UBC Discrete Math Seminar: Hanmeng (Harmony) Zhan

Discrete quantum walks are motivated by search problems. One of the best known quantum algorithms, Grover’s search, is a discrete quantum walk on the complete graph with loops. From an algebraic perspective, a discrete quantum walk is determined by a unitary matrix that encodes some graph, and—just like the adjacency matrix and the Laplacian matrix—its spectrum contains important information about the graph, which can be used to study the behaviour of the walk.

In this talk, I will give an overview of discrete quantum walks, show how properties of these walks relate to properties of the underlying graphs, and discuss some future directions in this area. Part of the talk is based on my joint book, Discrete Quantum Walks on Graphs and Digraphs, with Chris Godsil. No knowledge of quantum physics is required.