Numerical Approximation of Traces of Matrix Functions

This 48-minute lecture presented by Alice Cortinovis from Stanford University explores numerical methods for approximating traces of matrix functions, recorded during IPAM's Optimal Transport for Density Operators workshop at UCLA. Discover key techniques from numerical linear algebra for efficiently computing traces of functions like matrix logarithms, entropy, and exponentials—all crucial components in quantum optimal transport formulations. Learn about the Hutchinson trace estimator, a stochastic algorithm that approximates traces using quadratic forms with random vectors, along with its variants including partial trace approximation and variance reduction techniques. This presentation provides valuable insights for researchers working at the intersection of numerical analysis, quantum information, and optimal transport theory.