A note on the discrete-time evolutions of quantum walk on a graph
Mathematical Physics
2013-11-28 v4 math.MP
Quantum Physics
Abstract
For a quantum walk on a graph, there exist many kinds of operators for the discrete-time evolution. We give a general relation between the characteristic polynomial of the evolution matrix of a quantum walk on edges and that of a kind of transition matrix of a classical random walk on vertices. Furthermore we determine the structure of the positive support of the cube of some evolution matrix, which is said to be useful for isospectral problem in graphs, under a certain condition.
Keywords
Cite
@article{arxiv.1207.4987,
title = {A note on the discrete-time evolutions of quantum walk on a graph},
author = {Yusuke Higuchi and Norio Konno and Iwao Sato and Etsuo Segawa},
journal= {arXiv preprint arXiv:1207.4987},
year = {2013}
}
Comments
11 pages, revised version, title changed, Journal-ref added