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 $S^{+}(U^3)$, a matrix based on the amplitudes of walks in the quantum walk, distinguishes strongly regular graphs. We find the eigenvalues of $S^{+}(U)$ and $S^{+}(U^2)$ for regular graphs.

References in corpus (1)

• k-Boson Quantum Walks Do Not Distinguish Arbitrary Graphs