Algebraic Graph Theory Seminar - Bobae Johnson, August Liu, Malena Schmidt, Neo Yin

Title: Laplacian Quantum Fractional Revival On Graphs

Abstract:

Given a set of quantum bits, we can model their interactions using graphs. The continuous-time quantum walks on a graph can be viewed as the Schrödinger dynamics of a particle hopping between adjacent vertices. In this talk, the transition matrix of the continuous-time quantum walk is given by $e^{-itL}$, where $L$ is the graph’s Laplacian matrix.

We study the phenomenon of fractional revival (LaFR), useful in generating entanglement between two quantum bits. In particular, we characterize LaFR using spectral properties of the graph and present an infinite family of examples. We then prove the non-existence of LaFR on trees. Finally, we proceed to study an approximate version of LaFR called pretty good fractional revival on special families of trees.

This is joint work under the Fields Institute Undergraduate Summer Research Program 2020.