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Certified Quantum Computation in Isabelle/HOL

JOURNAL OF AUTOMATED REAsONING 2021年第5期65卷 691-709页

作者： Bordg, Anthony Lachnitt, Hanna He, Yijun Univ Cambridge Dept Comp Sci & Technol Cambridge England Stanford Univ Dept Comp Sci Stanford CA 94305 USA Univ Cambridge Cambridge England

In this article we present an ongoing effort to formalise quantum algorithms and results in quantum information theory using the proof assistant Isabelle/HOL. Formal methods being critical for the safety and security of algorithms and protocols, we foresee their widespread use for quantum computing in the future. We have developed a large library for quantum computing in Isabelle based on a matrix representation for quantum circuits, successfully formalising the no-cloning theorem, quantum teleportation, Deutsch's algorithm, the Deutsch-Jozsa algorithm and the quantum Prisoner's Dilemma. We discuss the design choices made and report on an outcome of our work in the field of quantum game theory.

关键词： Isabelle HOL Certification Quantum computing No-cloning Quantum teleportation Deutsch’ s algorithm Deutsch– Jozsa algorithm Quantum prisoner’ s dilemma

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simultaneous Reconfiguration and Optimal Capacitor Placement Using Adaptive Whale Optimization algorithm for Radial Distribution system

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JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY 2021年第1期16卷 181-190页

作者： Babu, M. Ramesh Kumar, C. Venkatesh Anitha, s. St Josephs Coll Engn Dept Elect & Elect Engn OMR Chennai 600119 Tamil Nadu India IFET Coll Engn Dept Elect & Elect Engn Viluppuram 605602 Tamil Nadu India

The losses in the distribution networks due to the line resistance decrease the overall efficiency of the power distribution. Reducing the power losses and regulating the voltages within the limits are necessary to provide quality power to the consumers. The power loss can be minimized by optimum network reconfiguration and the placement of the capacitors. Considering independent network reconfiguration and placement of the capacitor is not effective during heavy loading conditions. This paper proposes a simultaneous network reconfiguration and capacitor placement in radial distribution network to minimize the real power losses, operating cost and to improve the bus voltages. The Johnson's algorithm is used to find the minimal spanning tree during the network reconfiguration and an adaptive whale optimization algorithm is used as an optimization method. The proposed methodology is tested on standard IEEE 33-bus and 69-bus radial distribution systems. The effectiveness of the proposed method is validated by comparing the results with previous result reported in the literature in terms of cost saving and loss reduction.

关键词： Adaptive whale algorithm Network reconfiguration Johnson’ s algorithm Optimal capacitor placement Power loss reduction Operating cost minimization

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ML Criterion Based signal Detection of a MIMO-OFDM system Using Quantum and semi-Quantum Assisted Modified DHA/BBHT search algorithm

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IEEE TRANsACTIONs ON VEHICULAR TECHNOLOGY 2021年第2期70卷 1688-1698页

作者： Mondal, subhadeep Laskar, Mostafizur Rahaman Dutta, Amit Kumar Indian Inst Technol Kharagpur GS Sanyal Sch Telecommun Kharagpur 721302 W Bengal India

The quantum search algorithm (QsA) is one of the most recent developments in the era of quantum signal processing (QsP) and quantum information theory (QIT). It shows a faster performance in finding the solutions of system such as multiple-input multiple-output (MIMO) communication system, quantum error correction and others with a polynomial order over the classical one. Grover's algorithm is one of the first proposed QsA in identifying the index number of the solution of a system, whose solutions are known to the oracle. A further improved QsA called Boyer-Brassard-Hoyer-Tapp (BBHT) is followed by the Durr-Hoyer algorithm (DHA), which proposes to find the solutions, while the exact number of the solutions is not known. In this treatise, we propose two modifications to the existing DHA and BBHT algorithms. In DHA, we propose a semi-quantum framework, where after each iteration in DHA, the non-solution points are removed in classical framework. This makes the data set iteratively shorter. In the case of BBHT algorithm, we propose to choose the Grover search number based on the Gamma distribution instead of the uniform one, which gives more chances to the new larger values to improve probability of success. The performance of the proposed QsAs demonstrates plausible improvement in search success performance as compared to their existing BBHT and DHA counterparts. Numerical simulations are conducted with the proposed QsA algorithms on a MIMO orthogonal frequency division multiplexing (OFDM) system to demonstrate the performance improvement.

