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.

翻译：量子图神经网络（QGNN）为结合量子计算与图结构数据处理提供了一种前景广阔的方法。尽管经典图神经网络（GNN）以其可扩展性和鲁棒性著称，但现有QGNN常因采用针对特定图结构设计的量子电路而缺乏灵活性，限制了其适用于更广泛的图结构问题的能力，难以满足实际场景需求。为克服这些局限，我们受经典GraphSAGE方法启发，提出了一种以量子模型作为聚合器的通用QGNN框架。本研究将成熟的图归纳表示学习技术与参数化量子卷积层及池化层相结合，有效衔接了经典与量子范式。该卷积层具有灵活性，可根据具体问题定制设计。通过在QM9数据集上进行的节点回归任务基准测试，我们证明该框架能成功建模非平凡分子数据集，取得与经典GNN相当的性能。特别值得注意的是，我们的量子方法在处理不同原子数分子时展现出稳健的泛化能力，且无需修改电路，其表现略优于经典GNN。此外，我们通过数值实验研究了QGNN框架的可扩展性。具体而言，我们证明了该架构在量子比特数增加时不会出现贫瘠高原现象，这表明所提出的量子模型能够有效扩展至处理更大规模、更复杂的图结构问题。