论文标题
完整图的NEP中的完美状态转移
Perfect state transfer in NEPS of complete graphs
论文作者
论文摘要
图中的完美状态转移是量子物理和量子计算引起的一个概念。给定带有邻接矩阵$ a_g $的图$ g $，相对于$ a_g $，$ g $的过渡矩阵定义为$ h_ {a_ {a_ {g}}（t）= \ exp（ - \ exp（ - \ mathrm {i} ta_ {g}）ta_ {g}） \ mathrm {i} = \ sqrt {-1} $。我们说，如果$ u \ ne v $和$（u，v）$的模量，从$ g $ $ g $中出现了从顶点$ u $到顶点$ v $的完美状态转移。如果$ h_ {a_g}（τ）$的所有对角线条目的模量等于某些$τ$的$ 1 $，则$ g $称为定期$τ$。在本文中，我们给出了一些足够的条件，使完整图的NEP定期或表现出完美的状态转移。
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 $H_{A_{G}}(t) = \exp(-\mathrm{i}tA_{G})$, $t \in \mathbb{R},\ \mathrm{i}=\sqrt{-1}$. We say that perfect state transfer from vertex $u$ to vertex $v$ occurs in $G$ at time $τ$ if $u \ne v$ 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.
