相位不匹配的量子搜索算法

Phase-Unmatched Quantum Search Algorithm

当搜索空间局限在二维复子空间中时,如果无序数据库中的总个数足够大,那么倘若任意的两个完全独立的相位旋转角集合(但其中一个集合中元素的个数相对于无序数据库中的总个数相对较小)满足多相位匹配方程,则仍然能以较高的成功概率找到唯一的目标态.本文针对一种带有特定前提条件的量子搜索问题,说明了可通过结合多相位匹配方程和经典的穷举算法以使得该目标态能以几乎接近100%的成功概率找到.最后给出了一个实例.

For the case when the search space is confined to a two-dimensional complex subspace,if the total number of an unsorted database is sufficiently large,then a unique desired state can still be found with high success probability provided any two sets of phase rotation angles, which arc completely independent （unrelated to each other ） but the number of elements in one of the sets is relatively small compared to the total number of an unsorted database,satisfy the multiphase matching equation. In this paper we showed that for a quantum search problem with some specific requirements, one may combine the multiphase matching equation and the classical exhaustive algorithm such that a unique desired state can be found with success probabi/ity almost close to unity. Finally, we gave a numerical example.