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A low failure rate quantum algorithm for searching maximum or minimum

quantum INFORMATION PROCESSING 2020年第8期19卷 1-28页

作者： Chen, Yanhu Wei, Shijie Gao, Xiong Wang, Cen Tang, Yinan Wu, Jian Guo, Hongxiang Beijing Univ Posts & Telecommun Inst Informat Photon & Opt Commun Beijing 100876 Peoples R China Beijing Acad Quantum Informat Sci Beijing 100193 Peoples R China Tsinghua Univ State Key Lab Low Dimens Quantum Phys Beijing 100084 Peoples R China Tsinghua Univ Dept Phys Beijing 100084 Peoples R China

Although Durr and Hoyer have proposed state-of-the-art quantum algorithm (DHA) for searching minimum value, the lower limit of DHA's successful probability is 1/2. Also, DHA requires approximately (log(2) N)(2) copies of the initial state. In this paper, we propose a new quantum maximum or minimum searching algorithm (QUMMSA). In big data scenarios, according to sparse sampling with different densities, we can estimate the corresponding precision parameters. QUMMSA can improve the successful probability close to 100%. Furthermore, with the quantum exact search algorithm, QUMMSA only requires approximately log2 N copies of the initial state to solve this problem. Since preparing an arbitrary quantum state is a problem with exponential complexity, our algorithm has a greater advantage with the increasing database size. In addition, we first propose a general method for circuits construction, which can be used in any database. An experiment implemented in an IBM superconducting processor and a numerical simulation of a 6-qubit system to solve a real issue indicate the feasibility and efficiency of QUMMSA. QUMMSA can serve as a subroutine in various quantum algorithms which involves searching maximum or minimum.

关键词： quantum algorithm Searching minimum or maximum problem quantum circuits Superconducting experiments

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Three-Dimensional Reconstruction of Fuzzy Medical Images Using quantum algorithm

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IEEE ACCESS 2020年 8卷 218279-218288页

作者： Li, Xiaofeng Sui, Jun Wang, Yanwei Heilongjiang Int Univ Dept Informat Engn Harbin 150025 Peoples R China Heilongjiang Int Univ Off Acad Res Harbin 150025 Peoples R China Purdue Univ Dept Mech Engn W Lafayette IN 47906 USA

In order to deal with the problems of poor anti-interference, low reconstruction clarity and large errors in the traditional medical image reconstruction methods, we proposed a fuzzy medical images three-dimensional (3D) reconstruction method using quantum algorithm. First of all, a feature matching model of fuzzy medical image was built. Secondly, this study decomposed the edge contour features by using the Gaussian mixture feature matching method, extracted the edge contour vectors of fuzzy medical image, and enhanced the information of fuzzy medical images by adopting the region edge sharpening. Thirdly, this study reorganized the 3D texture structure of images and reconstructed the sparse scattered points according to its texture and detail regions. Finally, we combined with the gray histogram of fuzzy medical images to achieve the adaptive pixel reconstruction of fuzzy medical images, and completed the 3D reconstruction of fuzzy medical images by employing the quantum algorithm. The results show that the proposed method is characterized by high matching degree of image features and balanced distribution of point clouds, and the self-similarity coefficient of the reconstructed texture can reach 0.994;in addition, the SINR value of the reconstruction result can be maintained around 100dB, and it has lower error rate than the traditional method, thereby improving the detection and recognition capability of medical images, and the algorithm has certain practical application.

关键词： Biomedical imaging Three-dimensional displays Image reconstruction Feature extraction Image edge detection Solid modeling Topology quantum algorithm fuzzy medical images three-dimensional reconstruction characteristics of the reconstruction

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An Exact quantum algorithm for a Restricted Subtraction Game

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INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 2020年第5期59卷 1504-1511页

作者： Huang, Yunqi Ye, Zekun Zheng, Shenggen Li, Lvzhou Sun Yat Sen Univ Inst Comp Sci Theory Sch Data & Comp Sci Guangzhou 510006 Peoples R China Peng Cheng Lab Ctr Quantum Comp Shenzhen 518055 Peoples R China Sun Yat Sen Univ Minist Educ Key Lab Machine Intelligence & Adv Comp Guangzhou 510006 Peoples R China

An algorithm is exact if it always produces the correct answer on any input. Coming up with exact quantum algorithms that substantially outperform the best classical algorithm has been a quite challenging task. Nim game is a well-known combinatorial game which has a complete mathematical theory, and many kinds of Nim games have been studied in the literature. One famous kind of Nim games are subtraction games played with one heap of tokens, with players taking turns removing from the heap a number of tokens belonging to a specified subtraction set. The last player to move wins. In this paper, we propose a restricted subtraction game with the subtraction set determined by a specified matrix, and present an exact quantum algorithm to solve it. We show that the query complexity of our quantum algorithm is O(n(3/2)), while the classical exact query complexity is Theta(n(2)).

