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A Fixed-Phase Quantum Search Algorithm with More Flexible Behavior
School of Computer & Information Technology, Northeast Petroleum University, Daqing, China
School of Computer & Information Technology, Northeast Petroleum University, Daqing, China
- 1 School of Computer & Information Technology, Northeast Petroleum University, Daqing, China
- 2 School of Computer & Information Technology, Northeast Petroleum University, Daqing, China
Journal of Quantum Information Science·Volume 02 (2012)·Pages 28–34·Published 22 June 2012·DOI10.4236/jqis.2012.22006
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Abstract
When the Grover’s algorithm is applied to search an unordered database, the probability of success usually decreases with the increase of marked items. To address this phenomenon, a fixed-phase quantum search algorithm with more flexible behavior is proposed. In proposed algorithm, the phase shifts can be fixed at the different values to meet the needs of different practical problems. If research requires a relatively rapid speed, the value of the phase shifts should be appropriately increased, if search requires a higher success probability, the value of the phase shifts should be appropriately decreased. When the phase shifts are fixed at , the success probability of at least 99.38% can be obtained in iterations.
KeywordsQuantum ComputingQuantum SearchingGrover AlgorithmFixed Phase Shifting
- L. K. Grover, “A Fast Quantum Mechanical Algorithm for Database Search,” Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, Philadelphia, 22-24 May 1996, pp. 212-221.
- L. K. Grover, “Quantum Computers Can Search Rapidly by Using Any Transformation,” Physical Review Letters, Vol. 80, No. 19, 1998, pp. 4329-4332. doi:10.1103/PhysRevLett.80.4329
- G. L. Long, Y. S. Li and W. L. Zhang, “Phase Matching in Quantum Searching,” Physics Letters A, Vol. 262, No. 1, 1999, pp. 27-34. doi:10.1016/S0375-9601(99)00631-3
- G. L. Long, X. Li and Y. Sun, “Phase Matching Condition for Quantum Search with a Generalized Initial State,” Physics Letters A, Vol. 294, No. 3-4, 2002, pp. 143-152. doi:10.1016/S0375-9601(02)00055-5
- L. K. Grover, “Fixed-Point Quantum Search,” Physical Review Letters, Vol. 95, 2005, Article ID: 150501.
- D. F. Li, X. X. Li and H. T. Huang, “Phase Condition for the Grover Algorithm,” Theoretical and Mathematical Physics, Vol. 144, No. 3, 2005, pp. 1279-1287. doi:10.1007/s11232-005-0159-x
- A. Younes, et al., “Quantum Search Algorithm with More Reliable Behavior Using Partial Diffusion,” Quantum Communication, Vol. 734, 2006, pp. 171-174.
- G. L. Long, “Grover Algorithm with Zero Theoretical Failure Rate,” Physical Review A, Vol. 64, No. 2, 2001, Article ID: 022307. doi:10.1103/PhysRevA.64.022307
- A. Younes, “Fixed Phase Quantum Search Algorithm,” 2007. http://arxiv.org/pdf/0704.1585.pdf
- C. Cafaro and S. Mancini, “On Grover’s Search Algorithm from a Quantum Information Geometry Viewpoint”. Physica A, Vol. 391, No. 4, 2012, pp. 1610-1625. doi:10.1016/j.physa.2011.09.018
- H. Y. Li, C. W. Wu, W. T. Liu, et al., “Fast Quantum Search Algorithm for Databases of Arbitrary Size and Its Implementation in a Cavity QED System,” Physics Letters A, Vol. 375, No. 48, 2011, pp. 4249-4254. doi:10.1016/j.physleta.2011.10.016
- M. A. Nielsen and I. L. Chuang, “Quantum Computation and Quantum Information,” Cambridge University Press, Cambridge, 2000.