Perfect state transfer in NEPS of complete graphs

Yipeng Li; Xiaogang Liu; Shenggui Zhang; Sanming Zhou

doi:10.1016/j.dam.2020.09.024

Perfect state transfer in NEPS of complete graphs

Yipeng Li, Xiaogang Liu, Shenggui Zhang, Sanming Zhou

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

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(−itA_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.

Original language	English
Pages (from-to)	98-114
Number of pages	17
Journal	Discrete Applied Mathematics
Volume	289
DOIs	https://doi.org/10.1016/j.dam.2020.09.024
State	Published - 31 Jan 2021

Keywords

NEPS
Perfect state transfer
Periodic
Transition matrix

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10.1016/j.dam.2020.09.024

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title = "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.",

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AU - Li, Yipeng

AU - Liu, Xiaogang

AU - Zhang, Shenggui

AU - Zhou, Sanming

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N2 - 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.

AB - 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.

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KW - Transition matrix

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DO - 10.1016/j.dam.2020.09.024

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VL - 289

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JO - Discrete Applied Mathematics

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Perfect state transfer in NEPS of complete graphs

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Keywords

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