Discrete Mathematics Seminar Series
Quantum state transfer on graphs - using magnetic fields
ABSTRACT: 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.
Wednesday, January 23, 2019