Given a simple, undirected, regular graph G=(V,E) with adjacency matrix A, a continuous-time quantum walk on G is given by v(t) = exp(-iAt)v(0), where v(0) is a complex |V|-dimensional vector with unit magnitude. The probability distribution induced by such a walk at time t on vertex u is given by P(t)[u] = |v(t)[u]|^2.

A quantum walk on G is called uniform mixing if there is a time T for which P(T)[u] = 1/|V|, for all u in V. Classical random walks on well-behaved graphs are known to mix to uniform. But this is a property not shared by most quantum walks. This talk describes counter-intuitive differences in the mixing phenomena between classical and quantum walks on graphs.