram graphs indicate that the presented schemes exhibit acceptable performances and also theoretical analysis demonstrates that the networks complexity of the approaches scales squarely.

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

NASA Astrophysics Data System (ADS)

Wang, Hefeng; Fan, Heng; Li, Fuli

2014-01-01

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

A quantum heuristic algorithm for the traveling salesman problem

NASA Astrophysics Data System (ADS)

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

2012-12-01

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

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

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.

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.

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).

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.

Q-Learning-Based Adjustable Fixed-Phase Quantum Grover Search Algorithm

NASA Astrophysics Data System (ADS)

Guo, Ying; Shi, Wensha; Wang, Yijun; Hu, Jiankun

2017-02-01

We demonstrate that the rotation phase can be suitably chosen to increase the efficiency of the phase-based quantum search algorithm, leading to a dynamic balance between iterations and success probabilities of the fixed-phase quantum Grover search algorithm with Q-learning for a given number of solutions. In this search algorithm, the proposed Q-learning algorithm, which is a model-free reinforcement learning strategy in essence, is used for performing a matching algorithm based on the fraction of marked items λ and the rotation phase α. After establishing the policy function α = π(λ), we complete the fixed-phase Grover algorithm, where the phase parameter is selected via the learned policy. Simulation results show that the Q-learning-based Grover search algorithm (QLGA) enables fewer iterations and gives birth to higher success probabilities. Compared with the conventional Grover algorithms, it avoids the optimal local situations, thereby enabling success probabilities to approach one.

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.

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.

Quantum Graphical Models and Belief Propagation

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

Leifer, M.S.; Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo Ont., N2L 2Y5; Poulin, D.

Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markovmore » Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersley-Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described.« less

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.

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.

Quantum Teleportation and Grover's Algorithm Without the Wavefunction

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

2017-02-01

In the same way as the quantum no-cloning theorem and quantum key distribution in two preceding papers, entanglement-assisted quantum teleportation and Grover's search algorithm are generalized by transferring them to an abstract setting, including usual quantum mechanics as a special case. This again shows that a much more general and abstract access to these quantum mechanical features is possible than commonly thought. A non-classical extension of conditional probability and, particularly, a very special type of state-independent conditional probability are used instead of Hilbert spaces and wavefunctions.

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.

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.

Multivariate analysis and extraction of parameters in resistive RAMs using the Quantum Point Contact model

NASA Astrophysics Data System (ADS)

Roldán, J. B.; Miranda, E.; González-Cordero, G.; García-Fernández, P.; Romero-Zaliz, R.; González-Rodelas, P.; Aguilera, A. M.; González, M. B.; Jiménez-Molinos, F.

2018-01-01

A multivariate analysis of the parameters that characterize the reset process in Resistive Random Access Memory (RRAM) has been performed. The different correlations obtained can help to shed light on the current components that contribute in the Low Resistance State (LRS) of the technology considered. In addition, a screening method for the Quantum Point Contact (QPC) current component is presented. For this purpose, the second derivative of the current has been obtained using a novel numerical method which allows determining the QPC model parameters. Once the procedure is completed, a whole Resistive Switching (RS) series of thousands of curves is studied by means of a genetic algorithm. The extracted QPC parameter distributions are characterized in depth to get information about the filamentary pathways associated with LRS in the low voltage conduction regime.

Temporal Planning for Compilation of Quantum Approximate Optimization Algorithm Circuits

NASA Technical Reports Server (NTRS)

Venturelli, Davide; Do, Minh Binh; Rieffel, Eleanor Gilbert; Frank, Jeremy David

2017-01-01

We investigate the application of temporal planners to the problem of compiling quantum circuits to newly emerging quantum hardware. While our approach is general, we focus our initial experiments on Quantum Approximate Optimization Algorithm (QAOA) circuits that have few ordering constraints and allow highly parallel plans. We report on experiments using several temporal planners to compile circuits of various sizes to a realistic hardware. This early empirical evaluation suggests that temporal planning is a viable approach to quantum circuit compilation.

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

Quantum gates with controlled adiabatic evolutions

NASA Astrophysics Data System (ADS)

Hen, Itay

2015-02-01

We introduce a class of quantum adiabatic evolutions that we claim may be interpreted as the equivalents of the unitary gates of the quantum gate model. We argue that these gates form a universal set and may therefore be used as building blocks in the construction of arbitrary "adiabatic circuits," analogously to the manner in which gates are used in the circuit model. One implication of the above construction is that arbitrary classical boolean circuits as well as gate model circuits may be directly translated to adiabatic algorithms with no additional resources or complexities. We show that while these adiabatic algorithms fail to exhibit certain aspects of the inherent fault tolerance of traditional quantum adiabatic algorithms, they may have certain other experimental advantages acting as quantum gates.

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.

Chaos Quantum-Behaved Cat Swarm Optimization Algorithm and Its Application in the PV MPPT

PubMed Central

2017-01-01

Cat Swarm Optimization (CSO) algorithm was put forward in 2006. Despite a faster convergence speed compared with Particle Swarm Optimization (PSO) algorithm, the application of CSO is greatly limited by the drawback of “premature convergence,” that is, the possibility of trapping in local optimum when dealing with nonlinear optimization problem with a large number of local extreme values. In order to surmount the shortcomings of CSO, Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed in this paper. Firstly, Quantum-behaved Cat Swarm Optimization (QCSO) algorithm improves the accuracy of the CSO algorithm, because it is easy to fall into the local optimum in the later stage. Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed by introducing tent map for jumping out of local optimum in this paper. Secondly, CQCSO has been applied in the simulation of five different test functions, showing higher accuracy and less time consumption than CSO and QCSO. Finally, photovoltaic MPPT model and experimental platform are established and global maximum power point tracking control strategy is achieved by CQCSO algorithm, the effectiveness and efficiency of which have been verified by both simulation and experiment. PMID:29181020

Chaos Quantum-Behaved Cat Swarm Optimization Algorithm and Its Application in the PV MPPT.

PubMed

Nie, Xiaohua; Wang, Wei; Nie, Haoyao

2017-01-01

Cat Swarm Optimization (CSO) algorithm was put forward in 2006. Despite a faster convergence speed compared with Particle Swarm Optimization (PSO) algorithm, the application of CSO is greatly limited by the drawback of "premature convergence," that is, the possibility of trapping in local optimum when dealing with nonlinear optimization problem with a large number of local extreme values. In order to surmount the shortcomings of CSO, Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed in this paper. Firstly, Quantum-behaved Cat Swarm Optimization (QCSO) algorithm improves the accuracy of the CSO algorithm, because it is easy to fall into the local optimum in the later stage. Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed by introducing tent map for jumping out of local optimum in this paper. Secondly, CQCSO has been applied in the simulation of five different test functions, showing higher accuracy and less time consumption than CSO and QCSO. Finally, photovoltaic MPPT model and experimental platform are established and global maximum power point tracking control strategy is achieved by CQCSO algorithm, the effectiveness and efficiency of which have been verified by both simulation and experiment.

Faster search by lackadaisical quantum walk

NASA Astrophysics Data System (ADS)

Wong, Thomas G.

2018-03-01

In the typical model, a discrete-time coined quantum walk searching the 2D grid for a marked vertex achieves a success probability of O(1/log N) in O(√{N log N}) steps, which with amplitude amplification yields an overall runtime of O(√{N} log N). We show that making the quantum walk lackadaisical or lazy by adding a self-loop of weight 4 / N to each vertex speeds up the search, causing the success probability to reach a constant near 1 in O(√{N log N}) steps, thus yielding an O(√{log N}) improvement over the typical, loopless algorithm. This improved runtime matches the best known quantum algorithms for this search problem. Our results are based on numerical simulations since the algorithm is not an instance of the abstract search algorithm.

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.

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.

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.

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.

Computation Through Neuronal Oscillations

NASA Astrophysics Data System (ADS)

Hepp, K.

Some of us believe that natural sciences are governed by simple and predictive general principles. This hope has not yet been fulfilled in physics for unifying gravitation and quantum mechanics. Epigenetics has shaken the monopoly of the genetic code to determine inheritance (Alberts et al., Molecular Biology of the Cell. Garland, New York, 2008). It is therefore not surprising that quantum mechanics does not explain consciousness or more generally the coherence of the brain in perception, action and cognition. In an other context, others (Tegmark, Phys Rev E 61:4194-4206, 2000) and we (Koch and Hepp, Nature 440:611-612, 2006; Koch and Hepp, Visions of Discovery: New Light on Physics, Cosmology, and Consciousness. Cambridge University Press, Cambridge, 2011) have strongly argued against the absurdity of such a claim, because consciousness is a higher brain function and not a molecular binding mechanism. Decoherence in the warm and wet brain is by many orders of magnitude too strong. Moreover, there are no efficient algorithms for neural quantum computations. However, the controversy over classical and quantum consciousness will probably never be resolved (see e.g. Hepp, J Math Phys 53:095222, 2012; Hameroff and Penrose, Phys Life Rev 11:39-78, 2013).

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.

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.

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

Effect of Fourier transform on the streaming in quantum lattice gas algorithms

NASA Astrophysics Data System (ADS)

Oganesov, Armen; Vahala, George; Vahala, Linda; Soe, Min

2018-04-01

All our previous quantum lattice gas algorithms for nonlinear physics have approximated the kinetic energy operator by streaming sequences to neighboring lattice sites. Here, the kinetic energy can be treated to all orders by Fourier transforming the kinetic energy operator with interlaced Dirac-based unitary collision operators. Benchmarking against exact solutions for the 1D nonlinear Schrodinger equation shows an extended range of parameters (soliton speeds and amplitudes) over the Dirac-based near-lattice-site streaming quantum algorithm.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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.

A non-genetic approach to labelling acute myeloid leukemia and bone marrow cells with quantum dots.

PubMed

Zheng, Yanwen; Tan, Dongming; Chen, Zheng; Hu, Chenxi; Mao, Zhengwei J; Singleton, Timothy P; Zeng, Yan; Shao, Xuejun; Yin, Bin

2014-06-01

The difficulty in manipulation of leukemia cells has long hindered the dissection of leukemia pathogenesis. We have introduced a non-genetic approach of marking blood cells, using quantum dots. We compared quantum dots complexed with different vehicles, including a peptide Tat, cationic polymer Turbofect and liposome. Quantum dots-Tat showed the highest efficiency of marking hematopoietic cells among the three vehicles. Quantum dots-Tat could also label a panel of leukemia cell lines at varied efficiencies. More uniform intracellular distributions of quantum dots in mouse bone marrow and leukemia cells were obtained with quantum dots-Tat, compared with the granule-like formation obtained with quantum dots-liposome. Our results suggest that quantum dots have provided a photostable and non-genetic approach that labels normal and malignant hematopoietic cells, in a cell type-, vehicle-, and quantum dot concentration-dependent manner. We expect for potential applications of quantum dots as an easy and fast marking tool assisting investigations of various types of blood cells in the future.

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.

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.

Test-state approach to the quantum search problem

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

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

2011-05-15

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

General A Scheme to Share Information via Employing Discrete Algorithm to Quantum States

NASA Astrophysics Data System (ADS)

Kang, Guo-Dong; Fang, Mao-Fa

2011-02-01

We propose a protocol for information sharing between two legitimate parties (Bob and Alice) via public-key cryptography. In particular, we specialize the protocol by employing discrete algorithm under mod that maps integers to quantum states via photon rotations. Based on this algorithm, we find that the protocol is secure under various classes of attacks. Specially, owe to the algorithm, the security of the classical privacy contained in the quantum public-key and the corresponding ciphertext is guaranteed. And the protocol is robust against the impersonation attack and the active wiretapping attack by designing particular checking processing, thus the protocol is valid.

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 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.

Non-Markovianity-assisted high-fidelity Deutsch-Jozsa algorithm in diamond

NASA Astrophysics Data System (ADS)

Dong, Yang; Zheng, Yu; Li, Shen; Li, Cong-Cong; Chen, Xiang-Dong; Guo, Guang-Can; Sun, Fang-Wen

2018-01-01

The memory effects in non-Markovian quantum dynamics can induce the revival of quantum coherence, which is believed to provide important physical resources for quantum information processing (QIP). However, no real quantum algorithms have been demonstrated with the help of such memory effects. Here, we experimentally implemented a non-Markovianity-assisted high-fidelity refined Deutsch-Jozsa algorithm (RDJA) with a solid spin in diamond. The memory effects can induce pronounced non-monotonic variations in the RDJA results, which were confirmed to follow a non-Markovian quantum process by measuring the non-Markovianity of the spin system. By applying the memory effects as physical resources with the assistance of dynamical decoupling, the probability of success of RDJA was elevated above 97% in the open quantum system. This study not only demonstrates that the non-Markovianity is an important physical resource but also presents a feasible way to employ this physical resource. It will stimulate the application of the memory effects in non-Markovian quantum dynamics to improve the performance of practical QIP.

Genetic algorithms

NASA Technical Reports Server (NTRS)

Wang, Lui; Bayer, Steven E.

1991-01-01

Genetic algorithms are mathematical, highly parallel, adaptive search procedures (i.e., problem solving methods) based loosely on the processes of natural genetics and Darwinian survival of the fittest. Basic genetic algorithms concepts are introduced, genetic algorithm applications are introduced, and results are presented from a project to develop a software tool that will enable the widespread use of genetic algorithm technology.

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.

An advanced approach to traditional round robin CPU scheduling algorithm to prioritize processes with residual burst time nearest to the specified time quantum

NASA Astrophysics Data System (ADS)

Swaraj Pati, Mythili N.; Korde, Pranav; Dey, Pallav

2017-11-01

The purpose of this paper is to introduce an optimised variant to the round robin scheduling algorithm. Every algorithm works in its own way and has its own merits and demerits. The proposed algorithm overcomes the shortfalls of the existing scheduling algorithms in terms of waiting time, turnaround time, throughput and number of context switches. The algorithm is pre-emptive and works based on the priority of the associated processes. The priority is decided on the basis of the remaining burst time of a particular process, that is; lower the burst time, higher the priority and higher the burst time, lower the priority. To complete the execution, a time quantum is initially specified. In case if the burst time of a particular process is less than 2X of the specified time quantum but more than 1X of the specified time quantum; the process is given high priority and is allowed to execute until it completes entirely and finishes. Such processes do not have to wait for their next burst cycle.

Quantum associative memory with linear and non-linear algorithms for the diagnosis of some tropical diseases.

PubMed

Tchapet Njafa, J-P; Nana Engo, S G

2018-01-01

This paper presents the QAMDiagnos, a model of Quantum Associative Memory (QAM) that can be a helpful tool for medical staff without experience or laboratory facilities, for the diagnosis of four tropical diseases (malaria, typhoid fever, yellow fever and dengue) which have several similar signs and symptoms. The memory can distinguish a single infection from a polyinfection. Our model is a combination of the improved versions of the original linear quantum retrieving algorithm proposed by Ventura and the non-linear quantum search algorithm of Abrams and Lloyd. From the given simulation results, it appears that the efficiency of recognition is good when particular signs and symptoms of a disease are inserted given that the linear algorithm is the main algorithm. The non-linear algorithm helps confirm or correct the diagnosis or give some advice to the medical staff for the treatment. So, our QAMDiagnos that has a friendly graphical user interface for desktop and smart-phone is a sensitive and a low-cost diagnostic tool that enables rapid and accurate diagnosis of four tropical diseases. Copyright © 2017 Elsevier Ltd. All rights reserved.

Minimal-memory realization of pearl-necklace encoders of general quantum convolutional codes

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

Houshmand, Monireh; Hosseini-Khayat, Saied

2011-02-15

Quantum convolutional codes, like their classical counterparts, promise to offer higher error correction performance than block codes of equivalent encoding complexity, and are expected to find important applications in reliable quantum communication where a continuous stream of qubits is transmitted. Grassl and Roetteler devised an algorithm to encode a quantum convolutional code with a ''pearl-necklace'' encoder. Despite their algorithm's theoretical significance as a neat way of representing quantum convolutional codes, it is not well suited to practical realization. In fact, there is no straightforward way to implement any given pearl-necklace structure. This paper closes the gap between theoretical representation andmore » practical implementation. In our previous work, we presented an efficient algorithm to find a minimal-memory realization of a pearl-necklace encoder for Calderbank-Shor-Steane (CSS) convolutional codes. This work is an extension of our previous work and presents an algorithm for turning a pearl-necklace encoder for a general (non-CSS) quantum convolutional code into a realizable quantum convolutional encoder. We show that a minimal-memory realization depends on the commutativity relations between the gate strings in the pearl-necklace encoder. We find a realization by means of a weighted graph which details the noncommutative paths through the pearl necklace. The weight of the longest path in this graph is equal to the minimal amount of memory needed to implement the encoder. The algorithm has a polynomial-time complexity in the number of gate strings in the pearl-necklace encoder.« less

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.

Genetic Algorithms and Local Search

NASA Technical Reports Server (NTRS)

Whitley, Darrell

1996-01-01

The first part of this presentation is a tutorial level introduction to the principles of genetic search and models of simple genetic algorithms. The second half covers the combination of genetic algorithms with local search methods to produce hybrid genetic algorithms. Hybrid algorithms can be modeled within the existing theoretical framework developed for simple genetic algorithms. An application of a hybrid to geometric model matching is given. The hybrid algorithm yields results that improve on the current state-of-the-art for this problem.

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.

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

NASA Astrophysics Data System (ADS)

Castagnoli, Giuseppe

2017-05-01

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

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

Deterministic quantum annealing expectation-maximization algorithm

NASA Astrophysics Data System (ADS)

Miyahara, Hideyuki; Tsumura, Koji; Sughiyama, Yuki

2017-11-01

Maximum likelihood estimation (MLE) is one of the most important methods in machine learning, and the expectation-maximization (EM) algorithm is often used to obtain maximum likelihood estimates. However, EM heavily depends on initial configurations and fails to find the global optimum. On the other hand, in the field of physics, quantum annealing (QA) was proposed as a novel optimization approach. Motivated by QA, we propose a quantum annealing extension of EM, which we call the deterministic quantum annealing expectation-maximization (DQAEM) algorithm. We also discuss its advantage in terms of the path integral formulation. Furthermore, by employing numerical simulations, we illustrate how DQAEM works in MLE and show that DQAEM moderate the problem of local optima in EM.

Quantum Transmemetic Intelligence

NASA Astrophysics Data System (ADS)

Piotrowski, Edward W.; Sładkowski, Jan

The following sections are included: * Introduction * A Quantum Model of Free Will * Quantum Acquisition of Knowledge * Thinking as a Quantum Algorithm * Counterfactual Measurement as a Model of Intuition * Quantum Modification of Freud's Model of Consciousness * Conclusion * Acknowledgements * References

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

Quantum metrology with a transmon qutrit

NASA Astrophysics Data System (ADS)

Shlyakhov, A. R.; Zemlyanov, V. V.; Suslov, M. V.; Lebedev, A. V.; Paraoanu, G. S.; Lesovik, G. B.; Blatter, G.

