A Spatial-Based Quantum Graph Convolutional Neural Network and Its Full-Quantum Circuit Implementation

With the rapid advancement of quantum computing, the exploration of quantum graph neural networks is gradually emerging. However, the absence of a circuit framework for quantum implementation and limited physical qubits hinder their realization on real quantum computers. To address these challenges, this paper proposes a spatial-based quantum graph convolutional neural network and implements it on a superconducting quantum computer. Specifically, this model exclusively consists of quantum circuits, including quantum aggregation circuits in the quantum graph convolutional layer and quantum classification circuits in the quantum dense layer. To meet the requirements of Noisy Intermediate-Scale Quantum computing, a first-order extraction method to reduce circuit size is employed. Experimental results in node classification tasks demonstrate that this model achieves comparable or even superior performance compared to classical graph neural networks while utilizing fewer parameters. Therefore, this model can inspire further advancements in quantum graph neural networks and facilitate their implementation on physical quantum devices.