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General quantum Meet-in-the-Middle search algorithm Based on Target Solution of Fixed Weight

Communications in Theoretical Physics 2016年第4期66卷 401-406页

作者： Fu Xiangqun Bao Wansu Wang Xiang Shi Jianhong Informat Engn Univ Zhengzhou 450004 Peoples R China

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 Sigma(d)(j=0) (O (\/C-n-k+1(d-j) + O(C-k(j) log C-k(j)) with Sigma(d)(i=0) C-k(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.

关键词： quantum search algorithm meet-in-the-middle public-key crypto knapsack problem

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Implementation of efficient quantum search algorithms on NISQ computers

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quantum INFORMATION PROCESSING 2021年第7期20卷 233-233页

作者： Zhang, Kun Rao, Pooja Yu, Kwangmin Lim, Hyunkyung Korepin, Vladimir SUNY Stony Brook Dept Chem Stony Brook NY 11794 USA Math Sci Res Inst 1000 Centennial Dr Berkeley CA 94720 USA Brookhaven Natl Lab Computat Sci Initiat Upton NY 11973 USA SUNY Stony Brook Dept Appl Math & Stat Stony Brook NY 11794 USA SUNY Stony Brook CN Yang Inst Theoret Phys Stony Brook NY 11794 USA

Despite the advent of Grover's algorithm for the unstructured search, its successful implementation on near-term quantum devices is still limited. We apply three strategies to reduce the errors associated with implementing quantum search algorithms. Our improved search algorithms have been implemented on the IBM quantum processors. Using them, we demonstrate three- and four-qubit search algorithm with higher average success probabilities compared to previous works. We present the successful execution of the five-qubit search on the IBM quantum processor for the first time. The results have been benchmarked using degraded ratio, which is the ratio between the experimental and the theoretical success probabilities. The fast decay of the degraded ratio supports our divide-and-conquer strategy. Our proposed strategies are also useful for implementation of quantum search algorithms in the post-NISQ era.

关键词： quantum search algorithm Depth optimization Error mitigation NISQ

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quantum search in structured database using local adiabatic evolution and spectral methods

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quantum INFORMATION PROCESSING 2013年第8期12卷 2813-2831页

作者： Sufiani, R. Bahari, N. Univ Tabriz Dept Theoret Phys & Astrophys Tabriz 51664 Iran Inst Studies Theoret Phys & Math Tehran 193951795 Iran

Since Grover's seminal work which provides a way to speed up combinatorial search, quantum search has been studied in great detail. We propose a new method for designing quantum search algorithms for finding a marked element in the state space of a graph. The algorithm is based on a local adiabatic evolution of the Hamiltonian associated with the graph. The main new idea is to apply some techniques such as Krylov subspace projection methods, Lanczos algorithm and spectral distribution methods. Indeed, using these techniques together with the second-order perturbation theory, we give a systematic method for calculating the approximate search time at which the marked state can be reached. That is, for any undirected regular connected graph which is considered as the state space of the database, the introduced algorithm provides a systematic and programmable way for evaluation of the search time, in terms of the corresponding graph polynomials.

关键词： quantum search algorithm Local adiabatic evolution Graph Krylov subspace Lanczos algorithm Spectral distribution Second-order perturbation theory

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Fast quantum search driven by environmental engineering

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Communications in Theoretical Physics 2022年第4期74卷 31-41页

作者： Rui Zhang Tian Chen National Engineering Laboratory for Risk Perception and Prevention(NEL-RPP) CAEITBeijing 100041China Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems School of PhysicsBeijing Institute of TechnologyBeijing 100081China

Studies have demonstrated that a joined complete graph is a typical mathematical model that can support a fast quantum search. In this paper, we study the implementation of joined complete graphs in atomic systems and realize a quantum search of runtime ■ based on this implementation with a success probability of 50%. Even though the practical systems inevitably interact with the surrounding environment, we reveal that a successful quantum search can be realized through delicately engineering the environment itself. We consider that our study will bring about a feasible way to realize quantum information processing including quantum algorithms in reality.

关键词： quantum walk quantum search algorithm environmental engineering non-Markovian

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quantum search-Aided Multi-User Detection for Sparse Code Multiple Access

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IEEE ACCESS 2019年 7卷 52804-52817页

作者： Ye, Wenjing Chen, Wei Guo, Xin Sun, Chen Hanzo, Lajos Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China Sony China Ltd Sony China Res Lab Beijing 100028 Peoples R China Univ Southampton Sch Elect & Comp Sci Southampton SO17 1BJ Hants England

With the explosive proliferation of mobile devices, the scarcity of communication resources has emerged as a critical issue in the next generation (NG) communication systems. To overcome this, non-orthogonal multiple access (NOMA) has been shown to provide a beneficial spectral effi ciency gain, while supporting massive connectivity. Sparse code multiple access (SCMA) is one of the NOMA schemes, but its application is hampered by its high-complexity multi-user detection. Fortunately, quantum search techniques were shown to substantially reduce the complexity of multi-user detectors (MUD). However, the quantum search-aided multiuser detection of SCMA is an open problem at the time of writing. Hence, we conceive a pair of quantum search-aided MUDs for SCMA, namely, a quantum-assisted message passing algorithm (Q-MPA)-based MUD and a quantum-assisted sphere decoder-based MPA (QSD-MPA) MUD.

