Tutte seminar - Chris Godsil

State Transfer on Graphs

Abstract:

If A is the adjacency matrix of a graph X, then the matrix

is the transition matrix of a so-called continuous quantum walk on X. In this context we say that we have perfect state transfer from a vertex u to a vertex v at time τ if the uv-entry of H(τ) has absolute value 1. One fundamental problem is to characterize the pairs of vertices where perfect state transfer occurs. In all cases where it does, there is an automorphism of order two of X that swaps u and v, but it is not clear whether this condition is necessary. 
My talk will provide an introduction to this problem, and to some recent work in the area.