Though variational quantum algorithms (VQAs), which rely on a hybrid
quantum--classical architecture, represent a promising avenue for
addressing fundamental linear algebra problems in exponentially large
dimensions, the potential computational advantage they may have over
purely classical algorithms has not yet been determined. Moreover, VQAs
yield insight into a new paradigm for solving high-dimensional sparse
linear algebra problems, in particular for solving large linear systems.
Inspired by the existing quantum--classical Variational Quantum Linear
Solver (VQLS), the Variational Neural Linear Solver constitutes a fully
classical neural network linear system solver utilizing techniques from
variational quantum Monte Carlo. We introduce the VNLS and demonstrate
its potential for addressing high-dimensional, sufficiently sparse
linear systems in comparison with the established VQAs. Speaker(s): Oliver Knitter (University of Michigan)