arXiv:2503.24111

Inductive Graph Representation Learning with Quantum Graph Neural Networks

Arthur Mendonça Faria, Ignacio Fernández Graña, Savvas Varsamopoulos

Published Mar 31, 2025• 0 citations

Abstract

Graph Neural Networks (QGNNs) offer a promising approach to combining quantum computing with graph-structured data processing. While classical Graph Neural Networks (GNNs) are scalable and robust, existing QGNNs often lack flexibility due to graph-specific quantum circuit designs, limiting their applicability to diverse real-world problems. To address this, we propose a versatile QGNN framework inspired by GraphSAGE, using quantum models as aggregators to generate quantum-native node embeddings. We integrate inductive representation learning techniques with parameterized quantum convolutional and pooling layers, bridging classical and quantum paradigms. The convolutional layer is flexible, allowing tailored designs for specific tasks. Benchmarked on a node regression task with the QM9 dataset, our framework, using a single minimal circuit for all aggregation steps, handles molecules with varying numbers of atoms without changing qubits or circuit architecture. While classical GNNs achieve higher training performance, our quantum approach remains competitive and often shows enhanced generalization as molecular complexity increases. We also observe faster learning in early training epochs. To mitigate trainability limitations of a single-circuit setup, we extend the framework with multiple quantum aggregators on QM9. Assigning distinct circuits to each hop substantially improves training performance across all cases. Additionally, we numerically demonstrate the absence of barren plateaus as qubit numbers increase, suggesting that the proposed model remains trainable to larger, more complex graph-based problems.

DOI: 10.48550/arxiv.2503.24111

Related papers

Quantum Graph Attention Networks: Trainable Quantum Encoders for Inductive Graph Learning

Arthur Mendonça Faria, Mehdi Djellabi, Igor O. Sokolov +1 more

We introduce Quantum Graph Attention Networks (QGATs) as trainable quantum encoders for inductive learning on graphs, extending the Quantum Graph Neural Networks (QGNN) framework. QGATs leverage parameterized quantum circuits to encode node features and neighborhood structures, with quantum attention mechanisms modulating the contribution of each neighbor via dynamically learned unitaries. This allows for expressive, locality-aware quantum representations that can generalize across unseen graph instances. We evaluate our approach on the QM9 dataset, targeting the prediction of various chemical properties. Our experiments compare classical and quantum graph neural networks-with and without attention layers-demonstrating that attention consistently improves performance in both paradigms. Notably, we observe that quantum attention yields increasing benefits as graph size grows, with QGATs significantly outperforming their non-attentive quantum counterparts on larger molecular graphs. Furthermore, for smaller graphs, QGATs achieve predictive accuracy comparable to classical GAT models, highlighting their viability as expressive quantum encoders. These results show the potential of quantum attention mechanisms to enhance the inductive capacity of QGNN in chemistry and beyond.

arXiv:2509.11390Sep 14, 20250 citations

Quantum Heterogeneous Graph Neural Network for Molecular Property Prediction

XU Wan-li, Yang Shen

Quantum graph neural networks (QGNNs) have shown promise in leveraging quantum computing to enhance graph-structured data learning, yet they are typically limited to homogeneous graphs. In this paper, we introduce the quantum heterogeneous graph neural network (QHGNN), which integrates heterogeneity as an inductive bias within quantum circuits, enabling effective learning on heterogeneous graphs. By encoding diverse node and edge types directly into the quantum circuit architecture, QHGNN can capture complex relationships intrinsic to heterogeneous molecular data. Our experiments utilize PTC datasets to assess the performance of QHGNN in molecular property prediction tasks, showcasing superior prediction accuracy and efficiency, along with enhanced noise resilience when compared to existing QGNN models.

