Recent impressive progress in quantum technology, particularly in programmable quantum computers, has invigorated a renewed interest in quantum algorithm research. This excitement is largely fueled by the existence of quantum algorithms exhibiting exponential speedups, including those for large-scale linear algebra.

The absence of reliable quantum error correction combined with the limited insight about promising target states has motivated a new research direction called variational quantum algorithms (VQAs), in which the key idea is to encode a computational problem as an optimization problem for an unknown quantum state.

This project will bootstrap off the emerging overlaps between VQAs, VQMC, and ML to propose quantum and quantum-inspired solvers for linear equations appearing in scientific computing. Additionally, the project outlines a probabilistic computing paradigm that can potentially be applied to a wide range of linear algebraic tasks such as SVD, QR decomposition and others. The team envisions a research program that is, at a high-level, comprised of four tasks: variational formulation of linear algebraic problems, VQMC representation of variational linear algebra, imposition of sparsity assumptions, and accelerating and parallelizing VQMC.