A note on the discrete-time evolutions of quantum walk on a graph

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.

11 pages, revised version, title changed, Journal-ref added

References in corpus (1)

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

Cited by in corpus (6)

• Spectral properties of weighted line digraphs
• Quaternionic quantum walks of Szegedy type and zeta functions of graphs
• A remark on zeta functions of finite graphs via quantum walks
• A zeta function related to the transition matrix of the discrete-time quantum walk on a graph
• Phase measurement of quantum walks: application to structure theorem of the positive support of the Grover walk
• The quaternionic second weighted zeta function of a graph and the Study determinant