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.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Brown, Luke Candler

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-042419-190829

Advisor

• Martin, William J.

Year

• 2019

Date created

• 2019-04-24

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright