  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 $\beta$ to the
edge and a loop of weight $\gamma$ to each of $u$ and $v$. We characterize when
for 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 $\phi(X\setminus e)$
does not depend on the choice of $e$.
