普适投币算符作用的量子行走数值解以及安德森局域化仿真  

The Numerical Solution of Quantum Walk with General Coin Operator and Simulation Anderson Localization

作　　者：任春年[1,2] 李文东[1] 顾永建[1] 

机构地区：[1]中国海洋大学信息科学与工程学院,山东青岛266100 [2]青岛科技大学信息科学技术学院,山东青岛266061

出　　处：《中国海洋大学学报（自然科学版）》2017年第4期121-125,共5页Periodical of Ocean University of China

基　　金：国家自然科学基金项目(61402246);中国博士后基金项目(2013M531771)资助~~

摘　　要：量子行走在量子计算与量子系统仿真方面具有重要的应用价值,因而成为当前量子信息领域研究的热点之一。但量子行走的数值解和解析解,尤其是高维量子行走相关解的研究工作还比较少。另外,近期的研究表明:量子行走可用于模拟物理系统中十分重要的安德森局域化现象,因此研究普适投币情况下的量子行走的解具有一定的科研价值。本文在现有的一维普适算符基础上,通过直积的方式构造了二维普适投币算符,给出了其数值解,并利用数值解对二维的安德森局域化现象进行了仿真。为普适投币情况下的量子行走及安德森局域化提供了理论研究的工具。Quantum walk in the fields such as quantum computation and quantum simulator have im- portant application. Recent studies show that the general quantum walk can be used to simulate ex- tremely important Anderson localization phenomenon. The theory and experiment on quantum walk in one dimensional have been relatively comprehensive discussion, but the condition of the high dimensional quantum walk is still scarce. The article uses one dimensional universal operator to construct two-di- mensional universal coin operator, and derives the numerical solution. Finally the article accomplishs the simulation of two-dimensional Anderson localization. At first, we derive a pervasive matrix representation of one-dimensional quantum walk＇s coin, and use the general coin to calculate the recursive solution of one-dimensional quantum walks, then, the general quantum walk can be simulated by the recursive solution in our paper. Secendly, we use the method of the direct product to construct the pervasive coin of two-dimensional quantum walk. The recursive solu- tion of two-dimensional quantum walk can be used to perform the simulation algorithms, and the simula- tion results show that quantum walk occer disorder in using the general coin and Anderson localization is obtained. The analytical solutions of this paper can be used to further discusse three-dimeasional quan- tum walks, construction of a experimental physical system which is used to simulate Anderson localiza- tion and delocalization.

关 键 词：量子行走 普适投币算符 安德森局域化 量子仿真 

分 类 号：O431.2[机械工程—光学工程]