  Solving systems of linear equations is a fundamental problem, but it can be
computationally intensive for classical algorithms in high dimensions. Existing
quantum algorithms can achieve exponential speedups for the quantum linear
system problem (QLSP) in terms of the problem dimension, but even such a
theoretical advantage is bottlenecked by the condition number of the
coefficient matrix. In this work, we propose a new quantum algorithm for QLSP
inspired by the classical proximal point algorithm (PPA). Our proposed method
can be viewed as a meta-algorithm that allows inverting a modified matrix via
an existing \texttt{QLSP\_solver}, thereby directly approximating the solution
vector instead of approximating the inverse of the coefficient matrix. By
carefully choosing the step size $\eta$, the proposed algorithm can effectively
precondition the linear system to mitigate the dependence on condition numbers
that hindered the applicability of previous approaches.
