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 A G , the transition matrix of G with respect to A G is defined as H A G ( t ) = exp ( − i t A G ) , 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 H A G ( τ ) is equal to 1. If the moduli of all diagonal entries of H A G ( 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.

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