2018-02-01

Making use of coherence and entanglement as metrological quantum resources allows us to improve the measurement precision from the shot-noise or quantum limit to the Heisenberg limit. Quantum metrology then relies on the availability of quantum engineered systems that involve controllable quantum degrees of freedom which are sensitive to the measured quantity. Sensors operating in the qubit mode and exploiting their coherence in a phase-sensitive measurement have been shown to approach the Heisenberg scaling in precision. Here, we show that this result can be further improved by operating the quantum sensor in the qudit mode, i.e., by exploiting d rather than two levels. Specifically, we describe the metrological algorithm for using a superconducting transmon device operating in a qutrit mode as a magnetometer. The algorithm is based on the base-3 semiquantum Fourier transformation and enhances the quantum theoretical performance of the sensor by a factor of 2. Even more, the practical gain of our qutrit implementation is found in a reduction of the number of iteration steps of the quantum Fourier transformation by the factor ln(2 )/ln(3 )≈0.63 compared to the qubit mode. We show that a two-tone capacitively coupled radio-frequency signal is sufficient for implementation of the algorithm.

Renyi entanglement entropy of interacting fermions calculated using the continuous-time quantum Monte Carlo method.

PubMed

Wang, Lei; Troyer, Matthias

2014-09-12

We present a new algorithm for calculating the Renyi entanglement entropy of interacting fermions using the continuous-time quantum Monte Carlo method. The algorithm only samples the interaction correction of the entanglement entropy, which by design ensures the efficient calculation of weakly interacting systems. Combined with Monte Carlo reweighting, the algorithm also performs well for systems with strong interactions. We demonstrate the potential of this method by studying the quantum entanglement signatures of the charge-density-wave transition of interacting fermions on a square lattice.

Improving the quantum cost of reversible Boolean functions using reorder algorithm

NASA Astrophysics Data System (ADS)

Ahmed, Taghreed; Younes, Ahmed; Elsayed, Ashraf

2018-05-01

This paper introduces a novel algorithm to synthesize a low-cost reversible circuits for any Boolean function with n inputs represented as a Positive Polarity Reed-Muller expansion. The proposed algorithm applies a predefined rules to reorder the terms in the function to minimize the multi-calculation of common parts of the Boolean function to decrease the quantum cost of the reversible circuit. The paper achieves a decrease in the quantum cost and/or the circuit length, on average, when compared with relevant work in the literature.

Application of quantum-behaved particle swarm optimization to motor imagery EEG classification.

PubMed

Hsu, Wei-Yen

2013-12-01

In this study, we propose a recognition system for single-trial analysis of motor imagery (MI) electroencephalogram (EEG) data. Applying event-related brain potential (ERP) data acquired from the sensorimotor cortices, the system chiefly consists of automatic artifact elimination, feature extraction, feature selection and classification. In addition to the use of independent component analysis, a similarity measure is proposed to further remove the electrooculographic (EOG) artifacts automatically. Several potential features, such as wavelet-fractal features, are then extracted for subsequent classification. Next, quantum-behaved particle swarm optimization (QPSO) is used to select features from the feature combination. Finally, selected sub-features are classified by support vector machine (SVM). Compared with without artifact elimination, feature selection using a genetic algorithm (GA) and feature classification with Fisher's linear discriminant (FLD) on MI data from two data sets for eight subjects, the results indicate that the proposed method is promising in brain-computer interface (BCI) applications.

Cooperating or fighting with control noise in the optimal manipulation of quantum dynamics

NASA Astrophysics Data System (ADS)

Shuang, Feng; Rabitz, Herschel

2004-11-01

This paper investigates the impact of control field noise on the optimal manipulation of quantum dynamics. Simulations are performed on several multilevel quantum systems with the goal of population transfer in the presence of significant control noise. The noise enters as run-to-run variations in the control amplitude and phase with the observation being an ensemble average over many runs as is commonly done in the laboratory. A genetic algorithm with an improved elitism operator is used to find the optimal field that either fights against or cooperates with control field noise. When seeking a high control yield it is possible to find fields that successfully fight with the noise while attaining good quality stable results. When seeking modest control yields, fields can be found which are optimally shaped to cooperate with the noise and thereby drive the dynamics more efficiently. In general, noise reduces the coherence of the dynamics, but the results indicate that population transfer objectives can be met by appropriately either fighting or cooperating with noise, even when it is intense.

Cooperating or fighting with control noise in the optimal manipulation of quantum dynamics.

PubMed

Shuang, Feng; Rabitz, Herschel

2004-11-15

This paper investigates the impact of control field noise on the optimal manipulation of quantum dynamics. Simulations are performed on several multilevel quantum systems with the goal of population transfer in the presence of significant control noise. The noise enters as run-to-run variations in the control amplitude and phase with the observation being an ensemble average over many runs as is commonly done in the laboratory. A genetic algorithm with an improved elitism operator is used to find the optimal field that either fights against or cooperates with control field noise. When seeking a high control yield it is possible to find fields that successfully fight with the noise while attaining good quality stable results. When seeking modest control yields, fields can be found which are optimally shaped to cooperate with the noise and thereby drive the dynamics more efficiently. In general, noise reduces the coherence of the dynamics, but the results indicate that population transfer objectives can be met by appropriately either fighting or cooperating with noise, even when it is intense.

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 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

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 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.

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.

Analytic continuation of quantum Monte Carlo data by stochastic analytical inference.

PubMed

Fuchs, Sebastian; Pruschke, Thomas; Jarrell, Mark

2010-05-01

We present an algorithm for the analytic continuation of imaginary-time quantum Monte Carlo data which is strictly based on principles of Bayesian statistical inference. Within this framework we are able to obtain an explicit expression for the calculation of a weighted average over possible energy spectra, which can be evaluated by standard Monte Carlo simulations, yielding as by-product also the distribution function as function of the regularization parameter. Our algorithm thus avoids the usual ad hoc assumptions introduced in similar algorithms to fix the regularization parameter. We apply the algorithm to imaginary-time quantum Monte Carlo data and compare the resulting energy spectra with those from a standard maximum-entropy calculation.

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.

Cavity control as a new quantum algorithms implementation treatment

NASA Astrophysics Data System (ADS)

AbuGhanem, M.; Homid, A. H.; Abdel-Aty, M.

2018-02-01

Based on recent experiments [ Nature 449, 438 (2007) and Nature Physics 6, 777 (2010)], a new approach for realizing quantum gates for the design of quantum algorithms was developed. Accordingly, the operation times of such gates while functioning in algorithm applications depend on the number of photons present in their resonant cavities. Multi-qubit algorithms can be realized in systems in which the photon number is increased slightly over the qubit number. In addition, the time required for operation is considerably less than the dephasing and relaxation times of the systems. The contextual use of the photon number as a main control in the realization of any algorithm was demonstrated. The results indicate the possibility of a full integration into the realization of multi-qubit multiphoton states and its application in algorithm designs. Furthermore, this approach will lead to a successful implementation of these designs in future experiments.

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.

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.

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.

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.

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.

Analysis and improvement of the quantum image matching

NASA Astrophysics Data System (ADS)

Dang, Yijie; Jiang, Nan; Hu, Hao; Zhang, Wenyin

2017-11-01

We investigate the quantum image matching algorithm proposed by Jiang et al. (Quantum Inf Process 15(9):3543-3572, 2016). Although the complexity of this algorithm is much better than the classical exhaustive algorithm, there may be an error in it: After matching the area between two images, only the pixel at the upper left corner of the matched area played part in following steps. That is to say, the paper only matched one pixel, instead of an area. If more than one pixels in the big image are the same as the one at the upper left corner of the small image, the algorithm will randomly measure one of them, which causes the error. In this paper, an improved version is presented which takes full advantage of the whole matched area to locate a small image in a big image. The theoretical analysis indicates that the network complexity is higher than the previous algorithm, but it is still far lower than the classical algorithm. Hence, this algorithm is still efficient.

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.

Fast decoder for local quantum codes using Groebner basis

NASA Astrophysics Data System (ADS)

Haah, Jeongwan

2013-03-01

Based on arXiv:1204.1063. A local translation-invariant quantum code has a description in terms of Laurent polynomials. As an application of this observation, we present a fast decoding algorithm for translation-invariant local quantum codes in any spatial dimensions using the straightforward division algorithm for multivariate polynomials. The running time is O (n log n) on average, or O (n2 log n) on worst cases, where n is the number of physical qubits. The algorithm improves a subroutine of the renormalization-group decoder by Bravyi and Haah (arXiv:1112.3252) in the translation-invariant case. This work is supported in part by the Insitute for Quantum Information and Matter, an NSF Physics Frontier Center, and the Korea Foundation for Advanced Studies.

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.

Steganography on quantum pixel images using Shannon entropy

NASA Astrophysics Data System (ADS)

Laurel, Carlos Ortega; Dong, Shi-Hai; Cruz-Irisson, M.

2016-07-01

This paper presents a steganographical algorithm based on least significant bit (LSB) from the most significant bit information (MSBI) and the equivalence of a bit pixel image to a quantum pixel image, which permits to make the information communicate secretly onto quantum pixel images for its secure transmission through insecure channels. This algorithm offers higher security since it exploits the Shannon entropy for an image.

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.

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.

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.

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.

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.

Underwater sonar image detection: A combination of non-local spatial information and quantum-inspired shuffled frog leaping algorithm.

PubMed

Wang, Xingmei; Liu, Shu; Liu, Zhipeng

2017-01-01

This paper proposes a combination of non-local spatial information and quantum-inspired shuffled frog leaping algorithm to detect underwater objects in sonar images. Specifically, for the first time, the problem of inappropriate filtering degree parameter which commonly occurs in non-local spatial information and seriously affects the denoising performance in sonar images, was solved with the method utilizing a novel filtering degree parameter. Then, a quantum-inspired shuffled frog leaping algorithm based on new search mechanism (QSFLA-NSM) is proposed to precisely and quickly detect sonar images. Each frog individual is directly encoded by real numbers, which can greatly simplify the evolution process of the quantum-inspired shuffled frog leaping algorithm (QSFLA). Meanwhile, a fitness function combining intra-class difference with inter-class difference is adopted to evaluate frog positions more accurately. On this basis, recurring to an analysis of the quantum-behaved particle swarm optimization (QPSO) and the shuffled frog leaping algorithm (SFLA), a new search mechanism is developed to improve the searching ability and detection accuracy. At the same time, the time complexity is further reduced. Finally, the results of comparative experiments using the original sonar images, the UCI data sets and the benchmark functions demonstrate the effectiveness and adaptability of the proposed method.

Underwater sonar image detection: A combination of non-local spatial information and quantum-inspired shuffled frog leaping algorithm

PubMed Central

Liu, Zhipeng

2017-01-01

This paper proposes a combination of non-local spatial information and quantum-inspired shuffled frog leaping algorithm to detect underwater objects in sonar images. Specifically, for the first time, the problem of inappropriate filtering degree parameter which commonly occurs in non-local spatial information and seriously affects the denoising performance in sonar images, was solved with the method utilizing a novel filtering degree parameter. Then, a quantum-inspired shuffled frog leaping algorithm based on new search mechanism (QSFLA-NSM) is proposed to precisely and quickly detect sonar images. Each frog individual is directly encoded by real numbers, which can greatly simplify the evolution process of the quantum-inspired shuffled frog leaping algorithm (QSFLA). Meanwhile, a fitness function combining intra-class difference with inter-class difference is adopted to evaluate frog positions more accurately. On this basis, recurring to an analysis of the quantum-behaved particle swarm optimization (QPSO) and the shuffled frog leaping algorithm (SFLA), a new search mechanism is developed to improve the searching ability and detection accuracy. At the same time, the time complexity is further reduced. Finally, the results of comparative experiments using the original sonar images, the UCI data sets and the benchmark functions demonstrate the effectiveness and adaptability of the proposed method. PMID:28542266

Quantum Corral Wave-function Engineering

NASA Astrophysics Data System (ADS)

Correa, Alfredo; Reboredo, Fernando; Balseiro, Carlos

2005-03-01

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

Quantum Associative Neural Network with Nonlinear Search Algorithm

NASA Astrophysics Data System (ADS)

Zhou, Rigui; Wang, Huian; Wu, Qian; Shi, Yang

2012-03-01

Based on analysis on properties of quantum linear superposition, to overcome the complexity of existing quantum associative memory which was proposed by Ventura, a new storage method for multiply patterns is proposed in this paper by constructing the quantum array with the binary decision diagrams. Also, the adoption of the nonlinear search algorithm increases the pattern recalling speed of this model which has multiply patterns to O( {log2}^{2^{n -t}} ) = O( n - t ) time complexity, where n is the number of quantum bit and t is the quantum information of the t quantum bit. Results of case analysis show that the associative neural network model proposed in this paper based on quantum learning is much better and optimized than other researchers' counterparts both in terms of avoiding the additional qubits or extraordinary initial operators, storing pattern and improving the recalling speed.

Problem solving with genetic algorithms and Splicer

NASA Technical Reports Server (NTRS)

Bayer, Steven E.; Wang, Lui

1991-01-01

Genetic algorithms are highly parallel, adaptive search procedures (i.e., problem-solving methods) loosely based on the processes of population genetics and Darwinian survival of the fittest. Genetic algorithms have proven useful in domains where other optimization techniques perform poorly. The main purpose of the paper is to discuss a NASA-sponsored software development project to develop a general-purpose tool for using genetic algorithms. The tool, called Splicer, can be used to solve a wide variety of optimization problems and is currently available from NASA and COSMIC. This discussion is preceded by an introduction to basic genetic algorithm concepts and a discussion of genetic algorithm applications.

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.

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.

Quantum Algorithmic Readout in Multi-Ion Clocks.

PubMed

Schulte, M; Lörch, N; Leroux, I D; Schmidt, P O; Hammerer, K

2016-01-08

Optical clocks based on ensembles of trapped ions promise record frequency accuracy with good short-term stability. Most suitable ion species lack closed transitions, so the clock signal must be read out indirectly by transferring the quantum state of the clock ions to cotrapped logic ions of a different species. Existing methods of quantum logic readout require a linear overhead in either time or the number of logic ions. Here we describe a quantum algorithmic readout whose overhead scales logarithmically with the number of clock ions in both of these respects. The scheme allows a quantum nondemolition readout of the number of excited clock ions using a single multispecies gate operation which can also be used in other areas of ion trap technology such as quantum information processing, quantum simulations, metrology, and precision spectroscopy.

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.

Continuous-time quantum search on balanced trees

NASA Astrophysics Data System (ADS)

Philipp, Pascal; Tarrataca, Luís; Boettcher, Stefan

2016-03-01

We examine the effect of network heterogeneity on the performance of quantum search algorithms. To this end, we study quantum search on a tree for the oracle Hamiltonian formulation employed by continuous-time quantum walks. We use analytical and numerical arguments to show that the exponent of the asymptotic running time ˜Nβ changes uniformly from β =0.5 to β =1 as the searched-for site is moved from the root of the tree towards the leaves. These results imply that the time complexity of the quantum search algorithm on a balanced tree is closely correlated with certain path-based centrality measures of the searched-for site.

Quantum image processing: A review of advances in its security technologies

NASA Astrophysics Data System (ADS)

Yan, Fei; Iliyasu, Abdullah M.; Le, Phuc Q.

In this review, we present an overview of the advances made in quantum image processing (QIP) comprising of the image representations, the operations realizable on them, and the likely protocols and algorithms for their applications. In particular, we focus on recent progresses on QIP-based security technologies including quantum watermarking, quantum image encryption, and quantum image steganography. This review is aimed at providing readers with a succinct, yet adequate compendium of the progresses made in the QIP sub-area. Hopefully, this effort will stimulate further interest aimed at the pursuit of more advanced algorithms and experimental validations for available technologies and extensions to other domains.

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.

Genetic algorithms using SISAL parallel programming language

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

Tejada, S.

1994-05-06

Genetic algorithms are a mathematical optimization technique developed by John Holland at the University of Michigan [1]. The SISAL programming language possesses many of the characteristics desired to implement genetic algorithms. SISAL is a deterministic, functional programming language which is inherently parallel. Because SISAL is functional and based on mathematical concepts, genetic algorithms can be efficiently translated into the language. Several of the steps involved in genetic algorithms, such as mutation, crossover, and fitness evaluation, can be parallelized using SISAL. In this paper I will l discuss the implementation and performance of parallel genetic algorithms in SISAL.

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.

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

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.

Data-driven gradient algorithm for high-precision quantum control

NASA Astrophysics Data System (ADS)

Wu, Re-Bing; Chu, Bing; Owens, David H.; Rabitz, Herschel

2018-04-01

In the quest to achieve scalable quantum information processing technologies, gradient-based optimal control algorithms (e.g., grape) are broadly used for implementing high-precision quantum gates, but their performance is often hindered by deterministic or random errors in the system model and the control electronics. In this paper, we show that grape can be taught to be more effective by jointly learning from the design model and the experimental data obtained from process tomography. The resulting data-driven gradient optimization algorithm (d-grape) can in principle correct all deterministic gate errors, with a mild efficiency loss. The d-grape algorithm may become more powerful with broadband controls that involve a large number of control parameters, while other algorithms usually slow down due to the increased size of the search space. These advantages are demonstrated by simulating the implementation of a two-qubit controlled-not gate.

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.

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.

Quantum autoencoders for efficient compression of quantum data

NASA Astrophysics Data System (ADS)

Romero, Jonathan; Olson, Jonathan P.; Aspuru-Guzik, Alan

2017-12-01

Classical autoencoders are neural networks that can learn efficient low-dimensional representations of data in higher-dimensional space. The task of an autoencoder is, given an input x, to map x to a lower dimensional point y such that x can likely be recovered from y. The structure of the underlying autoencoder network can be chosen to represent the data on a smaller dimension, effectively compressing the input. Inspired by this idea, we introduce the model of a quantum autoencoder to perform similar tasks on quantum data. The quantum autoencoder is trained to compress a particular data set of quantum states, where a classical compression algorithm cannot be employed. The parameters of the quantum autoencoder are trained using classical optimization algorithms. We show an example of a simple programmable circuit that can be trained as an efficient autoencoder. We apply our model in the context of quantum simulation to compress ground states of the Hubbard model and molecular Hamiltonians.

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 search algorithms on a regular lattice

NASA Astrophysics Data System (ADS)

Hein, Birgit; Tanner, Gregor

2010-07-01

Quantum algorithms for searching for one or more marked items on a d-dimensional lattice provide an extension of Grover’s search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behavior for the search time and the localization probability in the limit of large lattice size including the leading order coefficients. For d=2 and d=3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions.

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.

An Adaptive Cultural Algorithm with Improved Quantum-behaved Particle Swarm Optimization for Sonar Image Detection.

