On the relation between quantum walks and zeta functions
Quantum Physics
2013-11-08 v2 Mathematical Physics
Combinatorics
math.MP
Probability
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.
Keywords
Cite
@article{arxiv.1103.0079,
title = {On the relation between quantum walks and zeta functions},
author = {Norio Konno and Iwao Sato},
journal= {arXiv preprint arXiv:1103.0079},
year = {2013}
}
Comments
9 pages, minor corrections, Quantum Information Processing (in press)