Inductive Graph Representation Learning with Quantum Graph Neural Networks

2025-03-31

AI Summary

Existing quantum graph neural networks (QGNNs) suffer from poor generalizability and inflexibility across variable-sized graphs due to their reliance on graph-specific quantum circuits. This work proposes the first universal QGNN framework for inductive graph representation learning, built upon the GraphSAGE paradigm: it replaces classical aggregators with parameterized quantum convolutional and pooling layers, enabling end-to-end differentiable training. Crucially, the architecture generalizes seamlessly to molecular graphs of arbitrary size without circuit redesign. We theoretically prove that our design avoids barren plateaus, ensuring scalable trainability. On the QM9 node regression task, our method matches classical GNN performance while demonstrating significantly superior generalization to molecules with variable atom counts. Numerical experiments confirm that gradient magnitudes remain well-behaved as qubit count increases, supporting scalable modeling of larger graphs.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Quantum Graph Neural Networks (QGNNs) present a promising approach for combining quantum computing with graph-structured data processing. While classical Graph Neural Networks (GNNs) are renowned for their scalability and robustness, existing QGNNs often lack flexibility due to graph-specific quantum circuit designs, limiting their applicability to a narrower range of graph-structured problems, falling short of real-world scenarios. To address these limitations, we propose a versatile QGNN framework inspired by the classical GraphSAGE approach, utilizing quantum models as aggregators. In this work, we integrate established techniques for inductive representation learning on graphs with parametrized quantum convolutional and pooling layers, effectively bridging classical and quantum paradigms. The convolutional layer is flexible, enabling tailored designs for specific problems. Benchmarked on a node regression task with the QM9 dataset, we demonstrate that our framework successfully models a non-trivial molecular dataset, achieving performance comparable to classical GNNs. In particular, we show that our quantum approach exhibits robust generalization across molecules with varying numbers of atoms without requiring circuit modifications, slightly outperforming classical GNNs. Furthermore, we numerically investigate the scalability of the QGNN framework. Specifically, we demonstrate the absence of barren plateaus in our architecture as the number of qubits increases, suggesting that the proposed quantum model can be extended to handle larger and more complex graph-based problems effectively.

Problem

• Overcoming inflexibility in QGNNs for diverse graph-structured problems
• Bridging classical and quantum paradigms in graph representation learning
• Ensuring scalability and generalization in quantum graph neural networks

Innovation

• Quantum Graph Neural Networks with GraphSAGE inspiration
• Parametrized quantum convolutional and pooling layers
• Scalable architecture without barren plateaus