PubMed

Wang, Xingmei; Hao, Wenqian; Li, Qiming

2017-12-18

This paper proposes an adaptive cultural algorithm with improved quantum-behaved particle swarm optimization (ACA-IQPSO) to detect the underwater sonar image. In the population space, to improve searching ability of particles, iterative times and the fitness value of particles are regarded as factors to adaptively adjust the contraction-expansion coefficient of the quantum-behaved particle swarm optimization algorithm (QPSO). The improved quantum-behaved particle swarm optimization algorithm (IQPSO) can make particles adjust their behaviours according to their quality. In the belief space, a new update strategy is adopted to update cultural individuals according to the idea of the update strategy in shuffled frog leaping algorithm (SFLA). Moreover, to enhance the utilization of information in the population space and belief space, accept function and influence function are redesigned in the new communication protocol. The experimental results show that ACA-IQPSO can obtain good clustering centres according to the grey distribution information of underwater sonar images, and accurately complete underwater objects detection. Compared with other algorithms, the proposed ACA-IQPSO has good effectiveness, excellent adaptability, a powerful searching ability and high convergence efficiency. Meanwhile, the experimental results of the benchmark functions can further demonstrate that the proposed ACA-IQPSO has better searching ability, convergence efficiency and stability.

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.

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.

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.

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.

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 algorithm for association rules mining

NASA Astrophysics Data System (ADS)

Yu, Chao-Hua; Gao, Fei; Wang, Qing-Le; Wen, Qiao-Yan

2016-10-01

Association rules mining (ARM) is one of the most important problems in knowledge discovery and data mining. Given a transaction database that has a large number of transactions and items, the task of ARM is to acquire consumption habits of customers by discovering the relationships between itemsets (sets of items). In this paper, we address ARM in the quantum settings and propose a quantum algorithm for the key part of ARM, finding frequent itemsets from the candidate itemsets and acquiring their supports. Specifically, for the case in which there are Mf(k ) frequent k -itemsets in the Mc(k ) candidate k -itemsets (Mf(k )≤Mc(k ) ), our algorithm can efficiently mine these frequent k -itemsets and estimate their supports by using parallel amplitude estimation and amplitude amplification with complexity O (k/√{Mc(k )Mf(k ) } ɛ ) , where ɛ is the error for estimating the supports. Compared with the classical counterpart, i.e., the classical sampling-based algorithm, whose complexity is O (k/Mc(k ) ɛ2) , our quantum algorithm quadratically improves the dependence on both ɛ and Mc(k ) in the best case when Mf(k )≪Mc(k ) and on ɛ alone in the worst case when Mf(k )≈Mc(k ) .

A Novel Quantum-Behaved Bat Algorithm with Mean Best Position Directed for Numerical Optimization

PubMed Central

Zhu, Wenyong; Liu, Zijuan; Duan, Qingyan; Cao, Long

2016-01-01

This paper proposes a novel quantum-behaved bat algorithm with the direction of mean best position (QMBA). In QMBA, the position of each bat is mainly updated by the current optimal solution in the early stage of searching and in the late search it also depends on the mean best position which can enhance the convergence speed of the algorithm. During the process of searching, quantum behavior of bats is introduced which is beneficial to jump out of local optimal solution and make the quantum-behaved bats not easily fall into local optimal solution, and it has better ability to adapt complex environment. Meanwhile, QMBA makes good use of statistical information of best position which bats had experienced to generate better quality solutions. This approach not only inherits the characteristic of quick convergence, simplicity, and easy implementation of original bat algorithm, but also increases the diversity of population and improves the accuracy of solution. Twenty-four benchmark test functions are tested and compared with other variant bat algorithms for numerical optimization the simulation results show that this approach is simple and efficient and can achieve a more accurate solution. PMID:27293424

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.

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.

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

The Quantum Binding Problem in the Context of Associative Memory

PubMed Central

Wichert, Andreas

2016-01-01

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

Quantum snake walk on graphs

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

Rosmanis, Ansis

2011-02-15

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

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.

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.

Single-hidden-layer feed-forward quantum neural network based on Grover learning.

PubMed

Liu, Cheng-Yi; Chen, Chein; Chang, Ching-Ter; Shih, Lun-Min

2013-09-01

In this paper, a novel single-hidden-layer feed-forward quantum neural network model is proposed based on some concepts and principles in the quantum theory. By combining the quantum mechanism with the feed-forward neural network, we defined quantum hidden neurons and connected quantum weights, and used them as the fundamental information processing unit in a single-hidden-layer feed-forward neural network. The quantum neurons make a wide range of nonlinear functions serve as the activation functions in the hidden layer of the network, and the Grover searching algorithm outstands the optimal parameter setting iteratively and thus makes very efficient neural network learning possible. The quantum neuron and weights, along with a Grover searching algorithm based learning, result in a novel and efficient neural network characteristic of reduced network, high efficient training and prospect application in future. Some simulations are taken to investigate the performance of the proposed quantum network and the result show that it can achieve accurate learning. Copyright © 2013 Elsevier Ltd. All rights reserved.

QSAR models based on quantum topological molecular similarity.

PubMed

Popelier, P L A; Smith, P J

2006-07-01

A new method called quantum topological molecular similarity (QTMS) was fairly recently proposed [J. Chem. Inf. Comp. Sc., 41, 2001, 764] to construct a variety of medicinal, ecological and physical organic QSAR/QSPRs. QTMS method uses quantum chemical topology (QCT) to define electronic descriptors drawn from modern ab initio wave functions of geometry-optimised molecules. It was shown that the current abundance of computing power can be utilised to inject realistic descriptors into QSAR/QSPRs. In this article we study seven datasets of medicinal interest : the dissociation constants (pK(a)) for a set of substituted imidazolines , the pK(a) of imidazoles , the ability of a set of indole derivatives to displace [(3)H] flunitrazepam from binding to bovine cortical membranes , the influenza inhibition constants for a set of benzimidazoles , the interaction constants for a set of amides and the enzyme liver alcohol dehydrogenase , the natriuretic activity of sulphonamide carbonic anhydrase inhibitors and the toxicity of a series of benzyl alcohols. A partial least square analysis in conjunction with a genetic algorithm delivered excellent models. They are also able to highlight the active site, of the ligand or the molecule whose structure determines the activity. The advantages and limitations of QTMS are discussed.

Chirped circular dielectric gratings for near-unity collection efficiency from quantum emitters in bulk diamond

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

Zheng, Jiabao; Liapis, Andreas C.; Chen, Edward H.

Effcient collection of fluorescence from nitrogen vacancy (NV) centers in diamond underlies the spin-dependent optical read-out that is necessary for quantum information processing and enhanced sensing applications. The optical collection effciency from NVs within diamond substrates is limited primarily due to the high refractive index of diamond and the non-directional dipole emission. Here we introduce a light collection strategy based on chirped, circular dielectric gratings that can be fabricated on a bulk diamond substrate to redirect an emitter’s far-field radiation pattern. Using a genetic optimization algorithm, these grating designs achieve 98.9% collection effciency for the NV zero-phonon emission line, collectedmore » from the back surface of the diamond with an objective of aperture 0.9. Across the broadband emission spectrum of the NV (600-800 nm), the chirped grating achieves 82.2% collection e ciency into a numerical aperture of 1.42, corresponding to an oil immersion objective again on the back side of the diamond. Our proposed bulk-dielectric grating structures are applicable to other optically active solid state quantum emitters in high index host materials.« less

Chirped circular dielectric gratings for near-unity collection efficiency from quantum emitters in bulk diamond

DOE PAGES

Zheng, Jiabao; Liapis, Andreas C.; Chen, Edward H.; ...

2017-12-13

Effcient collection of fluorescence from nitrogen vacancy (NV) centers in diamond underlies the spin-dependent optical read-out that is necessary for quantum information processing and enhanced sensing applications. The optical collection effciency from NVs within diamond substrates is limited primarily due to the high refractive index of diamond and the non-directional dipole emission. Here we introduce a light collection strategy based on chirped, circular dielectric gratings that can be fabricated on a bulk diamond substrate to redirect an emitter’s far-field radiation pattern. Using a genetic optimization algorithm, these grating designs achieve 98.9% collection effciency for the NV zero-phonon emission line, collectedmore » from the back surface of the diamond with an objective of aperture 0.9. Across the broadband emission spectrum of the NV (600-800 nm), the chirped grating achieves 82.2% collection e ciency into a numerical aperture of 1.42, corresponding to an oil immersion objective again on the back side of the diamond. Our proposed bulk-dielectric grating structures are applicable to other optically active solid state quantum emitters in high index host materials.« less

Optimal Design of Passive Power Filters Based on Pseudo-parallel Genetic Algorithm

NASA Astrophysics Data System (ADS)

Li, Pei; Li, Hongbo; Gao, Nannan; Niu, Lin; Guo, Liangfeng; Pei, Ying; Zhang, Yanyan; Xu, Minmin; Chen, Kerui

2017-05-01

The economic costs together with filter efficiency are taken as targets to optimize the parameter of passive filter. Furthermore, the method of combining pseudo-parallel genetic algorithm with adaptive genetic algorithm is adopted in this paper. In the early stages pseudo-parallel genetic algorithm is introduced to increase the population diversity, and adaptive genetic algorithm is used in the late stages to reduce the workload. At the same time, the migration rate of pseudo-parallel genetic algorithm is improved to change with population diversity adaptively. Simulation results show that the filter designed by the proposed method has better filtering effect with lower economic cost, and can be used in engineering.

Highlighting the Mechanism of the Quantum Speedup by Time-Symmetric and Relational Quantum Mechanics

NASA Astrophysics Data System (ADS)

Castagnoli, Giuseppe

2016-03-01

Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. The usual representation of the quantum algorithm is limited to the process of solving the problem. We extend it to the process of setting the problem. The number of the drawer with the ball becomes a unitary transformation of the random outcome of the preparation measurement. This extended, time-symmetric, representation brings in relational quantum mechanics. It is with respect to Bob and any external observer and cannot be with respect to Alice. It would tell her the number of the drawer with the ball before she opens any drawer. To Alice, the projection of the quantum state due to the preparation measurement should be retarded at the end of her search; in the input state of the search, the drawer number is determined to Bob and undetermined to Alice. We show that, mathematically, one can ascribe any part of the selection of the random outcome of the preparation measurement to the final Alice's measurement. Ascribing half of it explains the speedup of the present algorithm. This leaves the input state to Bob unaltered and projects that to Alice on a state of lower entropy where she knows half of the number of the drawer with the ball in advance. The quantum algorithm turns out to be a sum over histories in each of which Alice knows in advance that the ball is in a pair of drawers and locates it by opening one of the two. In the sample of quantum algorithms examined, the part of the random outcome of the initial measurement selected by the final measurement is one half or slightly above it. Conversely, given an oracle problem, the assumption it is one half always corresponds to an existing quantum algorithm and gives the order of magnitude of the number of oracle queries required by the optimal one.

Quantum microbiology.

PubMed

Trevors, J T; Masson, L

2011-01-01

During his famous 1943 lecture series at Trinity College Dublin, the reknown physicist Erwin Schrodinger discussed the failure and challenges of interpreting life by classical physics alone and that a new approach, rooted in Quantum principles, must be involved. Quantum events are simply a level of organization below the molecular level. This includes the atomic and subatomic makeup of matter in microbial metabolism and structures, as well as the organic, genetic information code of DNA and RNA. Quantum events at this time do not elucidate, for example, how specific genetic instructions were first encoded in an organic genetic code in microbial cells capable of growth and division, and its subsequent evolution over 3.6 to 4 billion years. However, due to recent technological advances, biologists and physicists are starting to demonstrate linkages between various quantum principles like quantum tunneling, entanglement and coherence in biological processes illustrating that nature has exerted some level quantum control to optimize various processes in living organisms. In this article we explore the role of quantum events in microbial processes and endeavor to show that after nearly 67 years, Schrödinger was prophetic and visionary in his view of quantum theory and its connection with some of the fundamental mechanisms of life.

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.

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.

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

Implementation of the semiclassical quantum Fourier transform in a scalable system.

PubMed

Chiaverini, J; Britton, J; Leibfried, D; Knill, E; Barrett, M D; Blakestad, R B; Itano, W M; Jost, J D; Langer, C; Ozeri, R; Schaetz, T; Wineland, D J

2005-05-13

We report the implementation of the semiclassical quantum Fourier transform in a system of three beryllium ion qubits (two-level quantum systems) confined in a segmented multizone trap. The quantum Fourier transform is the crucial final step in Shor's algorithm, and it acts on a register of qubits to determine the periodicity of the quantum state's amplitudes. Because only probability amplitudes are required for this task, a more efficient semiclassical version can be used, for which only single-qubit operations conditioned on measurement outcomes are required. We apply the transform to several input states of different periodicities; the results enable the location of peaks corresponding to the original periods. This demonstration incorporates the key elements of a scalable ion-trap architecture, suggesting the future capability of applying the quantum Fourier transform to a large number of qubits as required for a useful quantum factoring algorithm.

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

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

Single Channel Quantum Color Image Encryption Algorithm Based on HSI Model and Quantum Fourier Transform

NASA Astrophysics Data System (ADS)

Gong, Li-Hua; He, Xiang-Tao; Tan, Ru-Chao; Zhou, Zhi-Hong

2018-01-01

In order to obtain high-quality color images, it is important to keep the hue component unchanged while emphasize the intensity or saturation component. As a public color model, Hue-Saturation Intensity (HSI) model is commonly used in image processing. A new single channel quantum color image encryption algorithm based on HSI model and quantum Fourier transform (QFT) is investigated, where the color components of the original color image are converted to HSI and the logistic map is employed to diffuse the relationship of pixels in color components. Subsequently, quantum Fourier transform is exploited to fulfill the encryption. The cipher-text is a combination of a gray image and a phase matrix. Simulations and theoretical analyses demonstrate that the proposed single channel quantum color image encryption scheme based on the HSI model and quantum Fourier transform is secure and effective.

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.

Mixing times in quantum walks on two-dimensional grids

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

Marquezino, F. L.; Portugal, R.; Abal, G.

2010-10-15

Mixing properties of discrete-time quantum walks on two-dimensional grids with toruslike boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an exact expression for the stationary distribution of the coherent walk over odd-sided lattices is obtained after solving the eigenproblem for the evolution operator for this particular graph. The limiting distribution and mixing time of a quantum walk with a coin operator modified as in the abstract search algorithm are obtained numerically. On the basis of these results, the relation between the mixing time of the modified walk and themore » running time of the corresponding abstract search algorithm is discussed.« less

Mixing times in quantum walks on two-dimensional grids

NASA Astrophysics Data System (ADS)

Marquezino, F. L.; Portugal, R.; Abal, G.

2010-10-01

Mixing properties of discrete-time quantum walks on two-dimensional grids with toruslike boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an exact expression for the stationary distribution of the coherent walk over odd-sided lattices is obtained after solving the eigenproblem for the evolution operator for this particular graph. The limiting distribution and mixing time of a quantum walk with a coin operator modified as in the abstract search algorithm are obtained numerically. On the basis of these results, the relation between the mixing time of the modified walk and the running time of the corresponding abstract search algorithm is discussed.

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

Determining the Complexity of the Quantum Adiabatic Algorithm using Quantum Monte Carlo Simulations

DTIC Science & Technology

2012-12-18

of this printing. List the papers, including journal references, in the following categories: Received Paper 12/06/2012 4.00 Itay Hen, A. Young...PhysRevLett.104.020502 12/06/2012 3.00 A. P. Young, Itay Hen. Exponential complexity of the quantum adiabatic algorithm for certain satisfiability problems...Physical Review E, (12 2011): 0. doi: 10.1103/PhysRevE.84.061152 12/06/2012 5.00 Edward Farhi, David Gosset, Itay Hen, A. Sandvik, Peter Shor, A

Modelling Systems of Classical/Quantum Identical Particles by Focusing on Algorithms

ERIC Educational Resources Information Center

Guastella, Ivan; Fazio, Claudio; Sperandeo-Mineo, Rosa Maria

2012-01-01

A procedure modelling ideal classical and quantum gases is discussed. The proposed approach is mainly based on the idea that modelling and algorithm analysis can provide a deeper understanding of particularly complex physical systems. Appropriate representations and physical models able to mimic possible pseudo-mechanisms of functioning and having…

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

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.

Quantum Cryptography Based on the Deutsch-Jozsa Algorithm

NASA Astrophysics Data System (ADS)

Nagata, Koji; Nakamura, Tadao; Farouk, Ahmed

2017-09-01

Recently, secure quantum key distribution based on Deutsch's algorithm using the Bell state is reported (Nagata and Nakamura, Int. J. Theor. Phys. doi: 10.1007/s10773-017-3352-4, 2017). Our aim is of extending the result to a multipartite system. In this paper, we propose a highly speedy key distribution protocol. We present sequre quantum key distribution based on a special Deutsch-Jozsa algorithm using Greenberger-Horne-Zeilinger states. Bob has promised to use a function f which is of one of two kinds; either the value of f( x) is constant for all values of x, or else the value of f( x) is balanced, that is, equal to 1 for exactly half of the possible x, and 0 for the other half. Here, we introduce an additional condition to the function when it is balanced. Our quantum key distribution overcomes a classical counterpart by a factor O(2 N ).

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.

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.

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

Uni10: an open-source library for tensor network algorithms

NASA Astrophysics Data System (ADS)

Kao, Ying-Jer; Hsieh, Yun-Da; Chen, Pochung

2015-09-01

We present an object-oriented open-source library for developing tensor network algorithms written in C++ called Uni10. With Uni10, users can build a symmetric tensor from a collection of bonds, while the bonds are constructed from a list of quantum numbers associated with different quantum states. It is easy to label and permute the indices of the tensors and access a block associated with a particular quantum number. Furthermore a network class is used to describe arbitrary tensor network structure and to perform network contractions efficiently. We give an overview of the basic structure of the library and the hierarchy of the classes. We present examples of the construction of a spin-1 Heisenberg Hamiltonian and the implementation of the tensor renormalization group algorithm to illustrate the basic usage of the library. The library described here is particularly well suited to explore and fast prototype novel tensor network algorithms and to implement highly efficient codes for existing algorithms.

Quantum algorithm for linear systems of equations.

PubMed

Harrow, Aram W; Hassidim, Avinatan; Lloyd, Seth

2009-10-09

Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b(-->), find a vector x(-->) such that Ax(-->) = b(-->). We consider the case where one does not need to know the solution x(-->) itself, but rather an approximation of the expectation value of some operator associated with x(-->), e.g., x(-->)(dagger) Mx(-->) for some matrix M. In this case, when A is sparse, N x N and has condition number kappa, the fastest known classical algorithms can find x(-->) and estimate x(-->)(dagger) Mx(-->) in time scaling roughly as N square root(kappa). Here, we exhibit a quantum algorithm for estimating x(-->)(dagger) Mx(-->) whose runtime is a polynomial of log(N) and kappa. Indeed, for small values of kappa [i.e., poly log(N)], we prove (using some common complexity-theoretic assumptions) that any classical algorithm for this problem generically requires exponentially more time than our quantum algorithm.

