"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."

本代码配套PVLSPVLS模型，这是一种基于图神经网络（Graph Neural Network, GNN）的参数初始化器，可同时提升收敛速度与最终求解质量。该方法将线性方程组Ax = b重构为一张图，其中以矩阵A作为边权重、向量b作为节点特征，借此学习预测有效的变分量子电路（Variational Quantum Circuit, VQC）初始参数。我们的方法以维度范围为n∈[4,10]的数千个随机生成矩阵作为训练数据，并将优化后的VQC参数作为真值标签进行训练。在未见的测试样本上，与随机初始化方案相比，PVLS可将初始成本平均降低81.3%，将最终损失平均降低71%。此外，PVLS还可加速收敛，平均将优化迭代步数减少60%以上。我们进一步在10个真实世界稀疏矩阵上对PVLS进行了评估，验证了其泛化能力与鲁棒性。我们的研究结果证实了机器学习先验在提升变分量子线性求解器（Variational Quantum Linear Solver, VQLS）训练性能、解决变分量子算法优化难题方面的应用价值。