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Linear Algebra and its Applications

A quantum walk induced by Hoffman graphs and its periodicity

Sho Kubota, Etsuo Segawa, Tetsuji Taniguchi, Yusuke Yoshie

Published May 27, 2019• 8 citations
Publisher
DOI
10.1016/j.laa.2019.05.026

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Recently, a research on quantum walks has been developed in various areas.In this paper we focus on the periodicity of the Grover walk which is one of the quantum walks on the discrete graphs.Then we find some special graphs to induce a periodic Grover walk: At some time k, the quantum state φ k returns its initial quantum state φ 0 .Our purpose is to characterize graphs which induce a k-periodic Grover walk for a fixed integer k.We do it for k = 2, 3, 4, 5 and gain a necessary condition for odd k.