Perfect state transfer in Grover walks between states associated to vertices of a graph

Abstract

We study perfect state transfer in Grover walks, which are typical discretetime quantum walk models. In particular, we focus on states associated to vertices of a graph. We call such states vertex type states. Perfect state transfer between vertex type states can be studied via Chebyshev polynomials. We derive a necessary condition on eigenvalues of a graph for perfect state transfer between vertex type states to occur. In addition, we perfectly determine the complete multipartite graphs whose partite sets are the same size on which perfect state transfer occurs between vertex type states, together with the time.

Periodicity of Grover walks on bipartite regular graphs with at most five distinct eigenvalues

“…Periodicity is a special case of state transfer problems. The authors in [22] have applied periodicity to the study of perfect state transfer. In context of quantum cryptography, periodicity of quantum walks can be a focus of attention [28].…”