Algebraic Graph Theory Seminar - Chris Godsil

Title: Laplacian States

Abstract:

It is customary to assume that the initial state of a continuous quantum walk on a graph $X$ is a vertex. However the Laplacian matrix of a graph with vertex set $V(X)$ is positive semidefinite, and can be scaled to produce a density matrix, and so provides an initial state for a walk on $X$. Qiuting Chen and I have studied this set up, and this talk will present some of what we have learned, and some of the lot that we don’t know.