G/SPLINES: A hybrid of Friedman's Multivariate Adaptive Regression Splines (MARS) algorithm with Holland's genetic algorithm

NASA Technical Reports Server (NTRS)

Rogers, David

1991-01-01

G/SPLINES are a hybrid of Friedman's Multivariable Adaptive Regression Splines (MARS) algorithm with Holland's Genetic Algorithm. In this hybrid, the incremental search is replaced by a genetic search. The G/SPLINE algorithm exhibits performance comparable to that of the MARS algorithm, requires fewer least squares computations, and allows significantly larger problems to be considered.

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.

Recurrent neural network approach to quantum signal: coherent state restoration for continuous-variable quantum key distribution

NASA Astrophysics Data System (ADS)

Lu, Weizhao; Huang, Chunhui; Hou, Kun; Shi, Liting; Zhao, Huihui; Li, Zhengmei; Qiu, Jianfeng

2018-05-01

In continuous-variable quantum key distribution (CV-QKD), weak signal carrying information transmits from Alice to Bob; during this process it is easily influenced by unknown noise which reduces signal-to-noise ratio, and strongly impacts reliability and stability of the communication. Recurrent quantum neural network (RQNN) is an artificial neural network model which can perform stochastic filtering without any prior knowledge of the signal and noise. In this paper, a modified RQNN algorithm with expectation maximization algorithm is proposed to process the signal in CV-QKD, which follows the basic rule of quantum mechanics. After RQNN, noise power decreases about 15 dBm, coherent signal recognition rate of RQNN is 96%, quantum bit error rate (QBER) drops to 4%, which is 6.9% lower than original QBER, and channel capacity is notably enlarged.

Expeditious reconciliation for practical quantum key distribution

NASA Astrophysics Data System (ADS)

Nakassis, Anastase; Bienfang, Joshua C.; Williams, Carl J.

2004-08-01

The paper proposes algorithmic and environmental modifications to the extant reconciliation algorithms within the BB84 protocol so as to speed up reconciliation and privacy amplification. These algorithms have been known to be a performance bottleneck 1 and can process data at rates that are six times slower than the quantum channel they serve2. As improvements in single-photon sources and detectors are expected to improve the quantum channel throughput by two or three orders of magnitude, it becomes imperative to improve the performance of the classical software. We developed a Cascade-like algorithm that relies on a symmetric formulation of the problem, error estimation through the segmentation process, outright elimination of segments with many errors, Forward Error Correction, recognition of the distinct data subpopulations that emerge as the algorithm runs, ability to operate on massive amounts of data (of the order of 1 Mbit), and a few other minor improvements. The data from the experimental algorithm we developed show that by operating on massive arrays of data we can improve software performance by better than three orders of magnitude while retaining nearly as many bits (typically more than 90%) as the algorithms that were designed for optimal bit retention.

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 Clock Synchronization with a Single Qudit

NASA Astrophysics Data System (ADS)

Tavakoli, Armin; Cabello, Adán; Żukowski, Marek; Bourennane, Mohamed

2015-01-01

Clock synchronization for nonfaulty processes in multiprocess networks is indispensable for a variety of technologies. A reliable system must be able to resynchronize the nonfaulty processes upon some components failing causing the distribution of incorrect or conflicting information in the network. The task of synchronizing such networks is related to Byzantine agreement (BA), which can classically be solved using recursive algorithms if and only if less than one-third of the processes are faulty. Here we introduce a nonrecursive quantum algorithm, based on a quantum solution of the detectable BA, which achieves clock synchronization in the presence of arbitrary many faulty processes by using only a single quantum system.

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

Comparison of genetic algorithms with conjugate gradient methods

NASA Technical Reports Server (NTRS)

Bosworth, J. L.; Foo, N. Y.; Zeigler, B. P.

1972-01-01

Genetic algorithms for mathematical function optimization are modeled on search strategies employed in natural adaptation. Comparisons of genetic algorithms with conjugate gradient methods, which were made on an IBM 1800 digital computer, show that genetic algorithms display superior performance over gradient methods for functions which are poorly behaved mathematically, for multimodal functions, and for functions obscured by additive random noise. Genetic methods offer performance comparable to gradient methods for many of the standard functions.

Software For Genetic Algorithms

NASA Technical Reports Server (NTRS)

Wang, Lui; Bayer, Steve E.

1992-01-01

SPLICER computer program is genetic-algorithm software tool used to solve search and optimization problems. Provides underlying framework and structure for building genetic-algorithm application program. Written in Think C.

A Circuit-Based Quantum Algorithm Driven by Transverse Fields for Grover's Problem

NASA Technical Reports Server (NTRS)

Jiang, Zhang; Rieffel, Eleanor G.; Wang, Zhihui

2017-01-01

We designed a quantum search algorithm, giving the same quadratic speedup achieved by Grover's original algorithm; we replace Grover's diffusion operator (hard to implement) with a product diffusion operator generated by transverse fields (easy to implement). In our algorithm, the problem Hamiltonian (oracle) and the transverse fields are applied to the system alternatively. We construct such a sequence that the corresponding unitary generates a closed transition between the initial state (even superposition of all states) and a modified target state, which has a high degree of overlap with the original target state.

New knowledge-based genetic algorithm for excavator boom structural optimization

NASA Astrophysics Data System (ADS)

Hua, Haiyan; Lin, Shuwen

2014-03-01

Due to the insufficiency of utilizing knowledge to guide the complex optimal searching, existing genetic algorithms fail to effectively solve excavator boom structural optimization problem. To improve the optimization efficiency and quality, a new knowledge-based real-coded genetic algorithm is proposed. A dual evolution mechanism combining knowledge evolution with genetic algorithm is established to extract, handle and utilize the shallow and deep implicit constraint knowledge to guide the optimal searching of genetic algorithm circularly. Based on this dual evolution mechanism, knowledge evolution and population evolution can be connected by knowledge influence operators to improve the configurability of knowledge and genetic operators. Then, the new knowledge-based selection operator, crossover operator and mutation operator are proposed to integrate the optimal process knowledge and domain culture to guide the excavator boom structural optimization. Eight kinds of testing algorithms, which include different genetic operators, are taken as examples to solve the structural optimization of a medium-sized excavator boom. By comparing the results of optimization, it is shown that the algorithm including all the new knowledge-based genetic operators can more remarkably improve the evolutionary rate and searching ability than other testing algorithms, which demonstrates the effectiveness of knowledge for guiding optimal searching. The proposed knowledge-based genetic algorithm by combining multi-level knowledge evolution with numerical optimization provides a new effective method for solving the complex engineering optimization problem.

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.

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.

A cascaded QSAR model for efficient prediction of overall power conversion efficiency of all-organic dye-sensitized solar cells.

PubMed

Li, Hongzhi; Zhong, Ziyan; Li, Lin; Gao, Rui; Cui, Jingxia; Gao, Ting; Hu, Li Hong; Lu, Yinghua; Su, Zhong-Min; Li, Hui

2015-05-30

A cascaded model is proposed to establish the quantitative structure-activity relationship (QSAR) between the overall power conversion efficiency (PCE) and quantum chemical molecular descriptors of all-organic dye sensitizers. The cascaded model is a two-level network in which the outputs of the first level (JSC, VOC, and FF) are the inputs of the second level, and the ultimate end-point is the overall PCE of dye-sensitized solar cells (DSSCs). The model combines quantum chemical methods and machine learning methods, further including quantum chemical calculations, data division, feature selection, regression, and validation steps. To improve the efficiency of the model and reduce the redundancy and noise of the molecular descriptors, six feature selection methods (multiple linear regression, genetic algorithms, mean impact value, forward selection, backward elimination, and +n-m algorithm) are used with the support vector machine. The best established cascaded model predicts the PCE values of DSSCs with a MAE of 0.57 (%), which is about 10% of the mean value PCE (5.62%). The validation parameters according to the OECD principles are R(2) (0.75), Q(2) (0.77), and Qcv2 (0.76), which demonstrate the great goodness-of-fit, predictivity, and robustness of the model. Additionally, the applicability domain of the cascaded QSAR model is defined for further application. This study demonstrates that the established cascaded model is able to effectively predict the PCE for organic dye sensitizers with very low cost and relatively high accuracy, providing a useful tool for the design of dye sensitizers with high PCE. © 2015 Wiley Periodicals, Inc.

Ensemble of hybrid genetic algorithm for two-dimensional phase unwrapping

NASA Astrophysics Data System (ADS)

Balakrishnan, D.; Quan, C.; Tay, C. J.

2013-06-01

The phase unwrapping is the final and trickiest step in any phase retrieval technique. Phase unwrapping by artificial intelligence methods (optimization algorithms) such as hybrid genetic algorithm, reverse simulated annealing, particle swarm optimization, minimum cost matching showed better results than conventional phase unwrapping methods. In this paper, Ensemble of hybrid genetic algorithm with parallel populations is proposed to solve the branch-cut phase unwrapping problem. In a single populated hybrid genetic algorithm, the selection, cross-over and mutation operators are applied to obtain new population in every generation. The parameters and choice of operators will affect the performance of the hybrid genetic algorithm. The ensemble of hybrid genetic algorithm will facilitate to have different parameters set and different choice of operators simultaneously. Each population will use different set of parameters and the offspring of each population will compete against the offspring of all other populations, which use different set of parameters. The effectiveness of proposed algorithm is demonstrated by phase unwrapping examples and advantages of the proposed method are discussed.

Mobile robot dynamic path planning based on improved genetic algorithm

NASA Astrophysics Data System (ADS)

Wang, Yong; Zhou, Heng; Wang, Ying

2017-08-01

In dynamic unknown environment, the dynamic path planning of mobile robots is a difficult problem. In this paper, a dynamic path planning method based on genetic algorithm is proposed, and a reward value model is designed to estimate the probability of dynamic obstacles on the path, and the reward value function is applied to the genetic algorithm. Unique coding techniques reduce the computational complexity of the algorithm. The fitness function of the genetic algorithm fully considers three factors: the security of the path, the shortest distance of the path and the reward value of the path. The simulation results show that the proposed genetic algorithm is efficient in all kinds of complex dynamic environments.

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.

An Efficient Rank Based Approach for Closest String and Closest Substring

PubMed Central

2012-01-01

This paper aims to present a new genetic approach that uses rank distance for solving two known NP-hard problems, and to compare rank distance with other distance measures for strings. The two NP-hard problems we are trying to solve are closest string and closest substring. For each problem we build a genetic algorithm and we describe the genetic operations involved. Both genetic algorithms use a fitness function based on rank distance. We compare our algorithms with other genetic algorithms that use different distance measures, such as Hamming distance or Levenshtein distance, on real DNA sequences. Our experiments show that the genetic algorithms based on rank distance have the best results. PMID:22675483

A hybrid genetic algorithm for resolving closely spaced objects

NASA Technical Reports Server (NTRS)

Abbott, R. J.; Lillo, W. E.; Schulenburg, N.

1995-01-01

A hybrid genetic algorithm is described for performing the difficult optimization task of resolving closely spaced objects appearing in space based and ground based surveillance data. This application of genetic algorithms is unusual in that it uses a powerful domain-specific operation as a genetic operator. Results of applying the algorithm to real data from telescopic observations of a star field are presented.

Genetic Algorithm Tuned Fuzzy Logic for Gliding Return Trajectories

NASA Technical Reports Server (NTRS)

Burchett, Bradley T.

2003-01-01

The problem of designing and flying a trajectory for successful recovery of a reusable launch vehicle is tackled using fuzzy logic control with genetic algorithm optimization. The plant is approximated by a simplified three degree of freedom non-linear model. A baseline trajectory design and guidance algorithm consisting of several Mamdani type fuzzy controllers is tuned using a simple genetic algorithm. Preliminary results show that the performance of the overall system is shown to improve with genetic algorithm tuning.

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

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.

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.

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.

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.

Learning Intelligent Genetic Algorithms Using Japanese Nonograms

ERIC Educational Resources Information Center

Tsai, Jinn-Tsong; Chou, Ping-Yi; Fang, Jia-Cen

2012-01-01

An intelligent genetic algorithm (IGA) is proposed to solve Japanese nonograms and is used as a method in a university course to learn evolutionary algorithms. The IGA combines the global exploration capabilities of a canonical genetic algorithm (CGA) with effective condensed encoding, improved fitness function, and modified crossover and…

Benchmarking the D-Wave Two

NASA Astrophysics Data System (ADS)

Job, Joshua; Wang, Zhihui; Rønnow, Troels; Troyer, Matthias; Lidar, Daniel

2014-03-01

We report on experimental work benchmarking the performance of the D-Wave Two programmable annealer on its native Ising problem, and a comparison to available classical algorithms. In this talk we will focus on the comparison with an algorithm originally proposed and implemented by Alex Selby. This algorithm uses dynamic programming to repeatedly optimize over randomly selected maximal induced trees of the problem graph starting from a random initial state. If one is looking for a quantum advantage over classical algorithms, one should compare to classical algorithms which are designed and optimized to maximally take advantage of the structure of the type of problem one is using for the comparison. In that light, this classical algorithm should serve as a good gauge for any potential quantum speedup for the D-Wave Two.

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.

Genetic algorithms with memory- and elitism-based immigrants in dynamic environments.

PubMed

Yang, Shengxiang

2008-01-01

In recent years the genetic algorithm community has shown a growing interest in studying dynamic optimization problems. Several approaches have been devised. The random immigrants and memory schemes are two major ones. The random immigrants scheme addresses dynamic environments by maintaining the population diversity while the memory scheme aims to adapt genetic algorithms quickly to new environments by reusing historical information. This paper investigates a hybrid memory and random immigrants scheme, called memory-based immigrants, and a hybrid elitism and random immigrants scheme, called elitism-based immigrants, for genetic algorithms in dynamic environments. In these schemes, the best individual from memory or the elite from the previous generation is retrieved as the base to create immigrants into the population by mutation. This way, not only can diversity be maintained but it is done more efficiently to adapt genetic algorithms to the current environment. Based on a series of systematically constructed dynamic problems, experiments are carried out to compare genetic algorithms with the memory-based and elitism-based immigrants schemes against genetic algorithms with traditional memory and random immigrants schemes and a hybrid memory and multi-population scheme. The sensitivity analysis regarding some key parameters is also carried out. Experimental results show that the memory-based and elitism-based immigrants schemes efficiently improve the performance of genetic algorithms in dynamic environments.

Boiler-turbine control system design using a genetic algorithm

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

Dimeo, R.; Lee, K.Y.

1995-12-01

This paper discusses the application of a genetic algorithm to control system design for a boiler-turbine plant. In particular the authors study the ability of the genetic algorithm to develop a proportional-integral (PI) controller and a state feedback controller for a non-linear multi-input/multi-output (MIMO) plant model. The plant model is presented along with a discussion of the inherent difficulties in such controller development. A sketch of the genetic algorithm (GA) is presented and its strategy as a method of control system design is discussed. Results are presented for two different control systems that have been designed with the genetic algorithm.

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

Optimal Quantum Spatial Search on Random Temporal Networks

NASA Astrophysics Data System (ADS)

Chakraborty, Shantanav; Novo, Leonardo; Di Giorgio, Serena; Omar, Yasser

2017-12-01

To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a network of n nodes constituted by a time-ordered sequence of Erdös-Rényi random graphs G (n ,p ), where p is the probability that any two given nodes are connected: After every time interval τ , a new graph G (n ,p ) replaces the previous one. We prove analytically that, for any given p , there is always a range of values of τ for which the running time of the algorithm is optimal, i.e., O (√{n }), even when search on the individual static graphs constituting the temporal network is suboptimal. On the other hand, there are regimes of τ where the algorithm is suboptimal even when each of the underlying static graphs are sufficiently connected to perform optimal search on them. From this first study of quantum spatial search on a time-dependent network, it emerges that the nontrivial interplay between temporality and connectivity is key to the algorithmic performance. Moreover, our work can be extended to establish high-fidelity qubit transfer between any two nodes of the network. Overall, our findings show that one can exploit temporality to achieve optimal quantum information tasks on dynamical random networks.

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.

Similarity analysis between quantum images

NASA Astrophysics Data System (ADS)

Zhou, Ri-Gui; Liu, XingAo; Zhu, Changming; Wei, Lai; Zhang, Xiafen; Ian, Hou

2018-06-01

Similarity analyses between quantum images are so essential in quantum image processing that it provides fundamental research for the other fields, such as quantum image matching, quantum pattern recognition. In this paper, a quantum scheme based on a novel quantum image representation and quantum amplitude amplification algorithm is proposed. At the end of the paper, three examples and simulation experiments show that the measurement result must be 0 when two images are same, and the measurement result has high probability of being 1 when two images are different.

Fixed node diffusion Monte Carlo using a genetic algorithm: a study of the CO-(4)He(N) complex, N = 1…10.

PubMed

Ramilowski, Jordan A; Farrelly, David

2012-06-14

The diffusion Monte Carlo (DMC) method is a widely used algorithm for computing both ground and excited states of many-particle systems; for states without nodes the algorithm is numerically exact. In the presence of nodes approximations must be introduced, for example, the fixed-node approximation. Recently we have developed a genetic algorithm (GA) based approach which allows the computation of nodal surfaces on-the-fly [Ramilowski and Farrelly, Phys. Chem. Chem. Phys., 2010, 12, 12450]. Here GA-DMC is applied to the computation of rovibrational states of CO-(4)He(N) complexes with N≤ 10. These complexes have been the subject of recent high resolution microwave and millimeter-wave studies which traced the onset of microscopic superfluidity in a doped (4)He droplet, one atom at a time, up to N = 10 [Surin et al., Phys. Rev. Lett., 2008, 101, 233401; Raston et al., Phys. Chem. Chem. Phys., 2010, 12, 8260]. The frequencies of the a-type (microwave) series, which correlate with end-over-end rotation in the CO-(4)He dimer, decrease from N = 1 to 3 and then smoothly increase. This signifies the transition from a molecular complex to a quantum solvated system. The frequencies of the b-type (millimeter-wave) series, which evolves from free rotation of the rigid CO molecule, initially increase from N = 0 to N∼ 6 before starting to decrease with increasing N. An interesting feature of the b-type series, originally observed in the high resolution infra-red (IR) experiments of Tang and McKellar [J. Chem. Phys., 2003, 119, 754] is that, for N = 7, two lines are observed. The GA-DMC algorithm is found to be in good agreement with experimental results and possibly detects the small (∼0.7 cm(-1)) splitting in the b-series line at N = 7. Advantages and disadvantages of GA-DMC are discussed.

