A two-dimensional quantum walk driven by a single two-side coin

doi:10.1088/1674-1056/abaee8

中国物理B ›› 2020, Vol. 29 ›› Issue (11): 110303-.doi: 10.1088/1674-1056/abaee8

所属专题： SPECIAL TOPIC — Quantum computation and quantum simulation

Quan Lin(林泉)¹, Hao Qin(秦豪)², Kun-Kun Wang(王坤坤)¹, Lei Xiao(肖磊)¹, Peng Xue(薛鹏)¹^,^‡

收稿日期:2020-06-30 修回日期:2020-08-04 接受日期:2020-08-13 出版日期:2020-11-05 发布日期:2020-11-03

A two-dimensional quantum walk driven by a single two-side coin

Quan Lin(林泉)^{1, †}, Hao Qin(秦豪)^{2, †} Kun-Kun Wang(王坤坤)¹, Lei Xiao(肖磊)¹, and Peng Xue(薛鹏)^{1,, ‡}

1 Beijing Computational Science Research Center, Beijing 100084, China
2 Department of Physics, Southeast University, Nanjing 211189, China

Received:2020-06-30 Revised:2020-08-04 Accepted:2020-08-13 Online:2020-11-05 Published:2020-11-03
Contact: ^†These authors contributed equally. ^‡Corresponding author. E-mail: gnep.eux@gmail.com
Supported by:
the National Natural Science Foundation of China (Grant Nos. 11674056 and U1930402) and the startup fund from Beijing Computational Science Research Center. KKW acknowledges support from the Project funded by China Postdoctoral Science Foundation (Grant No. 2019M660016).

摘要/Abstract

Abstract:

We study a two-dimensional quantum walk with only one walker alternatively walking along the horizontal and vertical directions driven by a single two-side coin. We find the analytical expressions of the first two moments of the walker’s position distribution in the long-time limit, which indicates that the variance of the position distribution grows quadratically with walking steps, showing a ballistic spreading typically for quantum walks. Besides, we analyze the correlation by calculating the quantum mutual information and the measurement-induced disturbance respectively as the outcome of the walk in one dimension is correlated to the other with the coin as a bridge. It is shown that the quantum correlation between walker spaces increases gradually with the walking steps.

Key words: quantum walks, quantum mutual information, measurement-induced disturbance

Quan Lin(林泉), Hao Qin(秦豪), Kun-Kun Wang(王坤坤), Lei Xiao(肖磊), Peng Xue(薛鹏). [J]. 中国物理B, 2020, 29(11): 110303-.

Quan Lin(林泉), Hao Qin(秦豪) Kun-Kun Wang(王坤坤), Lei Xiao(肖磊), and Peng Xue(薛鹏). A two-dimensional quantum walk driven by a single two-side coin[J]. Chin. Phys. B, 2020, 29(11): 110303-.

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A two-dimensional quantum walk driven by a single two-side coin

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