Zeta functions of periodic graphs derived from quantum walk

TL;DR

This paper introduces a zeta function for finite and periodic graphs based on quantum walk dynamics, providing a determinant expression and extending the concept to periodic structures.

Contribution

It defines a new zeta function for graphs derived from quantum walks and generalizes it to periodic graphs, with a determinant formula.

Findings

Derived a zeta function from quantum walk time evolution matrices.

Provided a determinant expression for the zeta function.

Extended the concept to periodic graphs.

Abstract

We define a zeta function of a finite graph derived from time evolution matrix of quantum walk, and give its determinant expression. Furthermore, we generalize the above result to a periodic graph.