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 algorithms for topological and geometric analysis of data

PubMed Central

Lloyd, Seth; Garnerone, Silvano; Zanardi, Paolo

2016-01-01

Extracting useful information from large data sets can be a daunting task. Topological methods for analysing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying topological features and for determining how such features persist as the data is viewed at different scales. Here we present quantum machine learning algorithms for calculating Betti numbers—the numbers of connected components, holes and voids—in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian. The algorithms provide an exponential speed-up over the best currently known classical algorithms for topological data analysis. PMID:26806491

Method for hyperspectral imagery exploitation and pixel spectral unmixing

NASA Technical Reports Server (NTRS)

Lin, Ching-Fang (Inventor)

2003-01-01

An efficiently hybrid approach to exploit hyperspectral imagery and unmix spectral pixels. This hybrid approach uses a genetic algorithm to solve the abundance vector for the first pixel of a hyperspectral image cube. This abundance vector is used as initial state in a robust filter to derive the abundance estimate for the next pixel. By using Kalman filter, the abundance estimate for a pixel can be obtained in one iteration procedure which is much fast than genetic algorithm. The output of the robust filter is fed to genetic algorithm again to derive accurate abundance estimate for the current pixel. The using of robust filter solution as starting point of the genetic algorithm speeds up the evolution of the genetic algorithm. After obtaining the accurate abundance estimate, the procedure goes to next pixel, and uses the output of genetic algorithm as the previous state estimate to derive abundance estimate for this pixel using robust filter. And again use the genetic algorithm to derive accurate abundance estimate efficiently based on the robust filter solution. This iteration continues until pixels in a hyperspectral image cube end.

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

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems

NASA Astrophysics Data System (ADS)

Suwa, Hidemaro

2013-03-01

We have developed novel Monte Carlo methods for precisely calculating quantum spin-boson models and investigated the critical phenomena of the spin-Peierls systems. Three significant methods are presented. The first is a new optimization algorithm of the Markov chain transition kernel based on the geometric weight allocation. This algorithm, for the first time, satisfies the total balance generally without imposing the detailed balance and always minimizes the average rejection rate, being better than the Metropolis algorithm. The second is the extension of the worm (directed-loop) algorithm to non-conserved particles, which cannot be treated efficiently by the conventional methods. The third is the combination with the level spectroscopy. Proposing a new gap estimator, we are successful in eliminating the systematic error of the conventional moment method. Then we have elucidated the phase diagram and the universality class of the one-dimensional XXZ spin-Peierls system. The criticality is totally consistent with the J1 -J2 model, an effective model in the antiadiabatic limit. Through this research, we have succeeded in investigating the critical phenomena of the effectively frustrated quantum spin system by the quantum Monte Carlo method without the negative sign. JSPS Postdoctoral Fellow for Research Abroad

Quantum Adiabatic Algorithms and Large Spin Tunnelling

NASA Technical Reports Server (NTRS)

Boulatov, A.; Smelyanskiy, V. N.

2003-01-01

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

Effect of quantum noise on deterministic remote state preparation of an arbitrary two-particle state via various quantum entangled channels

NASA Astrophysics Data System (ADS)

Qu, Zhiguo; Wu, Shengyao; Wang, Mingming; Sun, Le; Wang, Xiaojun

2017-12-01

As one of important research branches of quantum communication, deterministic remote state preparation (DRSP) plays a significant role in quantum network. Quantum noises are prevalent in quantum communication, and it can seriously affect the safety and reliability of quantum communication system. In this paper, we study the effect of quantum noise on deterministic remote state preparation of an arbitrary two-particle state via different quantum channels including the χ state, Brown state and GHZ state. Firstly, the output states and fidelities of three DRSP algorithms via different quantum entangled channels in four noisy environments, including amplitude-damping, phase-damping, bit-flip and depolarizing noise, are presented, respectively. And then, the effects of noises on three kinds of preparation algorithms in the same noisy environment are discussed. In final, the theoretical analysis proves that the effect of noise in the process of quantum state preparation is only related to the noise type and the size of noise factor and independent of the different entangled quantum channels. Furthermore, another important conclusion is given that the effect of noise is also independent of how to distribute intermediate particles for implementing DRSP through quantum measurement during the concrete preparation process. These conclusions will be very helpful for improving the efficiency and safety of quantum communication in a noisy environment.

On the Critical Behaviour, Crossover Point and Complexity of the Exact Cover Problem

NASA Technical Reports Server (NTRS)

Morris, Robin D.; Smelyanskiy, Vadim N.; Shumow, Daniel; Koga, Dennis (Technical Monitor)

2003-01-01

Research into quantum algorithms for NP-complete problems has rekindled interest in the detailed study a broad class of combinatorial problems. A recent paper applied the quantum adiabatic evolution algorithm to the Exact Cover problem for 3-sets (EC3), and provided an empirical evidence that the algorithm was polynomial. In this paper we provide a detailed study of the characteristics of the exact cover problem. We present the annealing approximation applied to EC3, which gives an over-estimate of the phase transition point. We also identify empirically the phase transition point. We also study the complexity of two classical algorithms on this problem: Davis-Putnam and Simulated Annealing. For these algorithms, EC3 is significantly easier than 3-SAT.

Enabling Computational Nanotechnology through JavaGenes in a Cycle Scavenging Environment

NASA Technical Reports Server (NTRS)

Globus, Al; Menon, Madhu; Srivastava, Deepak; Biegel, Bryan A. (Technical Monitor)

2002-01-01

A genetic algorithm procedure is developed and implemented for fitting parameters for many-body inter-atomic force field functions for simulating nanotechnology atomistic applications using portable Java on cycle-scavenged heterogeneous workstations. Given a physics based analytic functional form for the force field, correlated parameters in a multi-dimensional environment are typically chosen to fit properties given either by experiments and/or by higher accuracy quantum mechanical simulations. The implementation automates this tedious procedure using an evolutionary computing algorithm operating on hundreds of cycle-scavenged computers. As a proof of concept, we demonstrate the procedure for evaluating the Stillinger-Weber (S-W) potential by (a) reproducing the published parameters for Si using S-W energies in the fitness function, and (b) evolving a "new" set of parameters using semi-empirical tightbinding energies in the fitness function. The "new" parameters are significantly better suited for Si cluster energies and forces as compared to even the published S-W potential.

Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

NASA Technical Reports Server (NTRS)

Williams Colin P.

1999-01-01

Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

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.

Genetics-based control of a mimo boiler-turbine plant

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

Dimeo, R.M.; Lee, K.Y.

1994-12-31

A genetic algorithm is used to develop an optimal controller for a non-linear, multi-input/multi-output boiler-turbine plant. The algorithm is used to train a control system for the plant over a wide operating range in an effort to obtain better performance. The results of the genetic algorithm`s controller designed from the linearized plant model at a nominal operating point. Because the genetic algorithm is well-suited to solving traditionally difficult optimization problems it is found that the algorithm is capable of developing the controller based on input/output information only. This controller achieves a performance comparable to the standard linear quadratic regulator.

Improved classification accuracy by feature extraction using genetic algorithms

NASA Astrophysics Data System (ADS)

Patriarche, Julia; Manduca, Armando; Erickson, Bradley J.

2003-05-01

A feature extraction algorithm has been developed for the purposes of improving classification accuracy. The algorithm uses a genetic algorithm / hill-climber hybrid to generate a set of linearly recombined features, which may be of reduced dimensionality compared with the original set. The genetic algorithm performs the global exploration, and a hill climber explores local neighborhoods. Hybridizing the genetic algorithm with a hill climber improves both the rate of convergence, and the final overall cost function value; it also reduces the sensitivity of the genetic algorithm to parameter selection. The genetic algorithm includes the operators: crossover, mutation, and deletion / reactivation - the last of these effects dimensionality reduction. The feature extractor is supervised, and is capable of deriving a separate feature space for each tissue (which are reintegrated during classification). A non-anatomical digital phantom was developed as a gold standard for testing purposes. In tests with the phantom, and with images of multiple sclerosis patients, classification with feature extractor derived features yielded lower error rates than using standard pulse sequences, and with features derived using principal components analysis. Using the multiple sclerosis patient data, the algorithm resulted in a mean 31% reduction in classification error of pure tissues.

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

Quantum Clique Gossiping.

PubMed

Li, Bo; Li, Shuang; Wu, Junfeng; Qi, Hongsheng

2018-02-09

This paper establishes a framework of quantum clique gossiping by introducing local clique operations to networks of interconnected qubits. Cliques are local structures in complex networks being complete subgraphs, which can be used to accelerate classical gossip algorithms. Based on cyclic permutations, clique gossiping leads to collective multi-party qubit interactions. We show that at reduced states, these cliques have the same acceleration effects as their roles in accelerating classical gossip algorithms. For randomized selection of cliques, such improved rate of convergence is precisely characterized. On the other hand, the rate of convergence at the coherent states of the overall quantum network is proven to be decided by the spectrum of a mean-square error evolution matrix. Remarkably, the use of larger quantum cliques does not necessarily increase the speed of the network density aggregation, suggesting quantum network dynamics is not entirely decided by its classical topology.

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.

Deterministic implementations of single-photon multi-qubit Deutsch-Jozsa algorithms with linear optics

NASA Astrophysics Data System (ADS)

Wei, Hai-Rui; Liu, Ji-Zhen

2017-02-01

It is very important to seek an efficient and robust quantum algorithm demanding less quantum resources. We propose one-photon three-qubit original and refined Deutsch-Jozsa algorithms with polarization and two linear momentums degrees of freedom (DOFs). Our schemes are constructed by solely using linear optics. Compared to the traditional ones with one DOF, our schemes are more economic and robust because the necessary photons are reduced from three to one. Our linear-optic schemes are working in a determinate way, and they are feasible with current experimental technology.

Deterministic implementations of single-photon multi-qubit Deutsch–Jozsa algorithms with linear optics

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

Wei, Hai-Rui, E-mail: hrwei@ustb.edu.cn; Liu, Ji-Zhen

2017-02-15

It is very important to seek an efficient and robust quantum algorithm demanding less quantum resources. We propose one-photon three-qubit original and refined Deutsch–Jozsa algorithms with polarization and two linear momentums degrees of freedom (DOFs). Our schemes are constructed by solely using linear optics. Compared to the traditional ones with one DOF, our schemes are more economic and robust because the necessary photons are reduced from three to one. Our linear-optic schemes are working in a determinate way, and they are feasible with current experimental technology.

Study of parameter identification using hybrid neural-genetic algorithm in electro-hydraulic servo system

NASA Astrophysics Data System (ADS)

Moon, Byung-Young

2005-12-01

The hybrid neural-genetic multi-model parameter estimation algorithm was demonstrated. This method can be applied to structured system identification of electro-hydraulic servo system. This algorithms consist of a recurrent incremental credit assignment(ICRA) neural network and a genetic algorithm. The ICRA neural network evaluates each member of a generation of model and genetic algorithm produces new generation of model. To evaluate the proposed method, electro-hydraulic servo system was designed and manufactured. The experiment was carried out to figure out the hybrid neural-genetic multi-model parameter estimation algorithm. As a result, the dynamic characteristics were obtained such as the parameters(mass, damping coefficient, bulk modulus, spring coefficient), which minimize total square error. The result of this study can be applied to hydraulic systems in industrial fields.

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.

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

Comparison of genetic algorithm methods for fuel management optimization

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

DeChaine, M.D.; Feltus, M.A.

1995-12-31

The CIGARO system was developed for genetic algorithm fuel management optimization. Tests are performed to find the best fuel location swap mutation operator probability and to compare genetic algorithm to a truly random search method. Tests showed the fuel swap probability should be between 0% and 10%, and a 50% definitely hampered the optimization. The genetic algorithm performed significantly better than the random search method, which did not even satisfy the peak normalized power constraint.

Training product unit neural networks with genetic algorithms

NASA Technical Reports Server (NTRS)

Janson, D. J.; Frenzel, J. F.; Thelen, D. C.

1991-01-01

The training of product neural networks using genetic algorithms is discussed. Two unusual neural network techniques are combined; product units are employed instead of the traditional summing units and genetic algorithms train the network rather than backpropagation. As an example, a neural netork is trained to calculate the optimum width of transistors in a CMOS switch. It is shown how local minima affect the performance of a genetic algorithm, and one method of overcoming this is presented.

New Results in Astrodynamics Using Genetic Algorithms

NASA Technical Reports Server (NTRS)

Coverstone-Carroll, V.; Hartmann, J. W.; Williams, S. N.; Mason, W. J.

1998-01-01

Generic algorithms have gained popularity as an effective procedure for obtaining solutions to traditionally difficult space mission optimization problems. In this paper, a brief survey of the use of genetic algorithms to solve astrodynamics problems is presented and is followed by new results obtained from applying a Pareto genetic algorithm to the optimization of low-thrust interplanetary spacecraft missions.

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.

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.

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.

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.

Quantum cluster variational method and message passing algorithms revisited

NASA Astrophysics Data System (ADS)

Domínguez, E.; Mulet, Roberto

2018-02-01

We present a general framework to study quantum disordered systems in the context of the Kikuchi's cluster variational method (CVM). The method relies in the solution of message passing-like equations for single instances or in the iterative solution of complex population dynamic algorithms for an average case scenario. We first show how a standard application of the Kikuchi's CVM can be easily translated to message passing equations for specific instances of the disordered system. We then present an "ad hoc" extension of these equations to a population dynamic algorithm representing an average case scenario. At the Bethe level, these equations are equivalent to the dynamic population equations that can be derived from a proper cavity ansatz. However, at the plaquette approximation, the interpretation is more subtle and we discuss it taking also into account previous results in classical disordered models. Moreover, we develop a formalism to properly deal with the average case scenario using a replica-symmetric ansatz within this CVM for quantum disordered systems. Finally, we present and discuss numerical solutions of the different approximations for the quantum transverse Ising model and the quantum random field Ising model in two-dimensional lattices.

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

A System-Level Throughput Model for Quantum Key Distribution

DTIC Science & Technology

2015-09-17

object. In quantum entanglement , the physical properties of particle pairs or groups of particles are correlated – the quantum state of each particle...One-Time Pad Algorithm ............................................................................. 8 Figure 2. Photon Polarization [19...64 Poisson distribution for multi- photon probability (29

Quantum Hamiltonian identification from measurement time traces.

PubMed

Zhang, Jun; Sarovar, Mohan

2014-08-22

Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this Letter, we consider a setting where system evolution is determined by a parametrized Hamiltonian, and the task is to estimate these parameters from temporal records of a restricted set of system observables (time traces). Based on the notion of system realization from linear systems theory, we develop a constructive algorithm that provides estimates of the unknown parameters directly from these time traces. We illustrate the algorithm and its robustness to measurement noise by applying it to a one-dimensional spin chain model with variable couplings.

Nonlinear inversion of potential-field data using a hybrid-encoding genetic algorithm

USGS Publications Warehouse

Chen, C.; Xia, J.; Liu, J.; Feng, G.

2006-01-01

Using a genetic algorithm to solve an inverse problem of complex nonlinear geophysical equations is advantageous because it does not require computer gradients of models or "good" initial models. The multi-point search of a genetic algorithm makes it easier to find the globally optimal solution while avoiding falling into a local extremum. As is the case in other optimization approaches, the search efficiency for a genetic algorithm is vital in finding desired solutions successfully in a multi-dimensional model space. A binary-encoding genetic algorithm is hardly ever used to resolve an optimization problem such as a simple geophysical inversion with only three unknowns. The encoding mechanism, genetic operators, and population size of the genetic algorithm greatly affect search processes in the evolution. It is clear that improved operators and proper population size promote the convergence. Nevertheless, not all genetic operations perform perfectly while searching under either a uniform binary or a decimal encoding system. With the binary encoding mechanism, the crossover scheme may produce more new individuals than with the decimal encoding. On the other hand, the mutation scheme in a decimal encoding system will create new genes larger in scope than those in the binary encoding. This paper discusses approaches of exploiting the search potential of genetic operations in the two encoding systems and presents an approach with a hybrid-encoding mechanism, multi-point crossover, and dynamic population size for geophysical inversion. We present a method that is based on the routine in which the mutation operation is conducted in the decimal code and multi-point crossover operation in the binary code. The mix-encoding algorithm is called the hybrid-encoding genetic algorithm (HEGA). HEGA provides better genes with a higher probability by a mutation operator and improves genetic algorithms in resolving complicated geophysical inverse problems. Another significant result is that final solution is determined by the average model derived from multiple trials instead of one computation due to the randomness in a genetic algorithm procedure. These advantages were demonstrated by synthetic and real-world examples of inversion of potential-field data. ?? 2005 Elsevier Ltd. All rights reserved.

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).

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).

Aerodynamic Optimization of a Supersonic Bending Body Projectile by a Vector-Evaluated Genetic Algorithm

DTIC Science & Technology

2016-12-01

Evaluated Genetic Algorithm prepared by Justin L Paul Academy of Applied Science 24 Warren Street Concord, NH 03301 under contract W911SR...Supersonic Bending Body Projectile by a Vector-Evaluated Genetic Algorithm prepared by Justin L Paul Academy of Applied Science 24 Warren Street... Genetic Algorithm 5a. CONTRACT NUMBER W199SR-15-2-001 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Justin L Paul 5d. PROJECT

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.

Nonlinear dynamics optimization with particle swarm and genetic algorithms for SPEAR3 emittance upgrade

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

Huang, Xiaobiao; Safranek, James

2014-09-01

Nonlinear dynamics optimization is carried out for a low emittance upgrade lattice of SPEAR3 in order to improve its dynamic aperture and Touschek lifetime. Two multi-objective optimization algorithms, a genetic algorithm and a particle swarm algorithm, are used for this study. The performance of the two algorithms are compared. The result shows that the particle swarm algorithm converges significantly faster to similar or better solutions than the genetic algorithm and it does not require seeding of good solutions in the initial population. These advantages of the particle swarm algorithm may make it more suitable for many accelerator optimization applications.

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

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.

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

Genetic Algorithm for Initial Orbit Determination with Too Short Arc (Continued)

NASA Astrophysics Data System (ADS)

Li, X. R.; Wang, X.

2016-03-01

When using the genetic algorithm to solve the problem of too-short-arc (TSA) determination, due to the difference of computing processes between the genetic algorithm and classical method, the methods for outliers editing are no longer applicable. In the genetic algorithm, the robust estimation is acquired by means of using different loss functions in the fitness function, then the outlier problem of TSAs is solved. Compared with the classical method, the application of loss functions in the genetic algorithm is greatly simplified. Through the comparison of results of different loss functions, it is clear that the methods of least median square and least trimmed square can greatly improve the robustness of TSAs, and have a high breakdown point.

Bio-Inspired Genetic Algorithms with Formalized Crossover Operators for Robotic Applications.

PubMed

Zhang, Jie; Kang, Man; Li, Xiaojuan; Liu, Geng-Yang

2017-01-01

Genetic algorithms are widely adopted to solve optimization problems in robotic applications. In such safety-critical systems, it is vitally important to formally prove the correctness when genetic algorithms are applied. This paper focuses on formal modeling of crossover operations that are one of most important operations in genetic algorithms. Specially, we for the first time formalize crossover operations with higher-order logic based on HOL4 that is easy to be deployed with its user-friendly programing environment. With correctness-guaranteed formalized crossover operations, we can safely apply them in robotic applications. We implement our technique to solve a path planning problem using a genetic algorithm with our formalized crossover operations, and the results show the effectiveness of our technique.

