著者

Yusuke HIGUCHI Norio KONNO Iwao SATO Etsuo SEGAWA

出版者

東北大学大学院情報科学研究科ジャーナル編集委員会

雑誌

Interdisciplinary Information Sciences (ISSN:13409050)

巻号頁・発行日

vol.23, no.1, pp.75-86, 2017 (Released:2017-03-31)

参考文献数

23

被引用文献数

1

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In this paper we discuss the periodicity of the evolution matrix of Szegedy walk, which is a special type of quantum walk induced by the classical simple random walk, on a finite graph. We completely characterize the periods of Szegedy walks for complete graphs, compete bipartite graphs and strongly regular graphs. In addition, we discuss the periods of Szegedy walk induced by a non-reversible random walk on a cycle.

著者

Norio KONNO Hideo MITSUHASHI Iwao SATO

出版者

東北大学大学院情報科学研究科ジャーナル編集委員会

雑誌

Interdisciplinary Information Sciences (ISSN:13409050)

巻号頁・発行日

vol.23, no.1, pp.9-17, 2017 (Released:2017-03-31)

参考文献数

14

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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.