### 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 | |

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

## Fingerprint Dive into the research topics of 'Periodicity of Grover walks on generalized Bethe trees'. Together they form a unique fingerprint.

## Cite this

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