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 physicsdriven 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-sciencebased 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. First, we propose a quantum-inspired input data normalization technique to ensure a consistent input scale and mitigate the influence of varying feature magnitudes. By integrating key physics-informed QAOA principles, such as parameter concentration, symmetry, and adiabatic evolution, this approach enhances QSeer's training stability and convergence. Second, we encode Max-Cut edge weights as edge attributes in QSeer's GNN framework, enabling parameter prediction for QAOA circuits solving both unweighted and weighted Max-Cut problems. Third, we incorporate the circuit depth $p$ as an input, allowing QSeer to generalize parameter predictions across different QAOA depths. 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 $6 \% \sim 68 \%$ and $5 \times \sim 10 \times$, respectively. The source code is publicly available at https://github.com/UnchartedRLab/QSeer.