  Recently the Ihara zeta function for the finite graph was extended to
infinite one by Clair and Chinta et al. In this paper, we obtain the same
expressions by a different approach from their analytical method. Our new
approach is to take a suitable limit of a sequence of finite graphs via the
Konno-Sato theorem. This theorem is related to explicit formulas of
characteristic polynomials for the evolution matrix of the Grover walk. The
walk is one of the most well-investigated quantum walks which are quantum
counterpart of classical random walks. We call the relation between the Grover
walk and the zeta function based on the Konno-Sato theorem "Grover/Zeta
Correspondence" here.
