Algebraic Graph Theory Seminar- Sabrina Lato

Title: Quantum Walks on Oriented Graphs

Abstract: A quantum walk on a graph is defined based on a Hermitian matrix associated with the graph, such as the adjacency matrix. Directed graphs do not have symmetric adjacency matrices, and therefore most of the study of continuous quantum walks has been restricted to undirected graphs. However, if we take a graph and give each edge a unique direction, then we may define a Hermitian and non-symmetric matrix associated to this oriented graph. This yields both a way to study quantum walks on a specific case of directed graphs, and a new kind of quantum walk to analyze. In this talk, we will discuss periodicity and perfect state transfer, two kinds of special behaviour quantum walks can have, and compare known results about undirected graphs to new results in the oriented case.