High performance reconciliation for continuous-variable quantum key distribution with LDPC code

NASA Astrophysics Data System (ADS)

Lin, Dakai; Huang, Duan; Huang, Peng; Peng, Jinye; Zeng, Guihua

2015-03-01

Reconciliation is a significant procedure in a continuous-variable quantum key distribution (CV-QKD) system. It is employed to extract secure secret key from the resulted string through quantum channel between two users. However, the efficiency and the speed of previous reconciliation algorithms are low. These problems limit the secure communication distance and the secure key rate of CV-QKD systems. In this paper, we proposed a high-speed reconciliation algorithm through employing a well-structured decoding scheme based on low density parity-check (LDPC) code. The complexity of the proposed algorithm is reduced obviously. By using a graphics processing unit (GPU) device, our method may reach a reconciliation speed of 25 Mb/s for a CV-QKD system, which is currently the highest level and paves the way to high-speed CV-QKD.

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.

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.

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.

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.

Oversimplifying quantum factoring.

PubMed

Smolin, John A; Smith, Graeme; Vargo, Alexander

2013-07-11

Shor's quantum factoring algorithm exponentially outperforms known classical methods. Previous experimental implementations have used simplifications dependent on knowing the factors in advance. However, as we show here, all composite numbers admit simplification of the algorithm to a circuit equivalent to flipping coins. The difficulty of a particular experiment therefore depends on the level of simplification chosen, not the size of the number factored. Valid implementations should not make use of the answer sought.

On the degree conjecture for separability of multipartite quantum states

NASA Astrophysics Data System (ADS)

Hassan, Ali Saif M.; Joag, Pramod S.

2008-01-01

We settle the so-called degree conjecture for the separability of multipartite quantum states, which are normalized graph Laplacians, first given by Braunstein et al. [Phys. Rev. A 73, 012320 (2006)]. The conjecture states that a multipartite quantum state is separable if and only if the degree matrix of the graph associated with the state is equal to the degree matrix of the partial transpose of this graph. We call this statement to be the strong form of the conjecture. In its weak version, the conjecture requires only the necessity, that is, if the state is separable, the corresponding degree matrices match. We prove the strong form of the conjecture for pure multipartite quantum states using the modified tensor product of graphs defined by Hassan and Joag [J. Phys. A 40, 10251 (2007)], as both necessary and sufficient condition for separability. Based on this proof, we give a polynomial-time algorithm for completely factorizing any pure multipartite quantum state. By polynomial-time algorithm, we mean that the execution time of this algorithm increases as a polynomial in m, where m is the number of parts of the quantum system. We give a counterexample to show that the conjecture fails, in general, even in its weak form, for multipartite mixed states. Finally, we prove this conjecture, in its weak form, for a class of multipartite mixed states, giving only a necessary condition for separability.

Determination of composition of non-homogeneous GaInNAs layers

NASA Astrophysics Data System (ADS)

Pucicki, D.; Bielak, K.; Ściana, B.; Radziewicz, D.; Latkowska-Baranowska, M.; Kováč, J.; Vincze, A.; Tłaczała, M.

2016-01-01

Dilute nitride GaInNAs alloys grown on GaAs have become perspective materials for so called low-cost GaAs-based devices working within the optical wavelength range up to 1.6 μm. The multilayer structures of GaInNAs/GaAs multi-quantum well (MQW) samples usually are analyzed by using high resolution X-ray diffraction (HRXRD) measurements. However, demands for precise structural characterization of the GaInNAs containing heterostructures requires taking into consideration all inhomogeneities of such structures. This paper describes some of the material challenges and progress in structural characterization of GaInNAs layers. A new algorithm for structural characterization of dilute nitrides which bounds contactless electro-reflectance (CER) or photo-reflectance (PR) measurements and HRXRD analysis results together with GaInNAs quantum well band diagram calculation is presented. The triple quantum well (3QW) GaInNAs/GaAs structures grown by atmospheric-pressure metalorganic vapor-phase epitaxy (AP-MOVPE) were investigated according to the proposed algorithm. Thanks to presented algorithm, more precise structural data including the nonuniformity in the growth direction of GaInNAs/GaAs QWs were achieved. Therefore, the proposed algorithm is mentioned as a nondestructive method for characterization of multicomponent inhomogeneous semiconductor structures with quantum wells.

Estimating the solute transport parameters of the spatial fractional advection-dispersion equation using Bees Algorithm

NASA Astrophysics Data System (ADS)

Mehdinejadiani, Behrouz

2017-08-01

This study represents the first attempt to estimate the solute transport parameters of the spatial fractional advection-dispersion equation using Bees Algorithm. The numerical studies as well as the experimental studies were performed to certify the integrity of Bees Algorithm. The experimental ones were conducted in a sandbox for homogeneous and heterogeneous soils. A detailed comparative study was carried out between the results obtained from Bees Algorithm and those from Genetic Algorithm and LSQNONLIN routines in FracFit toolbox. The results indicated that, in general, the Bees Algorithm much more accurately appraised the sFADE parameters in comparison with Genetic Algorithm and LSQNONLIN, especially in the heterogeneous soil and for α values near to 1 in the numerical study. Also, the results obtained from Bees Algorithm were more reliable than those from Genetic Algorithm. The Bees Algorithm showed the relative similar performances for all cases, while the Genetic Algorithm and the LSQNONLIN yielded different performances for various cases. The performance of LSQNONLIN strongly depends on the initial guess values so that, compared to the Genetic Algorithm, it can more accurately estimate the sFADE parameters by taking into consideration the suitable initial guess values. To sum up, the Bees Algorithm was found to be very simple, robust and accurate approach to estimate the transport parameters of the spatial fractional advection-dispersion equation.

Estimating the solute transport parameters of the spatial fractional advection-dispersion equation using Bees Algorithm.

PubMed

Mehdinejadiani, Behrouz

2017-08-01

This study represents the first attempt to estimate the solute transport parameters of the spatial fractional advection-dispersion equation using Bees Algorithm. The numerical studies as well as the experimental studies were performed to certify the integrity of Bees Algorithm. The experimental ones were conducted in a sandbox for homogeneous and heterogeneous soils. A detailed comparative study was carried out between the results obtained from Bees Algorithm and those from Genetic Algorithm and LSQNONLIN routines in FracFit toolbox. The results indicated that, in general, the Bees Algorithm much more accurately appraised the sFADE parameters in comparison with Genetic Algorithm and LSQNONLIN, especially in the heterogeneous soil and for α values near to 1 in the numerical study. Also, the results obtained from Bees Algorithm were more reliable than those from Genetic Algorithm. The Bees Algorithm showed the relative similar performances for all cases, while the Genetic Algorithm and the LSQNONLIN yielded different performances for various cases. The performance of LSQNONLIN strongly depends on the initial guess values so that, compared to the Genetic Algorithm, it can more accurately estimate the sFADE parameters by taking into consideration the suitable initial guess values. To sum up, the Bees Algorithm was found to be very simple, robust and accurate approach to estimate the transport parameters of the spatial fractional advection-dispersion equation. Copyright © 2017 Elsevier B.V. All rights reserved.

Generalized Grover's Algorithm for Multiple Phase Inversion States

NASA Astrophysics Data System (ADS)

Byrnes, Tim; Forster, Gary; Tessler, Louis

2018-02-01

Grover's algorithm is a quantum search algorithm that proceeds by repeated applications of the Grover operator and the Oracle until the state evolves to one of the target states. In the standard version of the algorithm, the Grover operator inverts the sign on only one state. Here we provide an exact solution to the problem of performing Grover's search where the Grover operator inverts the sign on N states. We show the underlying structure in terms of the eigenspectrum of the generalized Hamiltonian, and derive an appropriate initial state to perform the Grover evolution. This allows us to use the quantum phase estimation algorithm to solve the search problem in this generalized case, completely bypassing the Grover algorithm altogether. We obtain a time complexity of this case of √{D /Mα }, where D is the search space dimension, M is the number of target states, and α ≈1 , which is close to the optimal scaling.

Initial state-specific photodissociation dynamics of pyrrole via 1 π σ ∗/ S 0 conical intersection initiated with optimally controlled UV-laser pulses

NASA Astrophysics Data System (ADS)

Nandipati, K. R.; Kanakati, Arun Kumar; Singh, H.; Lan, Z.; Mahapatra, S.

2017-09-01

Optimal initiation of quantum dynamics of N-H photodissociation of pyrrole on the S0-1πσ∗(1A2) coupled electronic states by UV-laser pulses in an effort to guide the subsequent dynamics to dissociation limits is studied theoretically. Specifically, the task of designing optimal laser pulses that act on initial vibrational states of the system for an effective UV-photodissociation is considered by employing optimal control theory. The associated control mechanism(s) for the initial state dependent photodissociation dynamics of pyrrole in the presence of control pulses is examined and discussed in detail. The initial conditions determine implicitly the variation in the dissociation probabilities for the two channels, upon interaction with the field. The optimal pulse corresponds to the objective fixed as maximization of overall reactive flux subject to constraints of reasonable fluence and quantum dynamics. The simple optimal pulses obtained by the use of genetic algorithm based optimization are worth an experimental implementation given the experimental relevance of πσ∗-photochemistry in recent times.

A Test of Genetic Algorithms in Relevance Feedback.

ERIC Educational Resources Information Center

Lopez-Pujalte, Cristina; Guerrero Bote, Vicente P.; Moya Anegon, Felix de

2002-01-01

Discussion of information retrieval, query optimization techniques, and relevance feedback focuses on genetic algorithms, which are derived from artificial intelligence techniques. Describes an evaluation of different genetic algorithms using a residual collection method and compares results with the Ide dec-hi method (Salton and Buckley, 1990…

Transonic Wing Shape Optimization Using a Genetic Algorithm

NASA Technical Reports Server (NTRS)

Holst, Terry L.; Pulliam, Thomas H.; Kwak, Dochan (Technical Monitor)

2002-01-01

A method for aerodynamic shape optimization based on a genetic algorithm approach is demonstrated. The algorithm is coupled with a transonic full potential flow solver and is used to optimize the flow about transonic wings including multi-objective solutions that lead to the generation of pareto fronts. The results indicate that the genetic algorithm is easy to implement, flexible in application and extremely reliable.

Portfolio optimization by using linear programing models based on genetic algorithm

NASA Astrophysics Data System (ADS)

Sukono; Hidayat, Y.; Lesmana, E.; Putra, A. S.; Napitupulu, H.; Supian, S.

2018-01-01

In this paper, we discussed the investment portfolio optimization using linear programming model based on genetic algorithms. It is assumed that the portfolio risk is measured by absolute standard deviation, and each investor has a risk tolerance on the investment portfolio. To complete the investment portfolio optimization problem, the issue is arranged into a linear programming model. Furthermore, determination of the optimum solution for linear programming is done by using a genetic algorithm. As a numerical illustration, we analyze some of the stocks traded on the capital market in Indonesia. Based on the analysis, it is shown that the portfolio optimization performed by genetic algorithm approach produces more optimal efficient portfolio, compared to the portfolio optimization performed by a linear programming algorithm approach. Therefore, genetic algorithms can be considered as an alternative on determining the investment portfolio optimization, particularly using linear programming models.

An improved genetic algorithm and its application in the TSP problem

NASA Astrophysics Data System (ADS)

Li, Zheng; Qin, Jinlei

2011-12-01

Concept and research actuality of genetic algorithm are introduced in detail in the paper. Under this condition, the simple genetic algorithm and an improved algorithm are described and applied in an example of TSP problem, where the advantage of genetic algorithm is adequately shown in solving the NP-hard problem. In addition, based on partial matching crossover operator, the crossover operator method is improved into extended crossover operator in order to advance the efficiency when solving the TSP. In the extended crossover method, crossover operator can be performed between random positions of two random individuals, which will not be restricted by the position of chromosome. Finally, the nine-city TSP is solved using the improved genetic algorithm with extended crossover method, the efficiency of whose solution process is much higher, besides, the solving speed of the optimal solution is much faster.

Solving TSP problem with improved genetic algorithm

NASA Astrophysics Data System (ADS)

Fu, Chunhua; Zhang, Lijun; Wang, Xiaojing; Qiao, Liying

2018-05-01

The TSP is a typical NP problem. The optimization of vehicle routing problem (VRP) and city pipeline optimization can use TSP to solve; therefore it is very important to the optimization for solving TSP problem. The genetic algorithm (GA) is one of ideal methods in solving it. The standard genetic algorithm has some limitations. Improving the selection operator of genetic algorithm, and importing elite retention strategy can ensure the select operation of quality, In mutation operation, using the adaptive algorithm selection can improve the quality of search results and variation, after the chromosome evolved one-way evolution reverse operation is added which can make the offspring inherit gene of parental quality improvement opportunities, and improve the ability of searching the optimal solution algorithm.

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

Genetic algorithm based fuzzy control of spacecraft autonomous rendezvous

NASA Technical Reports Server (NTRS)

Karr, C. L.; Freeman, L. M.; Meredith, D. L.

1990-01-01

The U.S. Bureau of Mines is currently investigating ways to combine the control capabilities of fuzzy logic with the learning capabilities of genetic algorithms. Fuzzy logic allows for the uncertainty inherent in most control problems to be incorporated into conventional expert systems. Although fuzzy logic based expert systems have been used successfully for controlling a number of physical systems, the selection of acceptable fuzzy membership functions has generally been a subjective decision. High performance fuzzy membership functions for a fuzzy logic controller that manipulates a mathematical model simulating the autonomous rendezvous of spacecraft are learned using a genetic algorithm, a search technique based on the mechanics of natural genetics. The membership functions learned by the genetic algorithm provide for a more efficient fuzzy logic controller than membership functions selected by the authors for the rendezvous problem. Thus, genetic algorithms are potentially an effective and structured approach for learning fuzzy membership functions.

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.

Tree tensor network approach to simulating Shor's algorithm

NASA Astrophysics Data System (ADS)

Dumitrescu, Eugene

2017-12-01

Constructively simulating quantum systems furthers our understanding of qualitative and quantitative features which may be analytically intractable. In this paper, we directly simulate and explore the entanglement structure present in the paradigmatic example for exponential quantum speedups: Shor's algorithm. To perform our simulation, we construct a dynamic tree tensor network which manifestly captures two salient circuit features for modular exponentiation. These are the natural two-register bipartition and the invariance of entanglement with respect to permutations of the top-register qubits. Our construction help identify the entanglement entropy properties, which we summarize by a scaling relation. Further, the tree network is efficiently projected onto a matrix product state from which we efficiently execute the quantum Fourier transform. Future simulation of quantum information states with tensor networks exploiting circuit symmetries is discussed.

Quantum paradoxes, entanglement and their explanation on the basis of quantization of fields

NASA Astrophysics Data System (ADS)

Melkikh, A. V.

2017-01-01

Quantum entanglement is discussed as a consequence of the quantization of fields. The inclusion of quantum fields self-consistently explains some quantum paradoxes (EPR and Hardy’s paradox). The definition of entanglement was introduced, which depends on the maximum energy of the interaction of particles. The destruction of entanglement is caused by the creation and annihilation of particles. On this basis, an algorithm for quantum particle evolution was formulated.

Fault-tolerant composite Householder reflection

NASA Astrophysics Data System (ADS)

Torosov, Boyan T.; Kyoseva, Elica; Vitanov, Nikolay V.

2015-07-01

We propose a fault-tolerant implementation of the quantum Householder reflection, which is a key operation in various quantum algorithms, quantum-state engineering, generation of arbitrary unitaries, and entanglement characterization. We construct this operation using the modular approach of composite pulses and a relation between the Householder reflection and the quantum phase gate. The proposed implementation is highly insensitive to variations in the experimental parameters, which makes it suitable for high-fidelity quantum information processing.

A "Hands on" Strategy for Teaching Genetic Algorithms to Undergraduates

ERIC Educational Resources Information Center

Venables, Anne; Tan, Grace

2007-01-01

Genetic algorithms (GAs) are a problem solving strategy that uses stochastic search. Since their introduction (Holland, 1975), GAs have proven to be particularly useful for solving problems that are "intractable" using classical methods. The language of genetic algorithms (GAs) is heavily laced with biological metaphors from evolutionary…

The potential of genetic algorithms for conceptual design of rotor systems

NASA Technical Reports Server (NTRS)

Crossley, William A.; Wells, Valana L.; Laananen, David H.

1993-01-01

The capabilities of genetic algorithms as a non-calculus based, global search method make them potentially useful in the conceptual design of rotor systems. Coupling reasonably simple analysis tools to the genetic algorithm was accomplished, and the resulting program was used to generate designs for rotor systems to match requirements similar to those of both an existing helicopter and a proposed helicopter design. This provides a comparison with the existing design and also provides insight into the potential of genetic algorithms in design of new rotors.

Genetic Algorithm for Initial Orbit Determination with Too Short Arc (Continued)

NASA Astrophysics Data System (ADS)

Li, Xin-ran; Wang, Xin

2017-04-01

When the genetic algorithm is used to solve the problem of too short-arc (TSA) orbit determination, due to the difference of computing process between the genetic algorithm and the classical method, the original method for outlier deletion is no longer applicable. In the genetic algorithm, the robust estimation is realized by introducing different loss functions for the fitness function, then the outlier problem of the TSA orbit determination is solved. Compared with the classical method, the genetic algorithm is greatly simplified by introducing in different loss functions. Through the comparison on the calculations of multiple loss functions, it is found that the least median square (LMS) estimation and least trimmed square (LTS) estimation can greatly improve the robustness of the TSA orbit determination, and have a high breakdown point.

A Genetic Algorithm Tool (splicer) for Complex Scheduling Problems and the Space Station Freedom Resupply Problem

NASA Technical Reports Server (NTRS)

Wang, Lui; Valenzuela-Rendon, Manuel

1993-01-01

The Space Station Freedom will require the supply of items in a regular fashion. A schedule for the delivery of these items is not easy to design due to the large span of time involved and the possibility of cancellations and changes in shuttle flights. This paper presents the basic concepts of a genetic algorithm model, and also presents the results of an effort to apply genetic algorithms to the design of propellant resupply schedules. As part of this effort, a simple simulator and an encoding by which a genetic algorithm can find near optimal schedules have been developed. Additionally, this paper proposes ways in which robust schedules, i.e., schedules that can tolerate small changes, can be found using genetic algorithms.

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.

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.

