Quantum Walks on Graphs: Group State Transfer
Luke C. Brown · Digital WPI · 2019
Graphs that exhibit perfect state transfer (PST), by which a quantum walk beginning at one vertex is guaranteed to end at another after a nonzero displacement in time, are of great interest to researchers in the field of quantum computing. The conditions imposed by PST are strong, and many of the graphs that are known to exhibit PST are highly symmetric, which provides motivation to relax the restrictions imposed by perfect state transfer. This project introduces the property of group state transfer (GST), by which quantum walks are guaranteed to transfer states between nontrivial vertex sets. We define GST, examine its implications for finite simple graphs, and provide examples of graphs that exhibit GST.