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The quantum search algorithms for All Solutions

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 2013年第6期52卷 1893-1907页

作者： Li, Hai-Sheng Zhu Qingxin Lan, Song Wu, Qian Univ Elect Sci & Technol China Sch Comp Sci & Engn Chengdu 611731 Sichuan Peoples R China East China Jiao Tong Univ Coll Informat Engn Nanchang 330013 Jiangxi Peoples R China Wuhan Univ Comp Sch Wuhan 430072 Hubei Peoples R China

Two quantum search algorithms are proposed for known and unknown number of solutions. The first algorithm begins with an arbitrary rotation phase Grover search algorithm by recursive equations, then a sub-algorithm (G (alpha) algorithm) and the corresponding quantum circuits are designed, the probability of success and expected number of iterations of the sub-algorithm to find a solution are analyzed. Based on these results, we design the whole algorithm and estimate the expected number of iterations to search all solutions. The design of the second algorithm follows the same steps. We firstly study a quantum counting algorithm, then design a sub-algorithm (QCG algorithm), and analyze the probability of success and the expected number of iterations to find a solution. Finally the whole algorithm for all solutions is designed and analyzed. The analysis results show that these two algorithms find all solutions in the expected times of (t is a number of solutions and N is a total of states).

关键词： Grover algorithm quantum search algorithms Phase estimation quantum counting

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Two-Step quantum search Algorithm for Solving Traveling Salesman Problems

IEEE TRANSACTIONS ON QUANTUM ENGINEERING

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IEEE TRANSACTIONS ON quantum ENGINEERING 2025年第1期6卷 1-12页

作者： Sato, Rei Gordon, Cui Saito, Kazuhiro Kawashima, Hideyuki Nikuni, Tetsuro Watabe, Shohei KDDI Res Inc Quantum Comp Grp Fujimino 3568502 Japan Tokyo Univ Sci Dept Phys Tokyo 1628601 Japan Keio Univ Fac Environm & Informat Studies Fujisawa 2520882 Japan Shibaura Inst Technol Fac Engn Comp Sci & Engn Tokyo 1358548 Japan

quantum search algorithms, such as Grover's algorithm, are anticipated to efficiently solve constrained combinatorial optimization problems. However, applying these algorithms to the traveling salesman problem (TSP) on a quantum circuit presents a significant challenge. Existing quantum search algorithms for the TSP typically assume that an initial state-an equal superposition of all feasible solutions satisfying the problem's constraints-is pre-prepared. The query complexity of preparing this state using brute-force methods scales exponentially with the factorial growth of feasible solutions, creating a significant hurdle in designing quantum circuits for large-scale TSPs. To address this issue, we propose a two-step quantum search (TSQS) algorithm that employs two sets of operators. In the first step, all the feasible solutions are amplified into their equal superposition state. In the second step, the optimal solution state is amplified from this superposition state. The TSQS algorithm demonstrates greater efficiency compared to conventional search algorithms that employ a single oracle operator for finding a solution within the encoded space. Encoded in the higher order unconstrained binary optimization representation, our approach significantly reduces the qubit requirements. This enables efficient initial state preparation through a unified circuit design, offering a quadratic speedup in solving the TSP without prior knowledge of feasible solutions.

关键词： Costs Urban areas Optimization search problems Encoding quantum circuit Complexity theory Traveling salesman problems quantum algorithm Heuristic algorithms Grover's algorithm quantum search algorithms traveling salesman problems (TSPs)

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quantum search algorithm for Automated Test Pattern Generation in VLSI testing

Quantum search algorithm for Automated Test Pattern Generati...

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International Conference on VLSI

作者： Singh, A Deemed Univ Thapar Inst Engn & Technol Dept Comp Sci & Engn Patiala 147004 Punjab India

ISBN: (纸本)1932415106

This paper introduces a quantum search technique for Automated Test Pattern Generation (ATPG) to test the VLSI circuits. The VLSI testing is viewed as an optimization problem due to its complexity. The digital circuits are modeled as a neural network and the problem becomes to minimize the energy function of this neural network. The solution of the equation gives us the test vector. In this paper specific aspects of quantum theory like superposition and quantum parallelism are applied to this problem. The algorithm is so efficient that it requires only VS (where N is the total number of vectors) searches to find the desired test vector, as opposed to a search in classical computing, which on average needs N/2 searches. A comparison is made between exhaustive, simulated annealing and quantum based search techniques. Experimental results show that the quantum search algorithms are more efficient than classical algorithms and can be applied with more efficiency on quantum computers.

