論文

査読有り
2016年10月

Exact solutions and symmetry analysis for the limiting probability distribution of quantum walks

ANNALS OF PHYSICS
  • Xin-Ping Xu
  • ,
  • Yusuke Ide

373
開始ページ
682
終了ページ
693
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1016/j.aop.2016.08.019
出版者・発行元
ACADEMIC PRESS INC ELSEVIER SCIENCE

In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a general coin or swapping shift operator. In this paper, we derive exact solutions for the limiting probability distribution of quantum walks using a general coin and swapping shift operator on cycles for the first time. Based on the exact solutions, we show how to generate symmetric quantum walks and determine the condition under which a symmetric quantum walk appears. Our results suggest that choosing various coin and initial state parameters can achieve a symmetric quantum walk. By defining a quantity to measure the variation of symmetry, deviation and mixing time of symmetric quantum walks are also investigated. (C) 2016 Elsevier Inc. All rights reserved.

リンク情報
DOI
https://doi.org/10.1016/j.aop.2016.08.019
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000387734500043&DestApp=WOS_CPL
ID情報
  • DOI : 10.1016/j.aop.2016.08.019
  • ISSN : 0003-4916
  • eISSN : 1096-035X
  • Web of Science ID : WOS:000387734500043

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