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arXiv:2110.05068 · Quantum Information and Computation

A weighted graph zeta function involved in the Szegedy walk

Ayaka Ishikawa, Norio Konno

Published Dec 28, 2021• 1 citation
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Abstract

We define a new weighted zeta function for a finite graph and obtain its determinant expression. This result gives the characteristic polynomial of the transition matrix of the Szegedy walk on a graph.
DOI
10.26421/qic22.1-2-3

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We give a new determinant expression for the characteristic polynomial of the bond scattering matrix of a quantum graph G. Also, we give a decomposition formula for the characteristic polynomial of the bond scattering matrix of a regular covering of G. Furthermore, we define an L-function of G, and give a determinant expression of it. As a corollary, we express the characteristic polynomial of the bond scattering matrix of a regular covering of G by means of its L-functions. As an application, we introduce three types of quantum graph walks, and treat their relation.