关键词： neural network quantum computer quantum search algorithms ATPG simulated annealing and VLSI

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Applying quantum search to Automated Test Pattern Generation for VLSI circuits

Applying quantum search to Automated Test Pattern Generation...

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4th International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT 2003)

作者： Singh, S Singh, A Deemed Univ Thaper Inst Engn & Technol Dept Comp Sci & Engn Patiala Punjab India

ISBN: (纸本)0780378407

This paper presents a quantum search algorithm for Automated Test Pattern Generation (ATPG) of combinatorial VLSI circuits. This problem can be viewed as an optimization problem because digital circuits can be modeled as a neural network. and the problem become to minimize the energy function of this neural network. The solution of the equation gives us the test vector. In this paper specific aspects of quantum theory like superposition and quantum parallelism are applied to this problem. In quantum search algorithm this is viewed as a searching problem where the search function (also called oracle) f (x)=1 if the value of the energy function of the neural network is 0 otherwise f (x)=0. quantum mechanics help us to search a group of items simultaneously from the search space rather than one item at a time. The algorithm so efficient that it requires only, on average, roughly rootN (where N is the total number of vectors) searches to find the desired test vector, as opposed to a search in classical computing, which on average needs N/2 searches. A comparison is made between exhaustive, simulated annealing and quantum based search techniques. Experimental results show that the quantum search algorithms are more efficient than classical algorithms and can be applied with more efficiency on a quantum computer.

关键词： ATPG neural network quantum computer quantum search algorithms simulated annealing and VLSI

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Perfect state transfer, equitable partition and continuous-time quantum walk based search

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quantum STUDIES-MATHEMATICS AND FOUNDATIONS 2024年第2期11卷 275-285页

作者： Ide, Yusuke Narimatsu, Akihiro Nihon Univ Coll Humanities & Sci Dept Math Tokyo Tokyo 1568550 Japan Univ Fukuchiyama Ctr Math & Data Sci Fukuchiyama Kyoto 6200886 Japan

In this paper, we consider a continuous-time quantum walk based search algorithm. We discuss equitable partition of the graph and perfect state transfer on it. By these two methods, we can calculate the success probability and the running time of the search algorithm. In addition, we gave some examples of graphs that we can calculate the success probability and the running time.

关键词： quantum walks quantum search algorithms Perfect state transfer Equitable partition

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Asymmetrical quantum Encryption Protocol Based on quantum search Algorithm

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China Communications 2014年第9期11卷 104-111页

作者： LUO Wenjun LIU Guanli College of Computer Science and Technology Chongqing University of Posts and TelecommunicationsChongqing 400065 Chongqing City P. R. China

quantum cryptography and quantum search algorithm are considered as two important research topics in quantum information *** asymmetrical quantum encryption protocol based on the properties of quantum one-way function and quantum search algorithm is *** on the no-cloning theorem and trapdoor one-way functions of the publickey,the eavesdropper cannot extract any private-information from the public-keys and the *** key-generation randomized logarithm to improve security of our proposed protocol,i.e.,one privatekey corresponds to an exponential number of *** unitary operations and the single photon measurement,secret messages can be directly sent from the sender to the *** security of the proposed protocol is proved that it is informationtheoretically ***,compared the symmetrical quantum key distribution,the proposed protocol is not only efficient to reduce additional communication,but also easier to carry out in practice,because no entangled photons and complex operations are required.

关键词： quantum cryptography asymmetrical encryption information-theoreticalsecurity quantum search algorithms

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search via quantum walks with intermediate measurements

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INTERNATIONAL JOURNAL OF MODERN PHYSICS B 2015年第19期29卷 1550127-1550127页

作者： Buksman, Efrain de Oliveira, Andre L. Fonseca Lopez de Lacalle, Jesus Garcia Univ ORT Uruguay Fac Ingn Bernard Wand Polaken Montevideo 11100 Uruguay Univ Politecn Madrid Escuela Tecn Super Ingn Sistemas Informat Madrid 28031 Spain

A modification of Tulsi's quantum search algorithm with intermediate measurements of the control qubit is presented. In order to analyze the effect of measurements in quantum searches, a different choice of the angular parameter is used. The study is performed for several values of time lapses between measurements, finding close relationships between probabilities and correlations (mutual information and cumulative correlation measure). The order of this modified algorithm is estimated, showing that for some time lapses the performance is improved, and becomes of order O(N) (classical brute-force search) when measurements are taken in every step. The results provide a possible way to analyze improvements to other quantum algorithms using one, or more, control qubits.

