Periodicity of Grover walks on generalized Bethe trees

Sho Kubota; Etsuo Segawa; Tetsuji Taniguchi; Yusuke Yoshie

doi:10.1016/j.laa.2018.05.023

Periodicity of Grover walks on generalized Bethe trees

Sho Kubota, Etsuo Segawa, Tetsuji Taniguchi, Yusuke Yoshie

Information Sciences

Research output: Contribution to journal › Article › peer-review

6 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 language	English
Pages (from-to)	371-391
Number of pages	21
Journal	Linear Algebra and Its Applications
Volume	554
DOIs	https://doi.org/10.1016/j.laa.2018.05.023
Publication status	Published - 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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title = "Periodicity of Grover walks on generalized Bethe trees",

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.",

keywords = "Generalized Bethe trees, Grover walk, Periodicity",

author = "Sho Kubota and Etsuo Segawa and Tetsuji Taniguchi and Yusuke Yoshie",

note = "Funding Information: E.S. acknowledges financial support from the Grant-in-Aid for Young Scientists (B) and of Scientific Research (B) Japan Society for the Promotion of Science (Grant No. 16K17637 , No. 16K03939 ). T.T. was supported by Japan Society for the Promotion of Science KAKENHI (Grant No. 16K05263 ).",

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doi = "10.1016/j.laa.2018.05.023",

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journal = "Linear Algebra and Its Applications",

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T1 - Periodicity of Grover walks on generalized Bethe trees

AU - Kubota, Sho

AU - Segawa, Etsuo

AU - Taniguchi, Tetsuji

AU - Yoshie, Yusuke

N1 - Funding Information: E.S. acknowledges financial support from the Grant-in-Aid for Young Scientists (B) and of Scientific Research (B) Japan Society for the Promotion of Science (Grant No. 16K17637 , No. 16K03939 ). T.T. was supported by Japan Society for the Promotion of Science KAKENHI (Grant No. 16K05263 ).

PY - 2018/10/1

Y1 - 2018/10/1

N2 - 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.

AB - 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.

KW - Generalized Bethe trees

KW - Grover walk

KW - Periodicity

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

Periodicity of Grover walks on generalized Bethe trees

Abstract

Keywords

ASJC Scopus subject areas

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