A note on the Grover walk and the generalized Ihara zeta function of the one-dimensional integer lattice

2020/11/28 by Komatsu, Takashi, Konno, Norio, Sato, Iwao
#Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2011.14162

Abstract

Chinta, Jorgenson and Karlsson introduced a generalized version of the determinant formula for the Ihara zeta function associated to finite or infinite regular graphs. On the other hand, Konno and Sato obtained a formula of the characteristic polynomial of the Grover matrix by using the determinant expression for the second weighted zeta function of a finite graph. In this paper, we focus on a relationship between the Grover walk and the generalized Ihara zeta function. That is to say, we treat the generalized Ihara zeta function of the one-dimensional integer lattice as a limit of the Ihara zeta function of the cycle graph.

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