Tutte seminar - Chris Godsil

Perfect state transfer on graphs

Abstract:

A continuous quantum walk on a graph is a quantum analog of a continuous random walk on a graph. If the adjacency matrix of the graph is $A$, then the behaviour of the walk is governed by the unitary matrix $H(t) := \exp(iAt)$. If $u$ and $v$ are vertices, then perfect state transfer from $u$ to $v$ occurs at time $\tau$ if $|H(\tau)_{u,v}| = 1$. The basic problem is to determine the cases where perfect state transfer can occur. In this talk I will present the background to this problem and the information we have obtained recently.