Grover's unstructured search by using a transverse field

NASA Astrophysics Data System (ADS)

Jiang, Zhang; Rieffel, Eleanor; Wang, Zhihui

2017-04-01

We design a circuit-based quantum algorithm to search for a needle in a haystack, giving the same quadratic speedup achieved by Grover's original algorithm. In our circuit-based algorithm, the problem Hamiltonian (oracle) and a transverse field (instead of Grover's diffusion operator) are applied to the system alternatively. We construct a periodic time sequence such that the resultant unitary drives a closed transition between two states, which have high degrees of overlap with the initial state (even superposition of all states) and the target state, respectively. Let N =2n be the size of the search space. The transition rate in our algorithm is of order Θ(1 /√{ N}) , and the overlaps are of order Θ(1) , yielding a nearly optimal query complexity of T =√{ N}(π / 2√{ 2}) . Our algorithm is inspired by a class of algorithms proposed by Farhi et al., namely the Quantum Approximate Optimization Algorithm (QAOA); our method offers a route to optimizing the parameters in QAOA by restricting them to be periodic in time.

Objects of consciousness

PubMed Central

Hoffman, Donald D.; Prakash, Chetan

2014-01-01

Current models of visual perception typically assume that human vision estimates true properties of physical objects, properties that exist even if unperceived. However, recent studies of perceptual evolution, using evolutionary games and genetic algorithms, reveal that natural selection often drives true perceptions to extinction when they compete with perceptions tuned to fitness rather than truth: Perception guides adaptive behavior; it does not estimate a preexisting physical truth. Moreover, shifting from evolutionary biology to quantum physics, there is reason to disbelieve in preexisting physical truths: Certain interpretations of quantum theory deny that dynamical properties of physical objects have definite values when unobserved. In some of these interpretations the observer is fundamental, and wave functions are compendia of subjective probabilities, not preexisting elements of physical reality. These two considerations, from evolutionary biology and quantum physics, suggest that current models of object perception require fundamental reformulation. Here we begin such a reformulation, starting with a formal model of consciousness that we call a “conscious agent.” We develop the dynamics of interacting conscious agents, and study how the perception of objects and space-time can emerge from such dynamics. We show that one particular object, the quantum free particle, has a wave function that is identical in form to the harmonic functions that characterize the asymptotic dynamics of conscious agents; particles are vibrations not of strings but of interacting conscious agents. This allows us to reinterpret physical properties such as position, momentum, and energy as properties of interacting conscious agents, rather than as preexisting physical truths. We sketch how this approach might extend to the perception of relativistic quantum objects, and to classical objects of macroscopic scale. PMID:24987382

An Improved Heuristic Method for Subgraph Isomorphism Problem

NASA Astrophysics Data System (ADS)

Xiang, Yingzhuo; Han, Jiesi; Xu, Haijiang; Guo, Xin

2017-09-01

This paper focus on the subgraph isomorphism (SI) problem. We present an improved genetic algorithm, a heuristic method to search the optimal solution. The contribution of this paper is that we design a dedicated crossover algorithm and a new fitness function to measure the evolution process. Experiments show our improved genetic algorithm performs better than other heuristic methods. For a large graph, such as a subgraph of 40 nodes, our algorithm outperforms the traditional tree search algorithms. We find that the performance of our improved genetic algorithm does not decrease as the number of nodes in prototype graphs.

Conceptual versus Algorithmic Learning in High School Chemistry: The Case of Basic Quantum Chemical Concepts--Part 1. Statistical Analysis of a Quantitative Study

ERIC Educational Resources Information Center

Papaphotis, Georgios; Tsaparlis, Georgios

2008-01-01

Part 1 of the findings are presented of a quantitative study (n = 125) on basic quantum chemical concepts taught in the twelfth grade (age 17-18 years) in Greece. A paper-and-pencil test of fourteen questions was used. The study compared performance in five questions that tested recall of knowledge or application of algorithmic procedures (type-A…

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

25 MHz clock continuous-variable quantum key distribution system over 50 km fiber channel

PubMed Central

Wang, Chao; Huang, Duan; Huang, Peng; Lin, Dakai; Peng, Jinye; Zeng, Guihua

2015-01-01

In this paper, a practical continuous-variable quantum key distribution system is developed and it runs in the real-world conditions with 25 MHz clock rate. To reach high-rate, we have employed a homodyne detector with maximal bandwidth to 300 MHz and an optimal high-efficiency error reconciliation algorithm with processing speed up to 25 Mbps. To optimize the stability of the system, several key techniques are developed, which include a novel phase compensation algorithm, a polarization feedback algorithm, and related stability method on the modulators. Practically, our system is tested for more than 12 hours with a final secret key rate of 52 kbps over 50 km transmission distance, which is the highest rate so far in such distance. Our system may pave the road for practical broadband secure quantum communication with continuous variables in the commercial conditions. PMID:26419413

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.

Tartarus: A relativistic Green's function quantum average atom code

DOE PAGES

Gill, Nathanael Matthew; Starrett, Charles Edward

2017-06-28

A relativistic Green’s Function quantum average atom model is implemented in the Tartarus code for the calculation of equation of state data in dense plasmas. We first present the relativistic extension of the quantum Green’s Function average atom model described by Starrett [1]. The Green’s Function approach addresses the numerical challenges arising from resonances in the continuum density of states without the need for resonance tracking algorithms or adaptive meshes, though there are still numerical challenges inherent to this algorithm. We discuss how these challenges are addressed in the Tartarus algorithm. The outputs of the calculation are shown in comparisonmore » to PIMC/DFT-MD simulations of the Principal Shock Hugoniot in Silicon. Finally, we also present the calculation of the Hugoniot for Silver coming from both the relativistic and nonrelativistic modes of the Tartarus code.« less

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.

Transitionless driving on adiabatic search algorithm

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

Oh, Sangchul, E-mail: soh@qf.org.qa; Kais, Sabre, E-mail: kais@purdue.edu; Department of Chemistry, Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907

We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian,more » approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.« less

Tartarus: A relativistic Green's function quantum average atom code

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

Gill, Nathanael Matthew; Starrett, Charles Edward

A relativistic Green’s Function quantum average atom model is implemented in the Tartarus code for the calculation of equation of state data in dense plasmas. We first present the relativistic extension of the quantum Green’s Function average atom model described by Starrett [1]. The Green’s Function approach addresses the numerical challenges arising from resonances in the continuum density of states without the need for resonance tracking algorithms or adaptive meshes, though there are still numerical challenges inherent to this algorithm. We discuss how these challenges are addressed in the Tartarus algorithm. The outputs of the calculation are shown in comparisonmore » to PIMC/DFT-MD simulations of the Principal Shock Hugoniot in Silicon. Finally, we also present the calculation of the Hugoniot for Silver coming from both the relativistic and nonrelativistic modes of the Tartarus code.« less

25 MHz clock continuous-variable quantum key distribution system over 50 km fiber channel.

PubMed

Wang, Chao; Huang, Duan; Huang, Peng; Lin, Dakai; Peng, Jinye; Zeng, Guihua

2015-09-30

In this paper, a practical continuous-variable quantum key distribution system is developed and it runs in the real-world conditions with 25 MHz clock rate. To reach high-rate, we have employed a homodyne detector with maximal bandwidth to 300 MHz and an optimal high-efficiency error reconciliation algorithm with processing speed up to 25 Mbps. To optimize the stability of the system, several key techniques are developed, which include a novel phase compensation algorithm, a polarization feedback algorithm, and related stability method on the modulators. Practically, our system is tested for more than 12 hours with a final secret key rate of 52 kbps over 50 km transmission distance, which is the highest rate so far in such distance. Our system may pave the road for practical broadband secure quantum communication with continuous variables in the commercial conditions.

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.

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.

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.

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

Genetic algorithms for adaptive real-time control in space systems

NASA Technical Reports Server (NTRS)

Vanderzijp, J.; Choudry, A.

1988-01-01

Genetic Algorithms that are used for learning as one way to control the combinational explosion associated with the generation of new rules are discussed. The Genetic Algorithm approach tends to work best when it can be applied to a domain independent knowledge representation. Applications to real time control in space systems are discussed.

Cognitive Nonlinear Radar

DTIC Science & Technology

2013-01-01

intelligently selecting waveform parameters using adaptive algorithms. The adaptive algorithms optimize the waveform parameters based on (1) the EM...the environment. 15. SUBJECT TERMS cognitive radar, adaptive sensing, spectrum sensing, multi-objective optimization, genetic algorithms, machine...detection and classification block diagram. .........................................................6 Figure 5. Genetic algorithm block diagram

A Quantum Proxy Blind Signature Scheme Based on Genuine Five-Qubit Entangled State

NASA Astrophysics Data System (ADS)

Zeng, Chuan; Zhang, Jian-Zhong; Xie, Shu-Cui

2017-06-01

In this paper, a quantum proxy blind signature scheme based on controlled quantum teleportation is proposed. This scheme uses a genuine five-qubit entangled state as quantum channel and adopts the classical Vernam algorithm to blind message. We use the physical characteristics of quantum mechanics to implement delegation, signature and verification. Security analysis shows that our scheme is valid and satisfy the properties of a proxy blind signature, such as blindness, verifiability, unforgeability, undeniability.

On the robustness of bucket brigade quantum RAM

NASA Astrophysics Data System (ADS)

Arunachalam, Srinivasan; Gheorghiu, Vlad; Jochym-O'Connor, Tomas; Mosca, Michele; Varshinee Srinivasan, Priyaa

2015-12-01

We study the robustness of the bucket brigade quantum random access memory model introduced by Giovannetti et al (2008 Phys. Rev. Lett.100 160501). Due to a result of Regev and Schiff (ICALP ’08 733), we show that for a class of error models the error rate per gate in the bucket brigade quantum memory has to be of order o({2}-n/2) (where N={2}n is the size of the memory) whenever the memory is used as an oracle for the quantum searching problem. We conjecture that this is the case for any realistic error model that will be encountered in practice, and that for algorithms with super-polynomially many oracle queries the error rate must be super-polynomially small, which further motivates the need for quantum error correction. By contrast, for algorithms such as matrix inversion Harrow et al (2009 Phys. Rev. Lett.103 150502) or quantum machine learning Rebentrost et al (2014 Phys. Rev. Lett.113 130503) that only require a polynomial number of queries, the error rate only needs to be polynomially small and quantum error correction may not be required. We introduce a circuit model for the quantum bucket brigade architecture and argue that quantum error correction for the circuit causes the quantum bucket brigade architecture to lose its primary advantage of a small number of ‘active’ gates, since all components have to be actively error corrected.

Warehouse stocking optimization based on dynamic ant colony genetic algorithm

NASA Astrophysics Data System (ADS)

Xiao, Xiaoxu

2018-04-01

In view of the various orders of FAW (First Automotive Works) International Logistics Co., Ltd., the SLP method is used to optimize the layout of the warehousing units in the enterprise, thus the warehouse logistics is optimized and the external processing speed of the order is improved. In addition, the relevant intelligent algorithms for optimizing the stocking route problem are analyzed. The ant colony algorithm and genetic algorithm which have good applicability are emphatically studied. The parameters of ant colony algorithm are optimized by genetic algorithm, which improves the performance of ant colony algorithm. A typical path optimization problem model is taken as an example to prove the effectiveness of parameter optimization.

A controlled genetic algorithm by fuzzy logic and belief functions for job-shop scheduling.

PubMed

Hajri, S; Liouane, N; Hammadi, S; Borne, P

2000-01-01

Most scheduling problems are highly complex combinatorial problems. However, stochastic methods such as genetic algorithm yield good solutions. In this paper, we present a controlled genetic algorithm (CGA) based on fuzzy logic and belief functions to solve job-shop scheduling problems. For better performance, we propose an efficient representational scheme, heuristic rules for creating the initial population, and a new methodology for mixing and computing genetic operator probabilities.

Experimental Performance of a Genetic Algorithm for Airborne Strategic Conflict Resolution

NASA Technical Reports Server (NTRS)

Karr, David A.; Vivona, Robert A.; Roscoe, David A.; DePascale, Stephen M.; Consiglio, Maria

2009-01-01

The Autonomous Operations Planner, a research prototype flight-deck decision support tool to enable airborne self-separation, uses a pattern-based genetic algorithm to resolve predicted conflicts between the ownship and traffic aircraft. Conflicts are resolved by modifying the active route within the ownship s flight management system according to a predefined set of maneuver pattern templates. The performance of this pattern-based genetic algorithm was evaluated in the context of batch-mode Monte Carlo simulations running over 3600 flight hours of autonomous aircraft in en-route airspace under conditions ranging from typical current traffic densities to several times that level. Encountering over 8900 conflicts during two simulation experiments, the genetic algorithm was able to resolve all but three conflicts, while maintaining a required time of arrival constraint for most aircraft. Actual elapsed running time for the algorithm was consistent with conflict resolution in real time. The paper presents details of the genetic algorithm s design, along with mathematical models of the algorithm s performance and observations regarding the effectiveness of using complimentary maneuver patterns when multiple resolutions by the same aircraft were required.

Experimental Performance of a Genetic Algorithm for Airborne Strategic Conflict Resolution

NASA Technical Reports Server (NTRS)

Karr, David A.; Vivona, Robert A.; Roscoe, David A.; DePascale, Stephen M.; Consiglio, Maria

2009-01-01

The Autonomous Operations Planner, a research prototype flight-deck decision support tool to enable airborne self-separation, uses a pattern-based genetic algorithm to resolve predicted conflicts between the ownship and traffic aircraft. Conflicts are resolved by modifying the active route within the ownship's flight management system according to a predefined set of maneuver pattern templates. The performance of this pattern-based genetic algorithm was evaluated in the context of batch-mode Monte Carlo simulations running over 3600 flight hours of autonomous aircraft in en-route airspace under conditions ranging from typical current traffic densities to several times that level. Encountering over 8900 conflicts during two simulation experiments, the genetic algorithm was able to resolve all but three conflicts, while maintaining a required time of arrival constraint for most aircraft. Actual elapsed running time for the algorithm was consistent with conflict resolution in real time. The paper presents details of the genetic algorithm's design, along with mathematical models of the algorithm's performance and observations regarding the effectiveness of using complimentary maneuver patterns when multiple resolutions by the same aircraft were required.

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.

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.

Entanglement-assisted quantum quasicyclic low-density parity-check codes

NASA Astrophysics Data System (ADS)

Hsieh, Min-Hsiu; Brun, Todd A.; Devetak, Igor

2009-03-01

We investigate the construction of quantum low-density parity-check (LDPC) codes from classical quasicyclic (QC) LDPC codes with girth greater than or equal to 6. We have shown that the classical codes in the generalized Calderbank-Skor-Steane construction do not need to satisfy the dual-containing property as long as preshared entanglement is available to both sender and receiver. We can use this to avoid the many four cycles which typically arise in dual-containing LDPC codes. The advantage of such quantum codes comes from the use of efficient decoding algorithms such as sum-product algorithm (SPA). It is well known that in the SPA, cycles of length 4 make successive decoding iterations highly correlated and hence limit the decoding performance. We show the principle of constructing quantum QC-LDPC codes which require only small amounts of initial shared entanglement.

On the degree conjecture for separability of multipartite quantum states

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

Hassan, Ali Saif M.; Joag, Pramod S.

2008-01-15

We settle the so-called degree conjecture for the separability of multipartite quantum states, which are normalized graph Laplacians, first given by Braunstein et al. [Phys. Rev. A 73, 012320 (2006)]. The conjecture states that a multipartite quantum state is separable if and only if the degree matrix of the graph associated with the state is equal to the degree matrix of the partial transpose of this graph. We call this statement to be the strong form of the conjecture. In its weak version, the conjecture requires only the necessity, that is, if the state is separable, the corresponding degree matricesmore » match. We prove the strong form of the conjecture for pure multipartite quantum states using the modified tensor product of graphs defined by Hassan and Joag [J. Phys. A 40, 10251 (2007)], as both necessary and sufficient condition for separability. Based on this proof, we give a polynomial-time algorithm for completely factorizing any pure multipartite quantum state. By polynomial-time algorithm, we mean that the execution time of this algorithm increases as a polynomial in m, where m is the number of parts of the quantum system. We give a counterexample to show that the conjecture fails, in general, even in its weak form, for multipartite mixed states. Finally, we prove this conjecture, in its weak form, for a class of multipartite mixed states, giving only a necessary condition for separability.« less

Forecasting Nonlinear Chaotic Time Series with Function Expression Method Based on an Improved Genetic-Simulated Annealing Algorithm

PubMed Central

Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

2015-01-01

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior. PMID:26000011

Scalability problems of simple genetic algorithms.

PubMed

Thierens, D

1999-01-01

Scalable evolutionary computation has become an intensively studied research topic in recent years. The issue of scalability is predominant in any field of algorithmic design, but it became particularly relevant for the design of competent genetic algorithms once the scalability problems of simple genetic algorithms were understood. Here we present some of the work that has aided in getting a clear insight in the scalability problems of simple genetic algorithms. Particularly, we discuss the important issue of building block mixing. We show how the need for mixing places a boundary in the GA parameter space that, together with the boundary from the schema theorem, delimits the region where the GA converges reliably to the optimum in problems of bounded difficulty. This region shrinks rapidly with increasing problem size unless the building blocks are tightly linked in the problem coding structure. In addition, we look at how straightforward extensions of the simple genetic algorithm-namely elitism, niching, and restricted mating are not significantly improving the scalability problems.

Forecasting nonlinear chaotic time series with function expression method based on an improved genetic-simulated annealing algorithm.

PubMed

Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

2015-01-01

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.

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.

Improved quantum backtracking algorithms using effective resistance estimates

NASA Astrophysics Data System (ADS)

Jarret, Michael; Wan, Kianna

2018-02-01

We investigate quantum backtracking algorithms of the type introduced by Montanaro (Montanaro, arXiv:1509.02374). These algorithms explore trees of unknown structure and in certain settings exponentially outperform their classical counterparts. Some of the previous work focused on obtaining a quantum advantage for trees in which a unique marked vertex is promised to exist. We remove this restriction by recharacterizing the problem in terms of the effective resistance of the search space. In this paper, we present a generalization of one of Montanaro's algorithms to trees containing k marked vertices, where k is not necessarily known a priori. Our approach involves using amplitude estimation to determine a near-optimal weighting of a diffusion operator, which can then be applied to prepare a superposition state with support only on marked vertices and ancestors thereof. By repeatedly sampling this state and updating the input vertex, a marked vertex is reached in a logarithmic number of steps. The algorithm thereby achieves the conjectured bound of O ˜(√{T Rmax }) for finding a single marked vertex and O ˜(k √{T Rmax }) for finding all k marked vertices, where T is an upper bound on the tree size and Rmax is the maximum effective resistance encountered by the algorithm. This constitutes a speedup over Montanaro's original procedure in both the case of finding one and the case of finding multiple marked vertices in an arbitrary tree.

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.

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.

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.

A quantum proxy group signature scheme based on an entangled five-qubit state

NASA Astrophysics Data System (ADS)

Wang, Meiling; Ma, Wenping; Wang, Lili; Yin, Xunru

2015-09-01

A quantum proxy group signature (QPGS) scheme based on controlled teleportation is presented, by using the entangled five-qubit quantum state functions as quantum channel. The scheme uses the physical characteristics of quantum mechanics to implement delegation, signature and verification. The security of the scheme is guaranteed by the entanglement correlations of the entangled five-qubit state, the secret keys based on the quantum key distribution (QKD) and the one-time pad algorithm, all of which have been proven to be unconditionally secure and the signature anonymity.

