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arXiv:2505.06810 · IEEE International Conference on Quantum Computing and Engineering (QCE)

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

Lei Jiang, Chi Zhang, Fan Chen

Published Aug 30, 2025• 0 citations
arXivHTMLPDF

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.

DOI
10.1109/qce65121.2025.00167

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In recent years, quantum computing has emerged as a transformative force in the field of combinatorial optimization, offering novel approaches to tackling complex problems that have long challenged classical computational methods. Among these, the Quantum Approximate Optimization Algorithm (QAOA) stands out for its potential to efficiently solve the Max-Cut problem, a quintessential example of combinatorial optimization. However, practical application faces challenges due to current limitations on quantum computational resource. Our work optimizes QAOA initialization, using Graph Neural Networks (GNN) as a warm-start technique. This sacrifices affordable computational resource on classical computer to reduce quantum computational resource overhead, enhancing QAOA's effectiveness. Experiments with various GNN architectures demonstrate the adaptability and stability of our framework, highlighting the synergy between quantum algorithms and machine learning. Our findings show GNN's potential in improving QAOA performance, opening new avenues for hybrid quantum-classical approaches in quantum computing and contributing to practical applications.
In recent years, quantum computing has emerged as a transformative force in the field of combinatorial optimization, offering novel approaches to tackling complex problems that have long challenged classical computational methods. Among these, the Quantum Approximate Optimization Algorithm (QAOA) stands out for its potential to efficiently solve the Max-Cut problem, a quintessential example of combinatorial optimization. However, practical application faces challenges due to current limitations on quantum computational resource. Our work optimizes QAOA initialization, using Graph Neural Networks (GNN) as a warm-start technique. This sacrifices affordable computational resource on classical computer to reduce quantum computational resource overhead, enhancing QAOA's effectiveness. Experiments with various GNN architectures demonstrate the adaptability and stability of our framework, highlighting the synergy between quantum algorithms and machine learning. Our findings show GNN's potential in improving QAOA performance, opening new avenues for hybrid quantum-classical approaches in quantum computing and contributing to practical applications.
The recent interest in learning-augmented algorithms has motivated us to explore their applicability in quantum computing, specifically during the noisy intermediate-scale quantum (NISQ) era. This paper introduces a learning-augmented algorithm-like approach to enhance the Quantum Approximate Optimization Algorithm (QAOA) for max-cut problems, by improving initial parameter estimation. We trained a random forest regression model on the optimal solution parameters from various max-cut graphs, and then used this model to guess better initial parameters for previously unseen graphs. Experimental results demonstrate that our approach reduces the number of iterations of quantum computation required, thereby reducing noise and error. These findings indicate that integrating learning-augmented algorithm techniques can enhance the computational feasibility of solving QAOA problems in the NISQ era.
Quantum Computing promises to solve complex combinatorial optimization problems more efficiently than classical methods, with the Quantum Approximate Optimization Algorithm (QAOA) being a leading candidate. Recent fixed-parameter variations of QAOA eliminate costly run-time optimization, but determining their optimal initialization as well as the number of required layers (p) for a target solution remains a critical, unsolved challenge. In this work, we propose a novel approach using a Graph Neural Network (GNN) to predict QAOA performance: Based on a graph representation of the problem, the GNN forecasts the probability of the optimal solution in the resulting distribution across different parameter initializations and layer depths for a wide variety of combinatorial optimization problems. We demonstrate that the GNN accurately predicts QAOA performance within a 10% margin of the true values. Furthermore, the model exhibits strong generalization capabilities across unseen problem classes, larger problem sizes, and higher layer counts. Our approach allows to identify viable problem instances for QAOA and to select an adequate parameter initialization strategy with minimal layer depth, without the need of costly parameter optimization.
Variational Quantum Eigensolvers (VQEs) are a leading class of noisy intermediate-scale quantum (NISQ) algorithms with broad applications in quantum physics and quantum chemistry. However, as system size increases, VQE optimization is increasingly hindered by the barren plateau phenomenon, where gradients vanish and the loss function becomes trapped in local minima. While machine learning-based parameter initialization methods have been proposed to address this challenge, they often show limited effectiveness in complex VQE problems. This is primarily due to their inadequate ability to model the intricate correlations embedded in the Hamiltonian structure and the associated ansatz circuits. In this paper, we propose Qracle, a graph neural network (GNN)-based parameter initializer for VQEs. Qracle systematically encodes both the Hamiltonian and the associated ansatz circuit into a unified graph representation and leverages a GNN to learn a mapping from VQE problem graphs to optimized ansatz parameters. Compared to state-of-the-art initialization techniques, Qracle achieves a reduction in initial loss of up to 10.86, accelerates convergence by decreasing optimization steps by up to 64.42%, and improves final performance with up to a 26.43% reduction in Symmetric Mean Absolute Percentage Error (SMAPE), with all results averaged over the validation set of each respective application. The source code is publicly available at https://github.com/chizhang24/Qracle.
The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical algorithm that shows promise in efficiently solving the Max-Cut problem, a representative example of combinatorial optimization. However, its effectiveness heavily depends on the parameter optimization pipeline, where the parameter initialization strategy is nontrivial due to the non-convex and complex optimization landscapes characterized by issues with low-quality local minima. Recent inspiration comes from the diffusion of classical neural network parameters, which has demonstrated that neural network training can benefit from generating good initial parameters through diffusion models. However, whether the diffusion model can enhance the parameter optimization and performance of QAOA by generating well-performing initial parameters is still an open topic. Therefore, in this work, we formulate the problem of finding good initial parameters as a generative task and propose the initial parameter generation scheme through dataset-conditioned pre-trained parameter sampling. Concretely, the generative machine learning model, specifically the denoising diffusion probabilistic model (DDPM), is trained to learn the distribution of pre-trained parameters conditioned on the graph dataset. Intuitively, the proposed framework aims to effectively distill knowledge from pre-trained parameters to generate well-performing initial parameters for QAOA. To benchmark our framework, we adopt trotterized quantum annealing (TQA)-based and graph neural network (GNN) prediction-based initialization protocols as baselines. Through numerical experiments on Max-Cut problem instances of various sizes, we show that conditional DDPM can consistently generate high-quality initial parameters, improve convergence to the approximation ratio, and exhibit greater robustness against local minima over baselines. Additionally, the experimental results also indicate that the conditional DDPM trained on small problem instances can be extrapolated to larger ones, thus demonstrating the extrapolation capacity of our framework in terms of the qubit number.