Quantum walks on regular graphs and eigenvalues

Abstract

We study the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum of S+(U3), a matrix based on the amplitudes of walks in the quantum walk, distin- guishes strongly regular graphs. We find the eigenvalues of S+(U) and S+(U2) for regular graphs and show that S+(U2) = S+(U)2 + I.