Analysis and PDEs, "Quantum state transfer on graphs", G. Lippner (neu)

Thu, 15/06/201713:00-14:00
Ross 70
Title: Quantum state transfer on graphs.
Transmitting quantum information losslessly through a network of particles is an important problem in quantum computing. Mathematically this amounts to studying solutions of the discrete Schrödinger equation d/dt phi = i H phi, where H is typically the adjacency or Laplace matrix of the graph. This in turn leads to questions about subtle number-theoretic behavior of the eigenvalues of H.
It has proven to be difficult to find graphs which support such information transfer. I will talk about recent progress in understanding what happens when one is allowed to apply magnetic fields (that is, adding a diagonal matrix to H) to the system of particles.
(Joint work with Mark Kempton, S-T Yau, Krystal Guo, and Chris Godsil.)