Directional quantum random walk induced by coherence

作     者：Jin-Fu Chen Yu-Han Ma Chang-Pu Sun Jin-Fu Chen;Yu-Han Ma;Chang-Pu Sun

作者机构：Beijing Computational Science Research CenterBeijing 100193China Graduate School of China Academy of Engineering PhysicsNo.10 Xibeiwang East RoadHaidian DistrictBeijing 100193China 

出 版 物：《Frontiers of physics》 (物理学前沿（英文版）)

年 卷 期：2020年第15卷第2期

页      面：13-25页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

基　　金：国家973计划 国家自然科学基金 国家自然科学基金委员会-中国工程物理研究院“NSAF联合基金” 

主　　题：quantum walk random walk ensemble interpretation directional walking coherence 

摘      要：Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation between different steps in QW and leads to a non-binomial position distribution. In this paper, we propose an alternative quantum extension of CRW from the ensemble interpretation, named quantum random walk (QRW), where the walker has many unrelated coins, modeled as two-level systems, initially prepared in the same state. We calculate the walker s position distribution in QRW for different initial coin states with the coin operator chosen as Hadamard matrix. In one-dimensional case, the walker s position is the asymmetric binomial distribution. We further demonstrate that in QRW, coherence leads the walker to perform directional movement. For an initially decoherenced coin state, the walker s position distribution is exactly the same as that of CRW. Moreover, we study QRW in 2D lattice, where the coherence plays a more diversified role in the walker s position distribution.