International Conference on Big Data, Artificial Intelligence and Risk Management (ICBAR)Nov 15, 20240 citations

Quantum Graph Convolutional Networks: Implementation and Trainability Analysis

Paul San Sebastian Sein, Theodor Iosif, Tilen G. Limbäck-Stokin +2 more

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.

quant-pharXiv:2609.19983Sep 18, 20260 citations

Quantum Feature Embeddings for Graph Neural Networks

Sascha Xu, Frank K. Wilhelm, Wolfgang Maass

Quantum computing offers a promising avenue to reduce growing machine learning model complexity as required in large language models and simulation models for weather forecasts, financial forecasts, or engineering.Graph neural networks are a particular class of machine learning models that have garnered much attention for their ability to deal well with structured data.We investigate how to enhance existing GNNs and find through the inductive bias that quantum circuits are used best to encode node features.The proposed Quantum Feature Embeddings (QFEs) turn raw input features into quantum states, enabling non-linear and entangled representations.In particular, QFEs provide normalized, non-redundant weight matrices in an exponentially larger feature space and require much fewer qubits than fully quantum graph neural networks.On standard graph benchmark datasets, we showcase that for the same parameter count QFEs perform better than their classical counterpart, and are able to match the performance of an exponentially larger model.Finally, we study the potential benefit of using a hybrid quantum graph neural network over a classic alternative on a concrete use case, laser cutting.We find that the proposed model has the performance and thus the near-term potential to uplift these business applications.

Hawaii International Conference on System Sciences (HICSS)Jan 1, 20242 citations

Quantum Feature Embeddings for Graph Neural Networks

Sascha Xu, Frank K. Wilhelm, Wolfgang Maass

Quantum computing offers a promising avenue to reduce growing machine learning model complexity as required in large language models and simulation models for weather forecasts, financial forecasts, or engineering. Graph neural networks are a particular class of machine learning models that have garnered much attention for their ability to deal well with structured data. We investigate how to enhance existing GNNs and find through the inductive bias that quantum circuits are used best to encode node features. The proposed Quantum Feature Embeddings (QFEs) turn raw input features into quantum states, enabling non-linear and entangled representations. In particular, QFEs provide normalized, non-redundant weight matrices in an exponentially larger feature space and require much fewer qubits than fully quantum graph neural networks. On standard graph benchmark datasets, we showcase that for the same parameter count QFEs perform better than their classical counterpart, and are able to match the performance of an exponentially larger model. Finally, we study the potential benefit of using a hybrid quantum graph neural network over a classic alternative on a concrete use case, laser cutting. We find that the proposed model has the performance and thus the near-term potential to uplift these business applications.

Hawaii International Conference on System Sciences (HICSS)Jan 1, 20243 citations

Scalable Message-Passing Quantum Graph Neural Networks in the Weisfeiler-Leman Hierarchy

Snehal Raj, Brian Coyle, Léo Monbroussou +3 more

Graphs provide a natural language for relational data in chemistry, biology and optimisation. Graph neural networks (GNNs) have driven much of the recent progress in learning from such data through message passing, a single primitive that generalises convolution and attention. Quantum counterparts have been proposed, but with limited connection to message passing and few guarantees on performance or scalability. More broadly, the trainability of variational quantum circuits is a recognised bottleneck for their wide applicability, and pre-training has emerged as one way to address it. Yet for a quantum model to be useful, it must offer expressivity guarantees along with demonstrable scalability. Here we show how a quantum graph neural network can be built to perform message passing, to be permutation equivariant, and to sit at a chosen level of the Weisfeiler-Leman hierarchy, the standard measure of how finely a model can tell graphs apart. We show that, as for classical GNNs, the training can be done first on small graph instances, allowing for a pre-training that can mitigate usual training issues, and its output can be read out at a cost that stays low as the graph grows. We validate the framework in large-scale simulations of up to 56 qubits across three datasets, on synthetic graphs that ordinary message passing cannot separate, on molecular property prediction, and on the travelling salesperson problem. Our framework opens a path for near-term quantum algorithms with theoretical guarantees and practical scalability, bringing the principles of graph learning into quantum circuit design.

quant-pharXiv:2606.26873Jun 26, 20260 citations