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Many engineering problems involve solving large linear systems of equations.Conjugate gradient (CG) is one of the most popular iterative methods forsolving such systems. However, CG typically requires a good preconditioner tospeed up convergence. One such preconditioner is the sparse approximate inverse(SPAI).  In this paper, we explore the computation of an SPAI on quantum annealingmachines by solving a series of quadratic unconstrained binary optimization(QUBO) problems. Numerical experiments are conducted using bothwell-conditioned and poorly-conditioned linear systems arising from a 2D finitedifference formulation of the Poisson problem.

Computing a Sparse Approximate Inverse on Quantum Annealing Machines