PVLS: A Learning-based Parameter Prediction Technique for Variational Quantum Linear Solvers

some code for PVLSPVLS, a GNN-basedparameter initializer that enhances both convergence speedand final solution quality. By reformulating the linearsystem Ax = b as a graph with A as edge weights and bas node features, PVLS learns to predict effective initialVQC parameters. Our method is trained on thousandsof randomly generated matrices with varying dimensions(n \u2208 [4, 10]), using optimized VQC parameters as groundtruth labels. On unseen test instances, PVLS reduces theinitial cost by an average of 81.3% and the final loss by 71%compared to random initialization.PVLS also acceleratesconvergence, reducing the number of optimization stepsby more than 60% on average. We further evaluatePVLS on ten real-world sparse matrices, demonstratingits generalization capability and robustness. Our resultshighlight the utility of machine-learned priors in improvingthe trainability of VQLSs and addressing optimizationchallenges in variational quantum algorithms.