文章基本信息

标题：The Discrete-time Quaternionic Quantum Walk and the Second Weighted Zeta Function on a Graph
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作者：Norio KONNO ; Hideo MITSUHASHI ; Iwao SATO 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：9-17
DOI：10.4036/iis.2017.A.02
出版社：The Editorial Committee of the Interdisciplinary Information Sciences
摘要：We define the quaternionic quantum walk on a finite graph and investigate its properties. This walk can be considered as a natural quaternionic extension of the Grover walk on a graph. We explain the way to obtain all the right eigenvalues of a quaternionic matrix and a notable property derived from the unitarity condition for the quaternionic quantum walk. Our main results determine all the right eigenvalues of the quaternionic quantum walk by using complex eigenvalues of the quaternionic weighted matrix which is easily derivable from the walk. Since our derivation is owing to a quaternionic generalization of the determinant expression of the second weighted zeta function, we explain the second weighted zeta function and the relationship between the walk and the second weighted zeta function.
关键词：Quantum walk;Ihara zeta function;quaternion;quaternionic quantum walk