非对称量子行走是非对称经典随机行走在量子世界的对应,非对称性通过硬币操作和条件 行走体现。通过计算非对称量子行走的位置概率分布、回到原点的几率和位置平均值来表征其基 本性质。数值计算结果表明,一维链上的非对称量子行走是否具有可回复性与硬币初始状态的选择 及演化后分布是否对称无关,仅与非对称操作有关;一维经典随机行走只有分布对称时才具有可回 复性,这是量子行走区别于经典随机行走的显著特征之一。

Unbiased quantum walk corresponds to the classical asymmetric random walk in quantum world, and asymmetry is reflected by coin operation and conditional walk. The basic properties of unbiased quantum walk are characterized by calculating its position probability distribution, the probability and mean value back to the origin. Numerical results show that the recurrence property of unbiased quantum walk in one-dimensional chain is independent of the selection of coin initial state and whether the distribution after evolution is symmetric, but only related to asymmetric operation. One-dimensional classical random walk is recoverable only when it is distributed symmetrically. Different from classical random walk, it is one of the remarkable characteristics of quantum walk.