关键词： Quantum search algorithm (QsA) wireless communication MIMO OFDM grover&apos s algorithm BBHT DHA

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Lattice Reduction Over Imaginary Quadratic Fields

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IEEE TRANsACTIONs ON sIGNAL PROCEssING 2020年 68卷 6380-6393页

作者： Lyu, shanxiang Porter, Christian Ling, Cong Jinan Univ Coll Cyber Secur Guangzhou 510632 Peoples R China State Key Lab Cryptol Beijing 100878 Peoples R China Imperial Coll London Dept Elect & Elect Engn London SW7 2AZ England

Complex bases, along with direct-sums defined by rings of imaginary quadratic integers, induce algebraic lattices. In this work, we study such lattices and their reduction algorithms. Firstly, when the lattice is spanned over a two dimensional basis, we show that the algebraic variant of Gauss's algorithm returns a basis that corresponds to the successive minima of the lattice if the chosen ring is Euclidean. secondly, we extend the celebrated Lenstra-Lenstra-Lovasz (LLL) reduction from over real bases to over complex bases. Properties and implementations of the algorithm are examined. In particular, satisfying Lovasz's condition requires the ring to be Euclidean. Lastly, we numerically show the time-advantage of using algebraic LLL by considering lattice bases generated from wireless communications and cryptography.

关键词： Lattices signal processing algorithms Cryptography Information theory Wireless communication Conferences Generators Algebraic lattices euclidean gauss&apos s algorithm LLL lattice reduction

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Using small-scale quantum devices to solve algebraic equations

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QUANTUM INFORMATION PROCEssING 2021年第4期20卷 1-15页

作者： Li, Hongshu Ma, Zhi Wang, Hong Duan, Qianheng Fei, Yangyang Meng, Xiangdong State Key Lab Math Engn & Adv Comp Zhengzhou 450001 Peoples R China

solving algebraic equations over GF(2) is a problem which has a wide range of applications, including NP-Hard problems and problems related to cryptography. The existing mature algorithms are difficult to solve large-scale problems. Inspired by schoning's algorithm and its quantum version, we apply related methods to solve algebraic equations over GF (2). The new algorithm we proposed has a significant improvement of solving efficiency in large-scale and sparse algebraic equations. As a hybrid algorithm, the new algorithm can not only run on a classic computer alone, but also use small-scale quantum devices to assist acceleration. And the new algorithm can be seen as an example of solving a large-scale problem on a small-scale quantum device.

关键词： schö ning’ s algorithm Algebraic equations small-scale quantum devices

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Managing pharmaceuticals delivery service using a hybrid particle swarm intelligence approach

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ANNALs OF OPERATIONs REsEARCH 2022年第1-2期308卷 653-684页

作者： Wu, Xiaodan Li, Ruichang Chu, Chao-Hsien Amoasi, Richard Liu, shan Hebei Univ Technol Sch Econ & Management Tianjin 300401 Peoples R China Singapore Management Univ Singapore 178902 Singapore

Medicines or drugs have unique characteristics of short life cycle, small size, light weight, restrictive distribution time and the need of temperature and humidity control (selected items only). Thus, logistics companies often use different types of vehicles with different carrying capacities, and considering fixed and variable costs in service delivery, which make the vehicle assignment and route optimization more complicated. In this study, we formulate the problem to a multi-type vehicle assignment and mixed integer programming route optimization model with fixed fleet size under the constraints of distribution time and carrying capacity. Given non-deterministic polynomial hard and optimal algorithm can only be used to solve small-size problem, a hybrid particle swarm intelligence (PsI) heuristic approach, which adopts the crossover and mutation operators from genetic algorithm and 2-opt local search strategy, is proposed to solve the problem. We also adapt a principle based on cost network and Dijkstra's algorithm for vehicle scheduling to balance the distribution time limit and the high loading rate. We verify the relative performance of the proposed method against several known optimal or heuristic solutions using a standard data set for heterogeneous fleet vehicle routing problem. Additionally, we compare the relative performance of our proposed Hybrid PsI algorithm with two intelligent-based algorithms, Hybrid Population Heuristic algorithm and Improved Genetic algorithm, using a real-world data set to illustrate the practical and validity of the model and algorithm.

