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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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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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The quantum search algorithms for All Solutions

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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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Constructing approximately diagonal quantum gates

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INTERNATIONAL JOURNAL OF quantum INFORMATION 2022年第8期20卷 2250025-2250025页

作者： Griffin, Colton Cui, Shawn X. Purdue Univ Dept Math 150 N Univ St W Lafayette IN 47907 USA Purdue Univ Dept Phys & Astron 150 N Univ St W Lafayette IN 47907 USA

We study a method of producing approximately diagonal 1-qubit gates. For each positive integer, the method provides a sequence of gates that are defined iteratively from a fixed diagonal gate and an arbitrary gate. These sequences are conjectured to converge to diagonal gates doubly exponentially fast and are verified for small integers. We systemically study this conjecture and prove several important partial results. Some techniques are developed to pave the way for a final resolution of the conjecture. The sequences provided here have applications in quantum search algorithms, quantum circuit compilation, generation of leakage-free entangled gates in topological quantum computing, etc.

关键词： quantum search algorithms topological quantum computing leakage-free entangled gates quantum circuits

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Multiparty quantum key agreement based on Grover's algorithm and its implementation

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MODERN PHYSICS LETTERS A 2018年第36期33卷

作者： Yin, Aihan Han, Zhifei East China JiaoTong Univ Dept Informat Engn Shuanggang Rd 808 Nanchang 330013 Jiangxi Peoples R China

Multiparty quantum key agreement (MQKA) is a significant topic that the shared key must be negotiated equally by all participants. In this paper, we use Bell state as quantum resource and add controlled-not gate to avoid information leakage. There is very little research on the quantum key agreement protocol based on quantum search algorithms. Therefore, we propose a quantum key agreement protocol which is based on Grover's algorithm as one of the most famous quantum search algorithms. The security analysis appears very promising.

关键词： Multiparty quantum key agreement quantum search algorithms Grover's algorithm controlled-not gate security analysis

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quantum Walks on Two-Dimensional Grids with Multiple Marked Locations

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INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE 2018年第4期29卷 687-700页

作者： Nahimovs, Nikolajs Rivosh, Alexander Univ Latvia Fac Comp Raina Bulv 19 LV-1586 Riga Latvia

The running time of a quantum walk search algorithm depends on both the structure of the search space (graph) and the configuration (the placement and the number) of marked locations. While the first dependence has been studied in a number of papers, the second dependence remains mostly unstudied. We study search by quantum walks on the two-dimensional grid using the algorithm of Ambainis, Kempe and Rivosh [3]. The original paper analyses one and two marked locations only. We move beyond two marked locations and study the behaviour of the algorithm for several configurations of multiple marked locations. In this paper, we prove two results showing the importance of how the marked locations are arranged. First, we present two placements of k marked locations for which the number of steps of the algorithm differs by a factor of (Omega(root K). Second, we present two configurations of k and root k marked locations having the same number of steps and probability of finding a marked location.

关键词： quantum walks search multiple marked locations complexity gap 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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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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Low-Complexity Iterative quantum Multi-User Detection in SDMA systems

Low-Complexity Iterative Quantum Multi-User Detection in SDM...

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IEEE International Conference on Communications (ICC)

作者： Botsinis, Panagiotis Ng, Soon Xin Hanzo, Lajos Univ Southampton Elect & Comp Sci Southampton SO17 1BJ Hants England

ISBN: (纸本)9781479920037

The potentially excessive complexity of the Maximum Likelihood Multi-User Detector (ML MUD) in large-scale Spatial Division Multiple Access (SDMA) systems dictates the employment of low-complexity sub-optimal MUDs in the context of conventional systems. However, this limitation was circumvented by the recently proposed Durr-Hoyer Algorithm (DHA)-aided quantum Weighted Sum Algorithm (QWSA)-based quantum Multi-User Detector (QMUD) employed for performing optimal ML iterative detection in SDMA systems. Focusing our attention on the QWSA, we analyse the QMUD and the evolution of the quantum system with the aid of a simple SDMA uplink scenario. We characterize the performance of the DHA-QWSA QMUD advocated, which is capable of matching the performance of the ML MUD both in terms of its EXIT charts and BER curves.

关键词： Computational Complexity quantum Computing quantum search algorithms Spatial Division Multiple Access

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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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