Department of Mathematical Sciences
QIT Thinking Seminar
Wednesday, September 24th, 2025
4:00PM-4:50PM
Stratton Hall 207
Speaker: Bill Martin, WPI
Title: Semidefinite programming and quantum isomorphism
Abstract: This talk is based on the 2019 paper "Quantum and non-signalling graph isomorphisms” by Atserias, et al. Variations on the theme of graph isomorphism are formulated as various optimization problems. I will present these and focus on quantum isomorphism of graphs in the quantum tensor framework. My goal is to test the power and limitations of semidefinite programming vis a vis finding quantum permutation matrices with entries of a fixed finite size d that solve the quantum isomorphism problem. One priority of the talk is to give a basic introduction to semidefinite programming. So we will not go into any depth on the issue of quantum isomorphism itself. For quantum permutation matrices with 2 x 2 entries, we are working with rank one projectors parametrized by the projective line. As this set is non-convex, we instead explore the fantope of orthogonal projections and see how much is lost in this compromise.