On the relation between quantum walks and zeta functions

Authors:
Norio Konno;Iwao Sato
Affiliations:
Department of Applied Mathematics, Faculty of Engineering, Yokohama National University, Hodogaya, Yokohama, Japan 240-8501;Oyama National College of Technology, Oyama, Tochigi, Japan 323-0806
Venue:
Quantum Information Processing
Year:
2012

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Abstract

We present an explicit formula for the characteristic polynomial of the transition matrix of the discrete-time quantum walk on a graph via the second weighted zeta function. As applications, we obtain new proofs for the results on spectra of the transition matrix and its positive support.