Periodicity of Grover walks on generalized Bethe trees

Sho Kubota, Etsuo Segawa, Tetsuji Taniguchi, Yusuke Yoshie

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We focus on the periodicity of the Grover walk on the generalized Bethe tree, which is a rooted tree such that in each level the vertices have the same degree. Since the Grover walk is induced by the underlying graph, its properties depend on the graph. In this paper, we say that the graph induces periodic Grover walks if and only if there exists k∈N such that the k-th power of the time evolution operator becomes the identity operator. Our aim is to characterize such graphs. We give the perfect characterizations of the generalized Bethe trees which induce periodic Grover walks.

Original languageEnglish
Pages (from-to)371-391
Number of pages21
JournalLinear Algebra and Its Applications
Volume554
DOIs
Publication statusPublished - 2018 Oct 1

Keywords

  • Generalized Bethe trees
  • Grover walk
  • Periodicity

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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