Algebraic Graph Theory: Instantaneous uniform mixing:

Talk by Ada Chan.

Let A be the adjacency matrix of a graph X on n vertices. The transition matrix of the continuous-time quantum walk on X is exp(-itA). We are interested state transfer and mixing in quantum walks. While we have characterizations for perfect state transfer, pretty good state transfer and fractional revival, much less is known for mixing. In this talk, we focus on instantaneous uniform mixing which happens when all entries of the transition matrix have the same absolute value, or equivalently, when sqrt(n)exp(-itA) is a complex Hadamard matrix. We discuss instantaneous uniform mixing on graphs in association schemes, and related problems.