文章基本信息

标题：Adaptive Phase Matching in Grover's algorithm with Weighted Targets
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作者：Shuyun Yang ; Panchi Li
期刊名称：International Journal of Computer and Information Technology
印刷版ISSN：2279-0764
出版年度：2014
卷号：3
期号：1
页码：71
出版社：International Journal of Computer and Information Technology
摘要：When the Grover's algorithm is applied to search an unordered database, the difference in marked items is not taken into consideration. When the fraction of marked items is greater than 1/4, the successful probability rapidly decreases with the increase of marked items, and when the fraction of marked items is greater than 1/2, the algorithm is disabled. Aiming at these two problems, first, an improved Grover's algorithm with the weighted targets is proposed in which each target is endowed a weight coefficient according to its significance. Using these weight coefficients, we rewrite the targets as a quantum superposition, which can make the probability for getting each target is approximately equal to its weight coefficient. Secondly, the adaptive phase matching is proposed based on the weighted targets, in which the directions of two phase rotations are contrary, and the amplitudes of two phase rotations are determined by the inner-product of the target quantum superposition and the initial state of system. When this inner- product is greater than 0.3090, the successful probability is equal to 1 with at most two Grover iterations. The validity of the improved quantum searching algorithm and the new phase matching are verified by two search examples.
关键词：quantum computing; quantum searching; Grover's ; algorithm; weighted target; phase matching