关键词： Sparse code multiple access multiuser detection quantum search algorithm message passing algorithm sphere decoder

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Formulation of a family of sure-success quantum search algorithms

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INTERNATIONAL JOURNAL OF quantum INFORMATION 2004年第3期2卷 285-293页

作者： Hsieh, JY Li, CM Lin, JS Chuu, DS Ming Hsin Univ Sci & Technol Dept Mech Engn Hsinchu 30401 Taiwan Natl Chiao Tung Univ Inst Electrophys Hsinchu 30050 Taiwan Natl Chiao Tung Univ Dept Electrophys Hsinchu 30050 Taiwan Lien Ho Inst Technol Dept Mech Engn Maioli 36012 Taiwan

In this work, we consider a family of sure-success quantum algorithms, which is grouped into even and odd members for solving a generalized Grover search problem. We prove the matching conditions for both groups and give the corresponding formulae for evaluating the iterations or oracle calls required in the search computation. We also present how to adjust the phase angles in the generalized Grover operator to ensure the sure-success if minimal oracle calls axe demanded in the search.

关键词： quantum search algorithm

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search an unsorted database with quantum mechanics

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中国高等学校学术文摘·计算机科学 2007年第3期1卷 247-271页

作者： LONG Guilu LIU Yang Key Laboratory for Atomic and Molecular Nanosciences of Ministry of Eduation Department of PhysicsTsinghua UniversityBeijing 100084China Tsinghua National Laboratory for Information Science and Technology Tsinghua UniversityBeijing 100084China

In this article,we review quantum search algorithms for unsorted database search *** database search is a very important problem in science and *** a quantum computer,a marked state can be found with very high probability using the Grover's algorithm,or exactly with the Long *** review the Grover algorithm and related *** particular,we review the phase matching conditions in quantum search *** issues that may cause confusion about the quantum search algorithm are also clarified.

关键词： quantum search algorithm Grover algorithm Long algorithm Phase matching quantum amplitude amplification duality computer

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An efficient quantum search engine on unsorted database

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quantum INFORMATION PROCESSING 2013年第10期12卷 3265-3274页

作者： Lu, Songfeng Zhang, Yingyu Liu, Fang Huazhong Univ Sci & Technol Sch Comp Sci & Technol Wuhan 430074 Peoples R China Liaocheng Univ Sch Comp Sci Liaocheng 250000 Shandong Peoples R China

We consider the problem of finding one or more desired items out of an unsorted database. Patel has shown that if the database permits quantum queries, then mere digitization is sufficient for efficient search for one desired item. The algorithm, called factorized quantum search algorithm, presented by him can locate the desired item in an unsorted database using O() queries to factorized oracles. But the algorithm requires that all the attribute values must be distinct from each other. In this paper, we discuss how to make a database satisfy the requirements, and present a quantum search engine based on the algorithm. Our goal is achieved by introducing auxiliary files for the attribute values that are not distinct, and converting every complex query request into a sequence of calls to factorized quantum search algorithm. The query complexity of our algorithm is O() for most cases.

关键词： quantum search model quantum computation Database search quantum search algorithm

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Data search algorithms based on quantum Walk

Data Search Algorithms based on Quantum Walk

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International MultiConference of Engineers and Computer Scientists (IMECS 2012)

作者： Fujisaki, Masataka Miyajima, Hiromi Shigei, Noritaka Kagoshima Univ Grad Sch Sci & Engn 1-21-40 Korimoto Kagoshima 8900065 Japan

ISBN: (纸本)9789881925114

For searching any item in an unsorted database with N items, a classical computer takes O(N) steps but Grover's quantum searching algorithm takes only O(root N) steps. However, it is also known that Grover's algorithm is effective only in the case where the initial amplitude distribution of dataset is uniform, but is not always effective in the non-uniform case. In this paper, we propose some quantum search algorithms. First, we propose an algorithm in analog time based on quantum walk by solving the schrodinger equation. The proposed algorithm shows best performance in optimum time. Next, we will apply the result to Grover search algorithm. It is shown that the proposed algorithm shows better performance than the conventional one. Further, we propose the improved algorithm by introducing the idea of the phase rotation. The algorithm shows best performance compared with the conventional ones.

关键词： quantum search algorithm Grover search algorithm initial amplitude distributions of dataset observed probability

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quantum dialogue protocol based on Grover's search algorithms

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MODERN PHYSICS LETTERS A 2019年第21期34卷

作者： Yin, Aihan He, Kemeng Fan, Ping East China Jiao Tong Univ Dept Informat Engn Shuanggang Rd 808 Nanchang 330013 Jiangxi Peoples R China

Among many classic heuristic search algorithms, the Grover quantum search algorithm (QSA) can play a role of secondary acceleration. Based on the properties of the two-qubit Grover QSA, a quantum dialogue (QD) protocol is proposed. In addition, our protocol also utilizes the unitary operations and single-particle measurements. The transmitted quantum state (except for the decoy state used for detection) can transmit two-bits of security information simultaneously. Theoretical analysis shows that the proposed protocol has high security.

关键词： quantum search algorithm quantum dialogue controlled-not gate

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