Quantum Graph Convolutional Networks: Implementation and Trainability Analysis

2026-09-17

AI Summary

本文通过实现和评估两种量子图卷积网络模型（SGC和LGC），在解决大规模图数据学习的内存限制问题上，展示了量子方法的有效性和竞争力。

Abstract

Graph Neural Networks (GNNs) achieve state-of-the-art performance on graph-structured data, but training and inference on large graphs are often bottlenecked by memory constraints and sparse linear-algebra workloads. Quantum computing offers an alternative set of primitives that may improve scalability for graph learning. Building on the quantum graph neural network (QGNN) framework of Liao \textit{et al.}, this work implements two representative architectures --- the Simplified Graph Convolution (SGC) and Linear Graph Convolution (LGC) models --- and evaluates them on open benchmark graph datasets and semi-supervised learning tasks using quantum simulation. We compare predictive performance and optimization behavior against classical baselines, showing that the quantum models achieve competitive performance with fewer parameters. Finally, we present a cost gradient analysis that identifies the tasks for which the models showcased are trainable. This is followed by a classical simulability study to find regimes in which the proposed circuits remain robust during training.

Problem

• Graph Neural Networks
• memory constraints
• sparse linear-algebra workloads

Innovation

• Quantum Graph Convolutional Networks
• Simplified Graph Convolution
• Linear Graph Convolution
• Quantum Simulation
• Trainability Analysis