2016年10月
Exact solutions and symmetry analysis for the limiting probability distribution of quantum walks
ANNALS OF PHYSICS
- ,
- 巻
- 373
- 号
- 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
- ID情報
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- DOI : 10.1016/j.aop.2016.08.019
- ISSN : 0003-4916
- eISSN : 1096-035X
- Web of Science ID : WOS:000387734500043