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.