Perfect state transfer in NEPS of complete graphs

Abstract

Perfect state transfer in graphs is a concept arising from quantum physics and quantum computing. Given a graph G with adjacency matrix AG, the transition matrix of G with respect to AG is defined as HAG(t)=exp(−itAG), t∈R,i=−1. We say that perfect state transfer from vertex u to vertex v occurs in G at time τ if u≠v and the modulus of the (u,v)-entry of HAG(τ) is equal to 1. If the moduli of all diagonal entries of HAG(τ) are equal to 1 for some τ, then G is called periodic with period τ. In this paper we give a few sufficient conditions for NEPS of complete graphs to be periodic or exhibit perfect state transfer.