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.

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.

Conceptual versus Algorithmic Learning in High School Chemistry: The Case of Basic Quantum Chemical Concepts--Part 2. Students' Common Errors, Misconceptions and Difficulties in Understanding

ERIC Educational Resources Information Center

Papaphotis, Georgios; Tsaparlis, Georgios

2008-01-01

Part 2 of the findings are presented of a quantitative study (n = 125) on basic quantum chemical concepts taught at twelfth grade (age 17-18 years) in Greece. A paper-and-pencil test of fourteen questions was used that were of two kinds: five questions that tested recall of knowledge or application of algorithmic procedures (type-A questions);…

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.

An investigation of messy genetic algorithms

NASA Technical Reports Server (NTRS)

Goldberg, David E.; Deb, Kalyanmoy; Korb, Bradley

1990-01-01

Genetic algorithms (GAs) are search procedures based on the mechanics of natural selection and natural genetics. They combine the use of string codings or artificial chromosomes and populations with the selective and juxtapositional power of reproduction and recombination to motivate a surprisingly powerful search heuristic in many problems. Despite their empirical success, there has been a long standing objection to the use of GAs in arbitrarily difficult problems. A new approach was launched. Results to a 30-bit, order-three-deception problem were obtained using a new type of genetic algorithm called a messy genetic algorithm (mGAs). Messy genetic algorithms combine the use of variable-length strings, a two-phase selection scheme, and messy genetic operators to effect a solution to the fixed-coding problem of standard simple GAs. The results of the study of mGAs in problems with nonuniform subfunction scale and size are presented. The mGA approach is summarized, both its operation and the theory of its use. Experiments on problems of varying scale, varying building-block size, and combined varying scale and size are presented.

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.

Global Optimization of a Periodic System using a Genetic Algorithm

NASA Astrophysics Data System (ADS)

Stucke, David; Crespi, Vincent

2001-03-01

We use a novel application of a genetic algorithm global optimizatin technique to find the lowest energy structures for periodic systems. We apply this technique to colloidal crystals for several different stoichiometries of binary and trinary colloidal crystals. This application of a genetic algorithm is decribed and results of likely candidate structures are presented.

Research and application of multi-agent genetic algorithm in tower defense game

NASA Astrophysics Data System (ADS)

Jin, Shaohua

2018-04-01

In this paper, a new multi-agent genetic algorithm based on orthogonal experiment is proposed, which is based on multi-agent system, genetic algorithm and orthogonal experimental design. The design of neighborhood competition operator, orthogonal crossover operator, Son and self-learning operator. The new algorithm is applied to mobile tower defense game, according to the characteristics of the game, the establishment of mathematical models, and finally increases the value of the game's monster.

Aerodynamic Shape Optimization Using A Real-Number-Encoded Genetic Algorithm

NASA Technical Reports Server (NTRS)

Holst, Terry L.; Pulliam, Thomas H.

2001-01-01

A new method for aerodynamic shape optimization using a genetic algorithm with real number encoding is presented. The algorithm is used to optimize three different problems, a simple hill climbing problem, a quasi-one-dimensional nozzle problem using an Euler equation solver and a three-dimensional transonic wing problem using a nonlinear potential solver. Results indicate that the genetic algorithm is easy to implement and extremely reliable, being relatively insensitive to design space noise.

Quantum Algorithms Based on Physical Processes

DTIC Science & Technology

2013-12-03

quantum walks with hard-core bosons and the graph isomorphism problem,” American Physical Society March meeting, March 2011 Kenneth Rudinger, John...King Gamble, Mark Wellons, Mark Friesen, Dong Zhou, Eric Bach, Robert Joynt, and S.N. Coppersmith, “Quantum random walks of non-interacting bosons on...and noninteracting Bosons to distinguish nonisomorphic graphs. 1) We showed that quantum walks of two hard-core Bosons can distinguish all pairs of

Quantum Algorithms Based on Physical Processes

DTIC Science & Technology

2013-12-02

quantum walks with hard-core bosons and the graph isomorphism problem,” American Physical Society March meeting, March 2011 Kenneth Rudinger, John...King Gamble, Mark Wellons, Mark Friesen, Dong Zhou, Eric Bach, Robert Joynt, and S.N. Coppersmith, “Quantum random walks of non-interacting bosons on...and noninteracting Bosons to distinguish nonisomorphic graphs. 1) We showed that quantum walks of two hard-core Bosons can distinguish all pairs of

Improved mapping of the travelling salesman problem for quantum annealing

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

Genetic algorithms as global random search methods

NASA Technical Reports Server (NTRS)

Peck, Charles C.; Dhawan, Atam P.

1995-01-01

Genetic algorithm behavior is described in terms of the construction and evolution of the sampling distributions over the space of candidate solutions. This novel perspective is motivated by analysis indicating that the schema theory is inadequate for completely and properly explaining genetic algorithm behavior. Based on the proposed theory, it is argued that the similarities of candidate solutions should be exploited directly, rather than encoding candidate solutions and then exploiting their similarities. Proportional selection is characterized as a global search operator, and recombination is characterized as the search process that exploits similarities. Sequential algorithms and many deletion methods are also analyzed. It is shown that by properly constraining the search breadth of recombination operators, convergence of genetic algorithms to a global optimum can be ensured.

Genetic algorithms as global random search methods

NASA Technical Reports Server (NTRS)

Peck, Charles C.; Dhawan, Atam P.

1995-01-01

Genetic algorithm behavior is described in terms of the construction and evolution of the sampling distributions over the space of candidate solutions. This novel perspective is motivated by analysis indicating that that schema theory is inadequate for completely and properly explaining genetic algorithm behavior. Based on the proposed theory, it is argued that the similarities of candidate solutions should be exploited directly, rather than encoding candidate solution and then exploiting their similarities. Proportional selection is characterized as a global search operator, and recombination is characterized as the search process that exploits similarities. Sequential algorithms and many deletion methods are also analyzed. It is shown that by properly constraining the search breadth of recombination operators, convergence of genetic algorithms to a global optimum can be ensured.

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.

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.

Implementation of quantum game theory simulations using Python

NASA Astrophysics Data System (ADS)

Madrid S., A.

2013-05-01

This paper provides some examples about quantum games simulated in Python's programming language. The quantum games have been developed with the Sympy Python library, which permits solving quantum problems in a symbolic form. The application of these methods of quantum mechanics to game theory gives us more possibility to achieve results not possible before. To illustrate the results of these methods, in particular, there have been simulated the quantum battle of the sexes, the prisoner's dilemma and card games. These solutions are able to exceed the classic bottle neck and obtain optimal quantum strategies. In this form, python demonstrated that is possible to do more advanced and complicated quantum games algorithms.

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.

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

NASA Technical Reports Server (NTRS)

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

2015-01-01

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

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.

Genetic Algorithm Calibration of Probabilistic Cellular Automata for Modeling Mining Permit Activity

USGS Publications Warehouse

Louis, S.J.; Raines, G.L.

2003-01-01

We use a genetic algorithm to calibrate a spatially and temporally resolved cellular automata to model mining activity on public land in Idaho and western Montana. The genetic algorithm searches through a space of transition rule parameters of a two dimensional cellular automata model to find rule parameters that fit observed mining activity data. Previous work by one of the authors in calibrating the cellular automaton took weeks - the genetic algorithm takes a day and produces rules leading to about the same (or better) fit to observed data. These preliminary results indicate that genetic algorithms are a viable tool in calibrating cellular automata for this application. Experience gained during the calibration of this cellular automata suggests that mineral resource information is a critical factor in the quality of the results. With automated calibration, further refinements of how the mineral-resource information is provided to the cellular automaton will probably improve our model.

Hybrid genetic algorithm in the Hopfield network for maximum 2-satisfiability problem

NASA Astrophysics Data System (ADS)

Kasihmuddin, Mohd Shareduwan Mohd; Sathasivam, Saratha; Mansor, Mohd. Asyraf

2017-08-01

Heuristic method was designed for finding optimal solution more quickly compared to classical methods which are too complex to comprehend. In this study, a hybrid approach that utilizes Hopfield network and genetic algorithm in doing maximum 2-Satisfiability problem (MAX-2SAT) was proposed. Hopfield neural network was used to minimize logical inconsistency in interpretations of logic clauses or program. Genetic algorithm (GA) has pioneered the implementation of methods that exploit the idea of combination and reproduce a better solution. The simulation incorporated with and without genetic algorithm will be examined by using Microsoft Visual 2013 C++ Express software. The performance of both searching techniques in doing MAX-2SAT was evaluate based on global minima ratio, ratio of satisfied clause and computation time. The result obtained form the computer simulation demonstrates the effectiveness and acceleration features of genetic algorithm in doing MAX-2SAT in Hopfield network.

Genetic Algorithm for Traveling Salesman Problem with Modified Cycle Crossover Operator

PubMed Central

Mohamd Shoukry, Alaa; Gani, Showkat

2017-01-01

Genetic algorithms are evolutionary techniques used for optimization purposes according to survival of the fittest idea. These methods do not ensure optimal solutions; however, they give good approximation usually in time. The genetic algorithms are useful for NP-hard problems, especially the traveling salesman problem. The genetic algorithm depends on selection criteria, crossover, and mutation operators. To tackle the traveling salesman problem using genetic algorithms, there are various representations such as binary, path, adjacency, ordinal, and matrix representations. In this article, we propose a new crossover operator for traveling salesman problem to minimize the total distance. This approach has been linked with path representation, which is the most natural way to represent a legal tour. Computational results are also reported with some traditional path representation methods like partially mapped and order crossovers along with new cycle crossover operator for some benchmark TSPLIB instances and found improvements. PMID:29209364

Genetic Algorithm for Traveling Salesman Problem with Modified Cycle Crossover Operator.

PubMed

Hussain, Abid; Muhammad, Yousaf Shad; Nauman Sajid, M; Hussain, Ijaz; Mohamd Shoukry, Alaa; Gani, Showkat

2017-01-01

Genetic algorithms are evolutionary techniques used for optimization purposes according to survival of the fittest idea. These methods do not ensure optimal solutions; however, they give good approximation usually in time. The genetic algorithms are useful for NP-hard problems, especially the traveling salesman problem. The genetic algorithm depends on selection criteria, crossover, and mutation operators. To tackle the traveling salesman problem using genetic algorithms, there are various representations such as binary, path, adjacency, ordinal, and matrix representations. In this article, we propose a new crossover operator for traveling salesman problem to minimize the total distance. This approach has been linked with path representation, which is the most natural way to represent a legal tour. Computational results are also reported with some traditional path representation methods like partially mapped and order crossovers along with new cycle crossover operator for some benchmark TSPLIB instances and found improvements.

A modified genetic algorithm with fuzzy roulette wheel selection for job-shop scheduling problems

NASA Astrophysics Data System (ADS)

Thammano, Arit; Teekeng, Wannaporn

2015-05-01

The job-shop scheduling problem is one of the most difficult production planning problems. Since it is in the NP-hard class, a recent trend in solving the job-shop scheduling problem is shifting towards the use of heuristic and metaheuristic algorithms. This paper proposes a novel metaheuristic algorithm, which is a modification of the genetic algorithm. This proposed algorithm introduces two new concepts to the standard genetic algorithm: (1) fuzzy roulette wheel selection and (2) the mutation operation with tabu list. The proposed algorithm has been evaluated and compared with several state-of-the-art algorithms in the literature. The experimental results on 53 JSSPs show that the proposed algorithm is very effective in solving the combinatorial optimization problems. It outperforms all state-of-the-art algorithms on all benchmark problems in terms of the ability to achieve the optimal solution and the computational time.

Tomographic imaging of flourescence resonance energy transfer in highly light scattering media

NASA Astrophysics Data System (ADS)

Soloviev, Vadim Y.; McGinty, James; Tahir, Khadija B.; Laine, Romain; Stuckey, Daniel W.; Mohan, P. Surya; Hajnal, Joseph V.; Sardini, Alessandro; French, Paul M. W.; Arridge, Simon R.

2010-02-01

Three-dimensional localization of protein conformation changes in turbid media using Förster Resonance Energy Transfer (FRET) was investigated by tomographic fluorescence lifetime imaging (FLIM). FRET occurs when a donor fluorophore, initially in its electronic excited state, transfers energy to an acceptor fluorophore in close proximity through non-radiative dipole-dipole coupling. An acceptor effectively behaves as a quencher of the donor's fluorescence. The quenching process is accompanied by a reduction in the quantum yield and lifetime of the donor fluorophore. Therefore, FRET can be localized by imaging changes in the quantum yield and the fluorescence lifetime of the donor fluorophore. Extending FRET to diffuse optical tomography has potentially important applications such as in vivo studies in small animal. We show that FRET can be localized by reconstructing the quantum yield and lifetime distribution from time-resolved non-invasive boundary measurements of fluorescence and transmitted excitation radiation. Image reconstruction was obtained by an inverse scattering algorithm. Thus we report, to the best of our knowledge, the first tomographic FLIM-FRET imaging in turbid media. The approach is demonstrated by imaging a highly scattering cylindrical phantom concealing two thin wells containing cytosol preparations of HEK293 cells expressing TN-L15, a cytosolic genetically-encoded calcium FRET sensor. A 10mM calcium chloride solution was added to one of the wells to induce a protein conformation change upon binding to TN-L15, resulting in FRET and a corresponding decrease in the donor fluorescence lifetime. The resulting fluorescence lifetime distribution, the quantum efficiency, absorption and scattering coefficients were reconstructed.

A New Challenge for Compression Algorithms: Genetic Sequences.

ERIC Educational Resources Information Center

Grumbach, Stephane; Tahi, Fariza

1994-01-01

Analyzes the properties of genetic sequences that cause the failure of classical algorithms used for data compression. A lossless algorithm, which compresses the information contained in DNA and RNA sequences by detecting regularities such as palindromes, is presented. This algorithm combines substitutional and statistical methods and appears to…

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.

Ion-Stockmayer clusters: Minima, classical thermodynamics, and variational ground state estimates of Li+(CH3NO2)n (n = 1-20)

NASA Astrophysics Data System (ADS)

Curotto, E.

2015-12-01

Structural optimizations, classical NVT ensemble, and variational Monte Carlo simulations of ion Stockmayer clusters parameterized to approximate the Li+(CH3NO2)n (n = 1-20) systems are performed. The Metropolis algorithm enhanced by the parallel tempering strategy is used to measure internal energies and heat capacities, and a parallel version of the genetic algorithm is employed to obtain the most important minima. The first solvation sheath is octahedral and this feature remains the dominant theme in the structure of clusters with n ≥ 6. The first "magic number" is identified using the adiabatic solvent dissociation energy, and it marks the completion of the second solvation layer for the lithium ion-nitromethane clusters. It corresponds to the n = 18 system, a solvated ion with the first sheath having octahedral symmetry, weakly bound to an eight-membered and a four-membered ring crowning a vertex of the octahedron. Variational Monte Carlo estimates of the adiabatic solvent dissociation energy reveal that quantum effects further enhance the stability of the n = 18 system relative to its neighbors.

Firefly algorithm versus genetic algorithm as powerful variable selection tools and their effect on different multivariate calibration models in spectroscopy: A comparative study

NASA Astrophysics Data System (ADS)

Attia, Khalid A. M.; Nassar, Mohammed W. I.; El-Zeiny, Mohamed B.; Serag, Ahmed

2017-01-01

For the first time, a new variable selection method based on swarm intelligence namely firefly algorithm is coupled with three different multivariate calibration models namely, concentration residual augmented classical least squares, artificial neural network and support vector regression in UV spectral data. A comparative study between the firefly algorithm and the well-known genetic algorithm was developed. The discussion revealed the superiority of using this new powerful algorithm over the well-known genetic algorithm. Moreover, different statistical tests were performed and no significant differences were found between all the models regarding their predictabilities. This ensures that simpler and faster models were obtained without any deterioration of the quality of the calibration.

Refined genetic algorithm -- Economic dispatch example

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

Sheble, G.B.; Brittig, K.

1995-02-01

A genetic-based algorithm is used to solve an economic dispatch (ED) problem. The algorithm utilizes payoff information of perspective solutions to evaluate optimality. Thus, the constraints of classical LaGrangian techniques on unit curves are eliminated. Using an economic dispatch problem as a basis for comparison, several different techniques which enhance program efficiency and accuracy, such as mutation prediction, elitism, interval approximation and penalty factors, are explored. Two unique genetic algorithms are also compared. The results are verified for a sample problem using a classical technique.

Immune allied genetic algorithm for Bayesian network structure learning

NASA Astrophysics Data System (ADS)

Song, Qin; Lin, Feng; Sun, Wei; Chang, KC

2012-06-01

Bayesian network (BN) structure learning is a NP-hard problem. In this paper, we present an improved approach to enhance efficiency of BN structure learning. To avoid premature convergence in traditional single-group genetic algorithm (GA), we propose an immune allied genetic algorithm (IAGA) in which the multiple-population and allied strategy are introduced. Moreover, in the algorithm, we apply prior knowledge by injecting immune operator to individuals which can effectively prevent degeneration. To illustrate the effectiveness of the proposed technique, we present some experimental results.

Flexible Space-Filling Designs for Complex System Simulations

DTIC Science & Technology

2013-06-01

interior of the experimental region and cannot fit higher-order models. We present a genetic algorithm that constructs space-filling designs with...Computer Experiments, Design of Experiments, Genetic Algorithm , Latin Hypercube, Response Surface Methodology, Nearly Orthogonal 15. NUMBER OF PAGES 147...experimental region and cannot fit higher-order models. We present a genetic algorithm that constructs space-filling designs with minimal correlations

Genetic algorithms in conceptual design of a light-weight, low-noise, tilt-rotor aircraft

NASA Technical Reports Server (NTRS)

Wells, Valana L.

1996-01-01

This report outlines research accomplishments in the area of using genetic algorithms (GA) for the design and optimization of rotorcraft. It discusses the genetic algorithm as a search and optimization tool, outlines a procedure for using the GA in the conceptual design of helicopters, and applies the GA method to the acoustic design of rotors.

Self-calibration of a noisy multiple-sensor system with genetic algorithms

NASA Astrophysics Data System (ADS)

Brooks, Richard R.; Iyengar, S. Sitharama; Chen, Jianhua

1996-01-01

This paper explores an image processing application of optimization techniques which entails interpreting noisy sensor data. The application is a generalization of image correlation; we attempt to find the optimal gruence which matches two overlapping gray-scale images corrupted with noise. Both taboo search and genetic algorithms are used to find the parameters which match the two images. A genetic algorithm approach using an elitist reproduction scheme is found to provide significantly superior results. The presentation includes a graphic presentation of the paths taken by tabu search and genetic algorithms when trying to find the best possible match between two corrupted images.