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

翻译：许多工程问题涉及求解大型线性方程组。共轭梯度法（CG）是求解此类方程组最常用的迭代方法之一。然而，CG通常需要良好的预条件子以加速收敛，其中一种预条件子是稀疏近似逆矩阵（SPAI）。本文通过求解一系列二次无约束二元优化（QUBO）问题，探索了在量子退火机上计算SPAI的方法。数值实验采用源于泊松问题二维有限差分格式的良态与病态线性系统进行验证。