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arXiv · 2011.14162

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

Takashi Komatsu·Norio Konno·Iwao Sato
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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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Takashi Komatsu, Norio Konno, Iwao Sato. 2020-11-28. A note on the Grover walk and the generalized Ihara zeta function of the one-dimensional integer lattice. https://arxiv.org/abs/2011.14162

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