### 抜粋

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.

元の言語 | English |
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ページ（範囲） | 371-391 |

ページ数 | 21 |

ジャーナル | Linear Algebra and Its Applications |

巻 | 554 |

DOI | |

出版物ステータス | Published - 2018 10 1 |

### ASJC Scopus subject areas

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

## フィンガープリント Periodicity of Grover walks on generalized Bethe trees' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

## これを引用

Kubota, S., Segawa, E., Taniguchi, T., & Yoshie, Y. (2018). Periodicity of Grover walks on generalized Bethe trees.

*Linear Algebra and Its Applications*,*554*, 371-391. https://doi.org/10.1016/j.laa.2018.05.023