The spectra of the unitary matrix of an N-tessellable staggered quantum walk on a graph

Abstract

Recently, the staggered quantum walk (SQW) on a graph is discussed as a generalization of coined quantum walks on graphs and Szegedy walks. We present a formula for the time evolution matrix of a 2-tessellable SQW on a graph, and so directly give its spectra. Furthermore, we extend these results to a 3-tessellable SQW and an n(≥4)-tessellable SQW on a graph under some condition.