Algebraic Graph Theory Seminar - Steve Kirkland

Monday, June 28, 2021 11:30 am - 11:30 am EDT (GMT -04:00)

Title: State transfer for paths with weighted loops at the end vertices

Speaker: Steve Kirkland
Affiliation: University of Manitoba
Zoom: Contact Soffia Arnadottir


We consider a continuous time quantum walk on an unweighted path on n vertices, to which a loop of weight w has been added at each end vertex. Let f(t) denote the fidelity of state transfer from one end vertex to the other at time t. In this talk we give upper and lower bounds on f(t) in terms of w, n and t; further, given a > 0 we discuss the values of t for which f(t) > 1-a. The results show that f(t) can be made close to 1 via suitable choices of w, n and t. Throughout, the results rely on a detailed analysis of the eigenvalues and eigenvectors of the associated adjacency matrix.

This talk is based on joint work in progress with Christopher van Bommel.