English

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)

R2 v1 2026-06-21T17:33:20.756Z