State Transfer on Graphs
|Affiliation:||University of Waterloo|
|Room:||Mathematics & Computer Building (MC) 5158|
If A is the adjacency matrix of a graph X, then the matrix
|H(t) := exp(iAt)|
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.
200 University Avenue West
Waterloo, ON N2L 3G1