关键词： Query complexity Subtraction game quantum algorithm

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quantum PC algorithm: data-efficient and nonlinear causal discovery 5

Quantum PC algorithm: data-efficient and nonlinear causal di...

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2024 International Conference on quantum Computing and Engineering

作者： Maeda, Yota Arai, Ken Tanaka, Yu Terada, Yu Ueno, Hiroshi Tezuka, Hiroyuki Sony Grp Corp Adv Res Lab Res Platform Tokyo Japan

ISBN: (纸本)9798331541378

Causal discovery is the task of finding causal relationships between random variables from observed data. Typically, one assumes that the causal relationships can be represented by a directed acyclic graph (DAG), and makes additional assumptions to ensure that the DAG can be recovered from the observed data. In this study, we propose the quantum Peter Clark (qPC) algorithm for nonlinear causal discovery based on quantum kernel methods. The qPC algorithm takes advantage of the quantum kernel-based conditional independent test. Through the synthetic data experiment, we show that the qPC algorithm outperforms the classical method in the regime of a small number of samples. This suggests that the kernel-based causal discovery can significantly improve performance under such conditions. Our experiments highlight that the proposed algorithm can accurately support classical algorithms in causal discovery, paving the way for future advances with the utilization of quantum computation.

关键词： Causal discovery quantum algorithm quantum kernel method

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Experimental Implementation of Shor's quantum algorithm to Break RSA

Experimental Implementation of Shor's Quantum Algorithm to B...

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International Conference on Computational Intelligence and Communication Networks (CICN)

作者： Aminah Albuainain Jana Alansari Samiyah Alrashidi Wasmiyah Alqahtani Jana Alshaya Naya Nagy College of Computer Science and Information Technology Imam Abdulrahman bin Faisal University Khobar Kingdom of Saudi Arabia

ISBN: (纸本)9781665487726

Nowadays, quantum computing is an important topic since it allows computations to be completed in a small amount of the time. The goal of using quantum computers (QC) is to solve an increasing number of problems that were previously intractable to address with traditional computing. The classical approaches work with bits, which are made up of 0s and 1s, whereas QC uses qubits. Classical computing is limited by storage capacity and speed of calculations, even when parallel computation is conducted on it. Compared to traditional methods, quantum parallelism allows the storage to be reduced exponentially with the potential of a shorter amount of time. Besides, Peter Shor's algorithm can solve the factorization problem used in RSA in polynomial time, whereas in a classical computer, factoring any big integer is intractable. The purpose of this research is to explore and implement quantum computing schemes and how Shor's algorithm can break RSA algorithms.

关键词： Computers quantum algorithm Qubit Parallel processing Logic gates Mathematical models Registers

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A quantum algorithm for syndrome decoding of classical error-correcting linear block codes

A quantum algorithm for syndrome decoding of classical error...

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IEEE/ACM Symposium on Edge Computing (SEC)

作者： Mainak Bhattacharyya Ankur Raina Department of Physics National Institute of Technology Jamshedpur India Department of EECS Indian Institute of Science Education and Research Bhopal India

ISBN: (数字)9781665486118

ISBN: (纸本)9781665486125

Decoding of linear block codes using syndrome decoding and finding whether there exists a codeword of weight $w$ in a set of codewords are known to belong to a class of NP-complete problems. For syndrome decoding of linear block codes, we provide an algorithm that gives a probabilistic solution with least Hamming weight. The algorithm can speed up this process significantly with the help of quantum search algorithm. For this, we make use of a search algorithm inspired from Grover's search. We also suggest a general approach for building a quantum circuit for syndrome detection. We test the algorithm in IBM quantum Experience using qasm simulator and perform the complexity analysis identifying the algorithm's domain of utility.

关键词： quantum algorithm Upper bound Buildings Probabilistic logic Decoding Block codes NP-complete problem

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quantum algorithm for total least squares data fitting

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PHYSICS LETTERS A 2019年第19期383卷 2235-2240页

作者： Wang, Hefeng Xiang, Hua Xi An Jiao Tong Univ Sch Sci Dept Appl Phys Xian 710049 Shaanxi Peoples R China Shaanxi Prov Key Lab Quantum Informat & Quantum O Xian 710049 Shaanxi Peoples R China Wuhan Univ Sch Math & Stat Wuhan 430072 Hubei Peoples R China

The total least squares (TLS) method is widely used in data-fitting. Compared with the least squares fitting method, the TLS fitting takes into account not only observation errors, but also errors from the measurement matrix of the variables. In this work, the TLS problem is transformed to finding the ground state of a Hamiltonian matrix. We propose quantum algorithms for solving this problem based on quantum simulation of resonant transitions. Our algorithms can achieve at least polynomial speedup over the known classical algorithms. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Total least squares quantum simulation quantum algorithm

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Comparative Benchmark of a quantum algorithm for the Bin Packing Problem

Comparative Benchmark of a Quantum Algorithm for the Bin Pac...

