Quantum Graph Convolutional Networks: Implementation and Trainability Analysis
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.
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BibTeX
@misc{sein2026quantum,
title = {{Quantum Graph Convolutional Networks: Implementation and Trainability Analysis}},
author = {Paul San Sebastian Sein and Theodor Iosif and Tilen G. Limbäck-Stokin and Kin Ian Lo and Yidong Liao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19983},
eprint = {2609.19983},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19983},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Graph Convolutional Networks: Implementation and Trainability Analysis
AU - Paul San Sebastian Sein
AU - Theodor Iosif
AU - Tilen G. Limbäck-Stokin
AU - Kin Ian Lo
AU - Yidong Liao
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19983
UR - https://arxiv.org/abs/2609.19983
AB - 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.
ER -