Grover Algorithm for Multi-objective Searching with Iteration Auto-controlling

Zhu, Wanning; Chen, Hanwu; Liu, Zhihao; Xue, Xilin

doi:10.1007/978-3-319-11857-4_41

Cited by 2 publications

(4 citation statements)

References 6 publications

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“…In addition, it was found that when the phase of the superposition state became negative for the first time, the amplitude value of the search target reached its maximum, and the positivity and negativity of the phase in front of the | + + • • • +⟩ component based on X determined the positivity and negativity of the phase of the superposition state in the paper. [13] Therefore, the phase detection gate can be used to estimate the positive and negative phase. The position where the detection gate moves in should be behind the Oracle operator, that is, when the Oracle operator is applied, the amplitude value of the target component is the largest when the phase and the first negative change.…”

Section: Composition Of the Algorithmmentioning

confidence: 99%

“…In the case that the number of target states is unknown, when the operator just iterates to the maximum amplitude of the target state, the algorithm can be stopped automatically. [13] Since search algorithms and algorithms that can be transformed into search problems have a wide range of applicability, after these pioneering articles, scholars have conducted in-depth research. In China, Long [14] constantly improve Grover search algorithm; Sheng, [15][16][17] Zhou et al [18][19][20][21] also in the field of quantum search algorithm and quantum computing have made efforts.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum walk search algorithm for multi-objective searching with iteration auto-controlling on hypercube

Jiang¹,

Chu²,

Zhang³

et al. 2022

Chinese Phys. B

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Shenvi et al. have proposed a quantum algorithm based on quantum walking called Shenvi–Kempe–Whaley (SKW) algorithm, but this search algorithm can only search one target state and use a specific search target state vector. Therefore, when there are more than two target nodes in the search space, the algorithm has certain limitations. Even though a multi-objective SKW search algorithm was proposed later, when the number of target nodes is more than two, the SKW search algorithm cannot be mapped to the same quotient graph. In addition, the calculation of the optimal target state depends on the number of target states m. In previous studies, quantum computing and testing algorithms were used to solve this problem. But these solutions require more Oracle calls and cannot get a high accuracy rate. Therefore, to solve the above problems, we improve the multi-target quantum walk search algorithm, and construct a controllable quantum walk search algorithm under the condition of unknown number of target states. By dividing the Hilbert space into multiple subspaces, the accuracy of the search algorithm is improved from p c = (1/2) – O(1/n) to p c = 1 – O(1/n). And by adding detection gate phase, the algorithm can stop when the amplitude of the target state becomes the maximum for the first time, and the algorithm can always maintain the optimal number of iterations, so as to reduce the number of unnecessary iterations in the algorithm process and make the number of iterations reach t f = ( π / 2 ) 2 n − 2 .

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Section: Composition Of the Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum walk search algorithm for multi-objective searching with iteration auto-controlling on hypercube

Jiang¹,

Chu²,

Zhang³

et al. 2022

Chinese Phys. B

View full text Add to dashboard Cite

show abstract

“…In recent years, there has been substantial research focusing on enhancing Grover's algorithm for various applications. [31][32][33][34][35][36][37] These proposed methods have limited efficacy when it comes to solving the minimum dominating set problem. For instance, the approaches described in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the design complexity associated with the phase gate in Ref. [32] presents challenges. As an alternative, Aaronson and Rall presented an approximate counting algorithm in Ref.…”

Section: Introductionmentioning

confidence: 99%

Quantum algorithm for minimum dominating set problem with circuit design

Zhang 张,

Wang 王,

Liu 刘

et al. 2024

Chinese Phys. B

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In recent years, with the development of quantum computing, using quantum algorithms to solve various problems has attracted widespread attention. Researchers are particularly interested in using the acceleration properties of quantum algorithms to solve NP-complete problems. This paper focuses on the well-known NP-complete problem of finding the minimum dominating set in undirected graphs. To expedite the search process, a quantum algorithm employing Grover’s search is proposed. However, a challenge arises from the unknown number of solutions for the minimum dominating set, rendering direct usage of the original Grover’s search impossible. Thus, a swap test method is introduced to ascertain the number of iterations required. The oracle, diffusion operators, and swap test are designed with achievable quantum gates. The query complexity is O(1.414 n ) and the space complexity is O(n). To validate the proposed approach, qiskit software package is employed to simulate the quantum circuit, yielding the anticipated results.

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Grover Algorithm for Multi-objective Searching with Iteration Auto-controlling

Cited by 2 publications

References 6 publications

Quantum walk search algorithm for multi-objective searching with iteration auto-controlling on hypercube

Quantum walk search algorithm for multi-objective searching with iteration auto-controlling on hypercube

Quantum algorithm for minimum dominating set problem with circuit design

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