On the relation between quantum walks and zeta functions

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.

9 pages, minor corrections, Quantum Information Processing (in press)

References in corpus (1)

• Two-particle quantum walks applied to the graph isomorphism problem

Cited by in corpus (1)

• A Characterization of the Graphs to Induce Periodic Grover Walk