关键词： Medical logistics Pharmaceuticals delivery Vehicle routing problem Hybrid particle swarm intelligence algorithm Dijkstra’ s algorithm

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Global Least squares Path Modeling: A Full-Information Alternative to Partial Least squares Path Modeling

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PsYCHOMETRIKA 2020年第4期85卷 947-972页

作者： Hwang, Heungsun Cho, Gyeongcheol McGill Univ Montreal PQ Canada

Partial least squares path modeling has been widely used for component-based structural equation modeling, where constructs are represented by weighted composites or components of observed variables. This approach remains a limited-information method that carries out two separate stages sequentially to estimate parameters (component weights, loadings, and path coefficients), indicating that it has no single optimization criterion for estimating the parameters at once. In general, limited-information methods are known to provide less efficient parameter estimates than full-information ones. To address this enduring issue, we propose a full-information method for partial least squares path modeling, termed global least squares path modeling, where a single least squares criterion is consistently minimized via a simple iterative algorithm to estimate all the parameters simultaneously. We evaluate the relative performance of the proposed method through the analyses of simulated and real data. We also show that from algorithmic perspectives, the proposed method can be seen as a block-wise special case of another full-information method for component-based structural equation modeling-generalized structured component analysis.

关键词： partial least squares path modeling full-information single optimization criterion alternating least squares block-wise generalized structured component analysis component-based structural equation modeling regularized generalized canonical correlation analysis Lohmö ller’ s algorithm Wold’ s algorithm

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Compass Construction of Bezier Curves and B-splines

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NEXUs NETWORK JOURNAL 2021年第3期23卷 789-811页

作者： Yazar, Tugrul Istanbul Bilgi Univ Fac Architecture Santralistanbul Campus TR-34060 Istanbul Turkey

This article reveals a mathematical bridge between compass-only geometric constructions and parametric curves. A set of construction algorithms are presented which are used to locate points on any Bezier curve or B-spline by using an abstract compass. These constructions aim to translate the B-spline definition of Paul de Casteljau into the modified versions of compass-only constructions explained by Aleksandr Kostovskii. several computer scripts are developed and used to simulate these constructions while calculating and minimizing their computational complexities. The mathematical bridge explained in this article is expected to bring back to mind the synthetic and axiomatic roots of design geometries.

关键词： B-spline Compass-only construction de Casteljau’ s algorithm Bé zier curve Geometrography Architectural geometry

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A New Hybrid algorithm for Computing a Fast Discrete Fourier Transform

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IEEE Transactions on Computers 1979年第7期C-28卷 487-492页

作者： Reed, Irving s. Department of Electrical Engineering University of Southern California Los Angeles CA 90007 United States Communications Systems Research Section Telecommunications Science and Engineering Division Jet Propulsion Laboratory Californis Institute of Technology Pasadena CA 91103 United States

In this paper for certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform (DFT) is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne prime number-theoretic transform developed originally by Rader. This new algorithm requires fewer multiplications than eitber the standard fast Fourier transform (FFT) or Winograd's more conventional algorithm. However, more additions are required. Copyright © 1979 by The Institute of Electrical and Electronics Engineers, Inc.

关键词： Index Terms-Discrete Fourier transform (DFT) fast Fourier transform (FFT) Winograd s algorithm

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Two Local search Components that Move Along the Axes for Memetic Computing Frameworks

Two Local Search Components that Move Along the Axes for Mem...

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2014 IEEE symposium on Foundations of Computational Intelligence (FOCI)

作者： Neri, Ferrante Khan, Noel De Montfort Univ Ctr Computat Intelligence Sch Comp Sci & Informat Gateway Leicester LE1 9B1L Leics England

ISBN: (纸本)9781479944910

Within memetic computing frameworks, the structure as well as a correct choice of memes are important elements that drive successful optimization algorithms. This paper studies variations of a promising yet simple search operator, the s algorithm, which can easily be integrated within a memetic framework to improve candidate solutions. s is a single-solution optimizer that iteratively perturbs variables and conditionally evaluates solutions along the axes. The first s variant, namely s2, unconditionally evaluates solutions in both directions while s3 maintains D uncorrelated step sizes that are either expanded in the direction of improving fitness or else redirected and contracted. Numerical results from the CEC2010 and CEC2014 benchmarks show that the variants outperform s in terms of the number of function evaluations for a given fitness value and, further, that s3 outperforms s in terms of final fitness against a wide range of problems and dimensionality.

关键词： evolutionary computation iterative methods optimisation search problems CEC2010 benchmark CEC2014 benchmark s algorithm conditional evaluation function evaluation iterative variable perturbation local search components memetic computing frameworks optimization algorithm search operator single-solution optimizer algorithm design and analysis Benchmark testing Correlation Market research Memetics Optimization sociology Function evaluation algorithm design and analysis Benchmark testing Optimization algorithms tabu search market research sociology evolutionary algorithm iterative methods axe Axis, Cervical Vertebra sulfur Frameworks

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