Abstract

Let $A$ be the adjacency matrix of a graph $X$. The quantum walk based on $X$ is determined by the family of unitary matrices $U(t) = \exp(itA)$. The walk allows “perfect state transfer” from vertex $a$ to vertex $b$ if there is a time $t$ such that $\left|U(t)_{a,b}\right|=1$, and physicists are interested in knowing when this is possible. I will discuss how tools from algebraic graph theory and number theory can be used to study this question, and questions related to it.

Short Bio

Chris Godsil graduated from the University of Melbourne in 1969 with a degree in Biochemistry. After working for four years as a biochemist, he returned to the University of Melbourne and completed his Ph. D (“Graphs with Regular Groups”) in 1979, under the supervision of Derek Holton. He spent nine months of his study towards his Ph.D. in the Mathematics Department at Syracuse University.

From 1980 to 1981 he was employed as Vertragsassistent in the Institut fuer Angewandte Mathematik at the Montanunversitaet Leoben (in Austria). From there he moved to the Mathematics Department at Simon Fraser University. In 1987 Prof. Godsil came to the Department of Combinatorics and Optimization, at the University of Waterloo, where he is still lodged.

In 1992, Ian Goulden, David Jackson and Chris Godsil started the Journal of Algebraic Combinatorics. He is on the editorial board of a number of other journals, including Australasian J. Combinatorics and Electronic J. Combinatorics.

More info

https://www.math.uwaterloo.ca/~cgodsil/