Walk/Zeta Correspondence for quantum and correlated random walks

• URL: http://arxiv.org/abs/2109.07664v4
• Date: Thu, 3 Mar 2022 06:45:10 GMT
• Title: Walk/Zeta Correspondence for quantum and correlated random walks
• Authors: Norio Konno, Shunya Tamura
• Abstract summary: We compute the zeta function for the three- and four-state quantum walk and correlated random walk. We also deal with the four-state quantum walk and correlated random walk on the two-dimensional torus.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, following the recent paper on Walk/Zeta Correspondence by the first author and his coworkers, we compute the zeta function for the three- and four-state quantum walk and correlated random walk, and the multi-state random walk on the one-dimensional torus by using the Fourier analysis. We deal with also the four-state quantum walk and correlated random walk on the two-dimensional torus. In addition, we introduce a new class of models determined by the generalized Grover matrix bridging the gap between the Grover matrix and the positive-support of the Grover matrix. Finally, we give a generalized version of the Konno-Sato theorem for the new class. As a corollary, we calculate the zeta function for the generalized Grover matrix on the d-dimensional torus.

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