Explore the fascinating intersection of algebraic graph theory and quantum information in this 50-minute lecture by Chris Godsil from the University of Waterloo. Delve into topics such as perfect state transfer, oriented graphs, and spectral decomposition. Examine the concept of eigenvalue support and its implications for periodicity in quantum systems. Investigate real states, the ratio condition, and subset states, while uncovering the intricacies of perfect text transfer and universal perfect state transfer. Analyze traces and controllable vertices, and gain insights into skew-symmetric matrices. This talk, part of the Workshop on Algebraic Graph Theory and Quantum Information at the Fields Institute, offers a comprehensive overview of eigenvalue gaps and continuous walks, bridging the gap between abstract mathematical concepts and their applications in quantum information theory.