Journal article

Perfect state transfer in NEPS of complete graphs

Yipeng Li, Xiaogang Liu, Shenggui Zhang, Sanming Zhou

DISCRETE APPLIED MATHEMATICS | ELSEVIER | Published : 2021

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.

University of Melbourne Researchers

Grants

Awarded by National Natural Science Foundation of China


Awarded by Natural Science Foundation of Shaanxi Province, PR China


Awarded by Natural Science Foundation of Qinghai Province, PR China


Awarded by Fundamental Research Funds for the Central Universities, PR China


Funding Acknowledgements

Supported by the National Natural Science Foundation of China (Nos. 11601431 and 11871398), the Natural Science Foundation of Shaanxi Province, PR China (No. 2020JM-099), the Natural Science Foundation of Qinghai Province, PR China (No. 2020-ZJ-920).Supported by the National Natural Science Foundation of China (Nos. 11571135, 12071370 and 11671320) and the Fundamental Research Funds for the Central Universities, PR China (No. 3102019GHJD003).