Explore the fascinating world of oriented Cayley graphs in this 49-minute lecture by Xiaohong Zhang from the University of Waterloo. Delve into topics such as continuous quantum walks, transition matrices, and quantum walks on oriented graphs. Examine various examples, bases of association schemes, and parameters including Galois groups and special eigenvalues. Investigate cyclic and translation schemes, review key questions, and discover characterizations and applications. Conclude with a practical example to solidify understanding of these complex mathematical concepts. Part of the Workshop on Algebraic Graph Theory and Quantum Information held at the Fields Institute on August 26, 2021.
Overview
Syllabus
Intro
Cayley graphs
Continuous quantùm walk
Transition matrix of special form
Quantum walk on oriented graphs
One related question
More examples
Bases of an association scheme
Some parameters
Galois group
Special eigenvalues
Cyclic scheme
Translation scheme
Question review
A characterization
Applications
An example
Taught by
Fields Institute
