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

TL;DR

This work addresses the challenge of initializing QAOA parameters to mitigate barren plateaus on NISQ devices. It introduces QSeer, a quantum-inspired graph neural network that incorporates physics-informed data normalization, weighted Max-Cut support, and circuit-depth generalization to predict QAOA parameters. Empirical results show substantial improvements in the initial approximation ratio and convergence speed across both unweighted and weighted Max-Cut graphs, and across varying circuit depths, outperforming prior physics-based and ML-based baselines. The approach enhances robustness and efficiency of QAOA on near-term devices, broadening applicability to diverse graph instances and problem weights. The combination of physics-inspired priors with GNN-based prediction offers a practical path forward for scalable quantum optimization in the NISQ era.

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.

Figures (10)

• Figure 1: The optimal parameter concentration and symmetry in single-layer ($p=1$) QAOA circuits solving unweighted Max-Cut on regular graphs with degrees ranging from 2 to 8: (a) the time-reversal symmetry on odd-degree regular graphs, and (b) the time-reversal symmetry on even-degree regular graphs.
• Figure 2: The evolution of optimal $\gamma$ and $\beta$ parameters in QAOA circuits solving unweighted Max-Cut on a 10-node Erdös-Rényi graph with an edge probability of 0.7, shown as a function of angle index $j$ at a fixed circuit depth $p$.
• Figure 3: An overview of QSeer.
• Figure 4: The optimal parameter distribution of QAOA circuits solving unweighted Max-Cut without data normalization.
• Figure 5: The optimal parameter distribution of QAOA circuits solving unweighted Max-Cut with our quantum-inspired data normalization.