QSeer: A Quantum-Inspired Graph Neural Network for Parameter Initialization in Quantum Approximate Optimization Algorithm Circuits

Abstract

To mitigate the barren plateau problem, effective parameter initialization is crucial for optimizing the Quantum Approximate Optimization Algorithm (QAOA) in the near-term Noisy Intermediate-Scale Quantum (NISQ) era. Prior physics-driven approaches leveraged the optimal parameter concentration phenomenon, utilizing medium values of previously optimized QAOA parameters stored in databases as initialization for new graphs. However, this medium-value-based strategy lacks generalization capability. Conversely, prior computer-science-based approaches employed graph neural networks (GNNs) trained on previously optimized QAOA parameters to predict initialization values for new graphs. However, these approaches neglect key physics-informed QAOA principles, such as parameter concentration, symmetry, and adiabatic evolution, resulting in suboptimal parameter predictions and limited performance improvements. Furthermore, no existing GNN-based methods support parameter initialization for QAOA circuits with variable depths or for solving weighted Max-Cut problems. This paper introduces QSeer, a quantum-inspired GNN designed for accurate QAOA parameter prediction. Compared to prior physics- and computer-science-driven methods, QSeer improves the initial approximation ratio and convergence speed of QAOA circuits across diverse graphs by 6%-68% and 5x-10x, respectively.