Localization of quantum walks on finite graphs

doi:10.1088/1674-1056/25/12/120303

中国物理B ›› 2016, Vol. 25 ›› Issue (12): 120303-120303.doi: 10.1088/1674-1056/25/12/120303

Localization of quantum walks on finite graphs

Yang-Yi Hu(胡杨熠), Ping-Xing Chen(陈平形)

Department of Applied Physics, National University of Defense Technology, Changsha 410073, China

收稿日期:2016-05-12 修回日期:2016-08-17 出版日期:2016-12-05 发布日期:2016-12-05
通讯作者: Ping-Xing Chen E-mail:pxchen@nudt.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11174370).

Localization of quantum walks on finite graphs

Yang-Yi Hu(胡杨熠), Ping-Xing Chen(陈平形)

Department of Applied Physics, National University of Defense Technology, Changsha 410073, China

Received:2016-05-12 Revised:2016-08-17 Online:2016-12-05 Published:2016-12-05
Contact: Ping-Xing Chen E-mail:pxchen@nudt.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11174370).

摘要/Abstract

摘要：

We analyze the localization of quantum walks on a one-dimensional finite graph using vector-distance. We first vectorize the probability distribution of a quantum walker in each node. Then we compute out the probability distribution vectors of quantum walks in infinite and finite graphs in the presence of static disorder respectively, and get the distance between these two vectors. We find that when the steps taken are small and the boundary condition is tight, the localization between the infinite and finite cases is greatly different. However, the difference is negligible when the steps taken are large or the boundary condition is loose. It means quantum walks on a one-dimensional finite graph may also suffer from localization in the presence of static disorder. Our approach and results can be generalized to analyze the localization of quantum walks in higher-dimensional cases.

关键词: localization of quantum walks, vector distance, static disorder, boundary conditions

Abstract:

Key words: localization of quantum walks, vector distance, static disorder, boundary conditions

中图分类号: (Quantum algorithms, protocols, and simulations)

03.67.Ac

胡杨熠, 陈平形. Localization of quantum walks on finite graphs[J]. 中国物理B, 2016, 25(12): 120303-120303.

Yang-Yi Hu(胡杨熠), Ping-Xing Chen(陈平形). Localization of quantum walks on finite graphs[J]. Chin. Phys. B, 2016, 25(12): 120303-120303.

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Localization of quantum walks on finite graphs

Localization of quantum walks on finite graphs

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