Grover/Zeta Correspondence based on the Konno-Sato theorem
- URL: http://arxiv.org/abs/2103.12971v5
- Date: Thu, 19 Aug 2021 05:06:42 GMT
- Title: Grover/Zeta Correspondence based on the Konno-Sato theorem
- Authors: Takashi Komatsu, Norio Konno, Iwao Sato
- Abstract summary: We take a suitable limit of a sequence of finite graphs via the Konno-Sato theorem.
This is related to explicit formulas of characteristic theorems for the evolution matrix of the Grover walk.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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