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

TL;DR

PVLS introduces a GNN-based framework that predicts effective initial parameters for variational quantum linear solvers, significantly enhancing convergence speed and scalability on near-term quantum devices.

Contribution

It presents a novel learning-based parameter prediction method using GNNs to improve VQLS performance, addressing initialization challenges and scalability issues.

Findings

Achieves up to 2.6x speedup in optimization

Requires fewer iterations for convergence

Maintains comparable solution accuracy

Abstract

Variational Quantum Linear Solvers (VQLS) are a promising method for solving linear systems on near-term quantum devices. However, their performance is often limited by barren plateaus and inefficient parameter initialization, which significantly hinder trainability as the system size increases. In this work, we introduce PVLS, a learning-based parameter prediction framework that uses Graph Neural Networks (GNNs) to generate high-quality initial parameters for VQLS circuits. By leveraging structural information from the coefficient matrix, PVLS predicts expressive and scalable initializations that improve convergence and reduce optimization difficulty. Extensive experiments on matrix sizes ranging from 16 to 1024 show that PVLS provides up to a 2.6x speedup in optimization and requires fewer iterations while maintaining comparable solution accuracy. These results demonstrate the potential of machine-learning-guided initialization strategies for improving the practicality of hybrid quantum-classical algorithms in the NISQ era.