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

TL;DR

QSeer is a quantum-inspired graph neural network that improves parameter initialization for QAOA, enhancing optimization efficiency and solution quality across various graph types by integrating physics principles.

Contribution

QSeer introduces a physics-informed GNN for QAOA parameter prediction, addressing limitations of prior methods and supporting variable-depth circuits and weighted Max-Cut problems.

Findings

Improves initial approximation ratio by 6%-68%.

Speeds up convergence by 5x-10x.

Enhances QAOA performance across diverse graphs.

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.