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

Grover/Zeta Correspondence based on the Konno-Sato theorem