In recent years, graph neural networks have achieved notable success in processing complex structured data. However, traditional graph neural networks still face challenges in capturing long-range dependencies and higher-order structural information within graphs. To address these limitations, we propose two physics-informed graph neural network architectures based on the continuous time quantum walk-inspired complex graph convolution mechanism to accomplish the small-node and large-node classification tasks. Specifically, node features are mapped into the complex domain and subsequently propagated through a continuous time quantum walk, which enables effective capture of intricate spatial correlations across the graph topology. Furthermore, the framework incorporates complex-valued activation functions and complex weight update strategies, thereby enhancing both the nonlinear modeling capacity and training stability of the model. Experimental results on protein structure datasets show that the proposed methods consistently outperform standard graph convolutional networks and other state-of-the-art approaches in terms of classification accuracy and convergence speed, thus demonstrating the promise of quantum-inspired complex domain graph convolution for handling highly structured data.

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• Machine learning
• Quantum algorithms & computation