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IEEE Symposium Series on Computational Intelligence (SSCI)

作者： Mikel Garcia De Andoin Izaskun Oregi Esther Villar-Rodriguez Eneko Osaba Mikel Sanz Department of Physical Chemistry University of the Basque Country UPV/EHU Leioa Spain TECNALIA Basque Research and Technology Alliance (BRTA) Derio Spain EHU Quantum Center University of the Basque Country UPV/EHU Leioa Spain IKERBASQUE Basque Foundation for Science Bilbao Spain Basque Center for Applied Mathematics BCAM Bilbao Spain

ISBN: (纸本)9781665487696

The Bin Packing Problem (BPP) stands out as a paradigmatic combinatorial optimization problem in logistics. quantum and hybrid quantum-classical algorithms are expected to show an advantage over their classical counterparts in obtaining approximate solutions for optimization problems. We have recently proposed a hybrid approach to the one dimensional BPP in which a quantum annealing subroutine is employed to sample feasible solutions for single containers. From this reduced search space, a classical optimization subroutine can find the solution to the problem. With the aim of going a step further in the evaluation of our subroutine, in this paper we compare the performance of our procedure with other classical approaches. Concretely we test a random sampling and a random-walk-based heuristic. Employing a benchmark comprising 18 instances, we show that the quantum approach lacks the stagnation behaviour that slows down the classical algorithms. Based on this, we conclude that the quantum strategy can be employed jointly with the random walk to obtain a full sample of feasible solutions in fewer iterations. This work improves our intuition about the benefits of employing the scarce quantum resources to improve the results of a diminishingly efficient classical strategy.

关键词： Measurement Annealing quantum algorithm algorithms Heuristic algorithms Benchmark testing quantum annealing

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An exact quantum algorithm for testing 3-junta in Boolean functions with one uncomplemented product

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quantum INFORMATION PROCESSING 2021年第1期20卷 36-36页

作者： Chen, Chien-Yuan Natl Univ Kaohsiung Dept Comp Sci & Informat Engn 700 Kaohsiung Univ Rd Kaohsiung Taiwan

This paper modifies Chen's algorithm, which is the first exact quantum algorithm for testing 2-junta, and proposes an exact quantum learning algorithm for finding dependent variables of the Boolean function f: with one uncomplemented product of three variables. Typically, the dependent variables are obtained by evaluating the function 2n times in the worst case. However, our proposed quantum algorithm only requires O function operations in the worst case. In addition, the average number to perform the function is evaluated. Our algorithm requires an average of 7.23 function operations at the most when n >= 16. We also show that our algorithm cannot solve k-junta problem with one uncomplemented product if 4 <= k

关键词： quantum algorithm quantum learning algorithm The Bernstein-Vazirani algorithm

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An improved quantum algorithm for support matrix machines

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quantum INFORMATION PROCESSING 2021年第7期20卷 229-229页

作者： Zhang, Yanbing Song, Tingting Wu, Zhihao Jinan Univ Coll Informat Sci & Technol Guangzhou 510632 Peoples R China Guangxi Key Lab Cryptog & Informat Secur Guilin 541004 Peoples R China Jinan Univ Coll Cyber Secur Guangzhou 510632 Peoples R China

With the rapid growth of video and image technology, the binary classification of matrices has attracted much attention. In 2017, Duan et al. proposed a quantum algorithm for support matrix machines (QSMM) that efficiently addresses image classification problems. The QSMM consists of two core subroutines: an HHL algorithm and a quantum singularity threshold (QSVT) algorithm with complexities of O, respectively, where kappa is the condition number of the corresponding matrix of the HHL algorithm, E is the expected accuracy of the output state, N is the number of samples in the training set and mn is the size of the feature space. The QSMM achieves an exponential increase in speed over classical counterparts. However, we find that Duan's QSMM can be improved by applying an improved quantum matrix inversion (QMI) algorithm instead of the HHL algorithm. Compared with that of Duan's QSMM, the dependence on precision of our improved QSMM (IQSMM) is exponentially improved, and the complexity of our first subroutine is as low as O[kappa 2log1.5(kappa /E)log(Nmn)].

关键词： quantum algorithm quantum machine learning quantum computation

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