文章基本信息

标题：Periodicity for the Hadamard Walk on Cycles
本地全文：下载
作者：Norio KONNO ; Yuki SHIMIZU ; Masato TAKEI 等
期刊名称：Interdisciplinary Information Sciences
印刷版ISSN：1340-9050
电子版ISSN：1347-6157
出版年度：2017
卷号：23
期号：1
页码：1-8
DOI：10.4036/iis.2017.A.01
出版社：The Editorial Committee of the Interdisciplinary Information Sciences
摘要：The present paper treats the period T _N of the Hadamard walk on a cycle C _N with N vertices. Dukes (2014) considered the periodicity of more general quantum walks on C _N and showed T ₂=2, T ₄=8, T ₈=24 for the Hadamard walk case. We prove that the Hadamard walk does not have any period except for his case, i.e., N = 2,4,8. Our method is based on a path counting and cyclotomic polynomials which is different from his approach based on the property of eigenvalues for unitary matrix that determines the evolution of the walk.
关键词：Quantum walk;Hadamard walk;periodicity;cycle