- 综合性科技类中文核心期刊
- 中国科技论文统计源期刊
- 中国科学引文数据库来源期刊
- 中国学术期刊文摘数据库（核心版）来源期刊
- 中国学术期刊综合评价数据库来源期刊
| Citation: |
XIAO Hong, LIU Xintong, LI Panchi. Flexibly Fixed Phase Quantum Search Algorithm[J]. Journal of Beijing University of Technology, 2023, 49(6): 630-638. DOI: 10.11936/bjutxb2022090046
|
To address the problem that the universality of Grover's algorithm is not ideal, a flexible quantum search algorithm was proposed in this paper. The flexibility of the proposed algorithm was manifested in three aspects. First, by designing quantum equilibrium superposition states containing any number of basis states, the construction method of unordered database of any size was given. Second, by solving the iterative equation of the algorithm, the quantitative relationship between the rotation phase and the success probability and the number of search steps was derived, where the rotation phase could take any value within (0, π]. Third, through the statistical analysis of iteration steps and success probability, the optimal value of rotation phase was determined when the number of marked states was unknown, and the search scheme was designed. Finally, the numerical results of the probability of success and the number of iteration steps under different rotation phases and different numbers of marked states were investigated. The theoretical analysis shows that the proposed algorithm leads to a square-root speedup over the corresponding classical algorithm.
| [1] |
GROVER L K. A fast quantum mechanical algorithm for database search[C]//Proc of the 28th Annual ACM Symp on Theory of Computing. New York: ACM Press, 1996: 212-219.
|
| [2] |
CHI D U, KIM J. Quantum database searching by a single query[J/OL]. arXive, 1997[2022-09-20]. https://doi.org/10.48550/arXiv.quant-ph/9708005.
|
| [3] |
GROVER L K. Quantum search on structured problems[J]. Chaos, Solitons & Fractals, 1999, 10(10): 1695-1705.
|
| [4] |
LONG G L, LI Y S, ZHANG W L, et al. Phase matching in quantum searching[J]. Physics Letters A, 1999, 262(1): 27-34. doi: 10.1016/S0375-9601(99)00631-3
|
| [5] |
LONG G L, LI X, SUN Y. Phase matching condition for quantum search with a generalized initial state[J]. Physics Letters A, 2002, 294(3/4): 143-152.
|
| [6] |
HOYER P. Arbitrary phases in quantum amplitude amplification[J/OL]. Physical Review A, 2000, 62: 052304[2022-09-20]. https://doi.org/10.1103/PhysRevA.62.052304.
|
| [7] |
LI D F, LI X X. More general quantum search algorithm Q=IγVIτU and the precise formula for the amplitude and the non-symmetric effects of different rotating angles[J]. Physics Letters A, 2001, 287(5/6): 304-316.
|
| [8] |
LI D F, LI X X, HUANG H T. Phase condition for the Grover algorithm[J]. Theoretical and Mathematical Physics, 2005, 144(3): 1279-1287. doi: 10.1007/s11232-005-0159-x
|
| [9] |
LONG G L, ZHANG W L, LI Y S, et al. Arbitrary phase rotation of the marked state can not be used for Grover's quantum search algorithm[J]. Communications in Theoretical Physics, 1999, 32(3): 335-341. doi: 10.1088/0253-6102/32/3/335
|
| [10] |
LONG G L, TU C C, LI Y S, et al. A novel SO(3) picture for quantum searching[J/OL]. arXiv, 1999[2022-09-20]. https://doi.org/10.48550/arXiv.quant-ph/9911004
|
| [11] |
LONG G L. Grover algorithm with zero theoretical failure rate[J/OL]. Physical Review A, 2001, 64: 022307[2022-09-20]. https://doi.org/10.1103/PhysRevA.64.022307.
|
| [12] |
TOYAMA F M, DIJK W V, NOGAMI Y. Quantum search with certainty based on modified Grover algorithms: optimum choice of parameters[J]. Quantum Inf Process, 2013, 12(10): 1897-1914.
|
| [13] |
GROVER L K. Fixed-point quantum search[J/OL]. Physical Review Letters, 2005, 95: 150501[2022-09-20]. https://doi.org/10.48550/arXiv.quant-ph/0505007.
|
| [14] |
LI D F, Li X R, HUANG H T, et al. Fixed-point quantum search for different phase shifts[J]. Physics Letters A, 2007, 362(4/5): 260-264.
|
| [15] |
YOUNES A. Fixed phase quantum search algorithm[J/OL]. arXive, 2007[2022-09 -20]. https://doi.org/10.48550/arXiv.0704.1585
|
| [16] |
BRION D, BIHAM O, BIHAM E, et al. Generalized Grover search algorithm for arbitrary initial amplitude distribution[J/OL]. arXive, 1998[2022-09-20]. https://doi.org/10.48550/arXiv.quant-ph/9801066.
|
| [17] |
BIHAM E, BIHAM O, BIRON D, et al. Analysis of generalized Grover's quantum search algorithms using recursion equations[J/OL]. Physical Review A, 2001, 63: 012310[2022-09-20]. https://doi.org/10.1103/PhysRevA.63.012310.
|
| [18] |
GROVER L K. Quantum computers can search rapidly by using almost any transformation[J]. Physical Review Letters, 1998, 80(19): 4329-4332. doi: 10.1103/PhysRevLett.80.4329
|
| [19] |
TULSI A. Quantum computers can search rapidly by using almost any selective transformation[J/OL]. Physical Review A, 2008, 78: 022332[2022-09-20]. https://doi.org/10.1103/PhysRevA.78.022332.
|
| [20] |
BOYER M, HOYER P, TAPP A. Tight bounds on quantum searching[J]. Fortschritte der Physik Progress of Physics, 1998, 46(4/5): 493- 505.
|
| [21] |
DURR C, HOYER P. A quantum algorithm for finding the minimum[J/OL]. arXive, 1996[2022-09-20]. https://doi.org/10.48550/arXiv.quant-ph/9607014.
|
| [22] |
BRASSARD G, HOYER P, TAPP A. Quantum counting[J/OL]. arXiv, 1998[2022-09-20]. https://doi.org/10.48550/arXiv.quant-ph/9805082.
|
| [23] |
GIRI P R, KOREPIN V E. A review on quantum search algorithms[J]. Quantum Inf Process, 2017, 16(12): 1-36.
|
| [24] |
WILLIAN N N, SONG X Y, YANG G W, et al. Optimal synthesis of multiple output boolean functions using a set of quantum gates by symbolic reachability analysis[J]. IEEE Transactions on Computer-aided Design of Integrated Circuits and Systems, 2006, 25(9): 1652-1663. doi: 10.1109/TCAD.2005.858352
|
| [25] |
BARENCO A, BENNETT C H, CLEVE R, et al. Elementary gates for quantum computation[J]. Physical Review A, 1995, 52(5): 3457-3467.
|
| 1. |
肖红，刘新彤. 基于Hamming距离和量子搜索算法的联想分类器设计. 吉林大学学报(理学版). 2024(06): 1426-1438 .
|
Supported by: Beijing Renhe Information Technology Co., Ltd. 
DownLoad: