A Four-Phase Improvement of Grover's Algorithm

作者:Ma, Bo-Wen; Bao, Wan-Su*; Li, Tan; Li, Feng-Guang; Zhang, Shuo; Fu, Xiang-Qun
来源:Chinese Physics Letters, 2017, 34(7): 070305.
DOI:10.1088/0256-307X/34/7/070305

摘要

When applying Grover's algorithm to an unordered database, the probability of obtaining correct results usually decreases as the quantity of target increases. A four-phase improvement of Grover's algorithm is proposed to fix the deficiency, and the unitary and the phase-matching condition are also proposed. With this improved scheme, when the proportion of target is over 1/3, the probability of obtaining correct results is greater than 97.82% with only one iteration using two phases. When the computational complexity is. O(root M/N), the algorithm can succeed with a probability no less than 99.63%.