Tensor Methods for Quantum Systems and Beyond
Edgar Solomonik, University of Illinois at Urbana-Champaign
Tensors are an effective numerical representation for both computation with and analysis of multidimensional datasets and operators. In this talk, we review and motivate how tensor rank, decompositions, and eigenvalues can be used for computational simulation and for hardness measures, such as bilinear complexity and quantum entanglement. We then survey algorithms for computing low-rank decompositions of tensors. We highlight a new algorithm for CP decomposition, which has advantages in convergence rate and numerical stability when compared to the standard alternating least squares method. For quantum systems, we demonstrate new techniques for approximate simulation of quantum circuits via tensor networks, and use tensor network rank to characterize communication cost requirements of a given unitary/problem.
Join the in-person colloquium in QNC 0101.