关键词： quantum search algorithms quantum walks projective measurements

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Image storage, retrieval, compression and segmentation in a quantum system

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quantum INFORMATION PROCESSING 2013年第6期12卷 2269-2290页

作者： Li, Hai-Sheng Zhu Qingxin Lan, Song Shen, Chen-Yi Zhou, Rigui Mo, Jia Univ Elect Sci & Technol China Sch Comp Sci & Engn Chengdu 611731 Sichuan Peoples R China East China JiaoTong Univ Coll Informat Engn Nanchang 330013 Jiangxi Peoples R China Wuhan Univ Comp Sch Wuhan 430072 Hubei Peoples R China

A set of quantum states for colors and another set of quantum states for coordinates are proposed in this paper to represent colors and coordinates of the pixels in an image respectively. We design an algorithm by which an image of pixels and different colors is stored in a quantum system just using qubits. An algorithm for quantum image compression is proposed. Simulation result on the Lena image shows that compression ratio of lossless is 2.058. Moreover, an image segmentation algorithm based on quantum search quantum search which can find all solutions in the expected times in is proposed, where is the number of pixels and is the number of targets to be segmented.

关键词： quantum image processing Image storage and retrieval Image compression Image segmentation quantum search algorithms quantum computation

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Applying quantum search to Automated Test Pattern Generation for VLSI Circuits

Applying Quantum Search to Automated Test Pattern Generation...

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The Fourth International Conference on Parallel and Distributed Computing, Applications and Technologies

作者： Sarbjeet Singh Amardeep Singh Department of Computer Science & Engineering Thapar Institute of Engineering & TechnologyDeemed UniversityPatialaPunjabINDIA.

ISBN: (纸本)0780378407

This paper presents a quantum search algorithm for Automated Test Pattern Generation（ATPG） of combinatorial VLSI *** problem can be viewed as an optimization problem because digital circuits can be modeled as a neural network and the problem become to minimize the energy function of this neural *** solution of the equation gives us the test *** this paper specific aspects of quantum theory like superposition and quantum parallelism are applied to this *** quantum search algorithm this problem is viewed as a searching problem where the search function （also called oracle） f（x）=l if the value of the energy function of the neural network is 0 otherwise f（x）=0. quantum mechanics help us to search a group of items simultaneously from the search space rather than one item at a *** *** efficient that it requires only, on average,roughly N（where N is the total number of vectors） searches to find the desired test vector,as opposed to a search in classical computing,which on average needs N/2 searches.A comparison is made between exhaustive,simulated annealing and quantum based search *** results show that the quantum search algorithms are more efficient than classical algorithms and can be applied with more efficiency on a quantum computer.

关键词： ATPG Neural Network quantum Computer quantum search algorithms Simulated Annealing and VLSI

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APPLYING quantum search TO AUTOMATED TEST PATTERN GENERATION FOR VLSI CIRCUITS

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INTERNATIONAL JOURNAL OF quantum INFORMATION 2003年第1期1卷 79-91页

作者： Singh, Amardeep Singh, Sarbjeet Deemed Univ Thapar Inst Engn & Technol Dept Comp Sci & Engn Patiala 147004 Punjab India Panjab Univ Univ Inst Engn & Technol Dept Software Engn Chandigarh 160014 India

This paper presents a quantum search algorithm for Automated Test Pattern Generation (ATPG) of VLSI circuits. For given digital circuits, a neural network is created that represents the digital gates with their interconnections as neurons. This neural network is characterized by an energy function E, which is the mathematics representation of neural network. The solution of the energy function gives us the test vector. The test vector is a combination of input values of digital circuits that detects a particular fault. In this paper, specific aspects of quantum theory like superposition and quantum parallelism are applied to find the solution of this energy function. The algorithm developed is so efficient that it requires only root N (where N is the total number of vectors) iterations to find the desired test vector whereas in classical computing, it takes N/2 iterations. At the end, a comparison is made between exhaustive, simulated annealing and quantum based techniques. Experimental results show that the quantum search algorithms are more efficient than classical algorithms and can be applied with more efficiency.

关键词： ATPG neural network quantum computer quantum search algorithms simulated annealing VLSI

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