Quantum walks, an important tool in quantum computing, have been very successfully investigated using techniques in algebraic graph theory. We are motivated by the study of state transfer in continuous-time quantum walks, which is understood to be a rare and interesting phenomenon. We consider a perturbation on an edge uv of a graph where we add a weight β to the edge and a loop of weight γ to each of u and v. We characterize when this perturbation results in strongly cospectral vertices u and v. Applying this to strongly regular graphs, we give infinite families of strongly regular graphs where some perturbation results in perfect state transfer. Further, we show that, for every strongly regular graph, there is some perturbation which results in pretty good state transfer. We also show for any strongly regular graph X and edge $e\in E(X)$, that $\varphi (X\mathrm{\backslash }e)$ does not depend on the choice of e.

使用代数图论技术已经非常成功地研究了量子行走，它是量子计算中的重要工具。我们受到连续时间量子行走中状态转移研究的推动，这被认为是一种罕见而有趣的现象。我们考虑在图的边uv上的扰动，在边上添加权重β，在u和v中分别添加权重γ的环。我们表征了何时该扰动导致强烈共谱的顶点u和v。将其应用于强正则图，我们给出了无限族的强正则图，其中一些扰动导致完美的状态转移。此外，我们表明，对于每个强正则图，都有一些扰动会导致相当好的状态转移。我们还显示了任何强正则图X和边$Ë\in Ë（X）$， $\varphi （X\mathrm{\backslash }Ë）$不依赖于e的选择。