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Neural Networks

Quantum-enhanced learning: Leveraging von Neumann entropy for enhanced graph neural network performance

Muhammad Awais, Octavian Adrian Postolache, Sancho Moura Oliveira

Published Apr 9, 2026• 0 citations
Publisher

Abstract

Graph Neural Networks (GNNs) have established themselves as powerful tools for learning from graph-structured data. However, their reliance on local message-passing mechanisms leads to over-squashing-the compression of exponentially growing neighborhood information into fixed-size vectors-which severely limits long-range dependency modeling. We introduce the Quantum-Inspired Graph Neural Network (QGNN) with a novel Quantum Entanglement Loss (QEL) function that addresses this challenge through a fundamentally different mechanism than existing approaches. Unlike spectral regularization (which enforces smoothness) or maximum entropy methods (which encourage representation diversity), QEL minimizes the von Neumann entropy of the node embedding correlation matrix, thereby concentrating eigenvalues in dominant eigenmodes that preserve global structural patterns. This entropy minimization creates direct information pathways between distant but functionally related nodes, effectively bypassing multi-hop bottlenecks. We evaluate QGNN on both standard benchmarks (Cora, Citeseer, PPI, Electronic Circuits) and the Long Range Graph Benchmark (LRGB) suite, which features graphs with average diameters up to 56.99 (Peptides). On LRGB datasets, QGNN achieves substantial improvements: 37.6% relative MAE reduction on Peptides-struct compared to GCN, 4.0% improvement over Graph Transformers (GraphGPS), and notably, 97% better performance than GCN on node pairs separated by 7+ hops. Despite these gains, QGNN requires only 20-30% additional computational overhead compared to standard GCN, while being 5-6 × faster than Graph Transformer approaches. Our results establish entropy-based regularization as a principled and efficient approach for long-range dependency modeling in graphs.

DOI
10.1016/j.neunet.2026.108958

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Graph Neural Networks (GNNs) have established themselves as powerful tools for learning from graph-structured data. However, their reliance on local message-passing mechanisms leads to over-squashing-the compression of exponentially growing neighborhood information into fixed-size vectors-which severely limits long-range dependency modeling. We introduce the Quantum-Inspired Graph Neural Network (QGNN) with a novel Quantum Entanglement Loss (QEL) function that addresses this challenge through a fundamentally different mechanism than existing approaches. Unlike spectral regularization (which enforces smoothness) or maximum entropy methods (which encourage representation diversity), QEL minimizes the von Neumann entropy of the node embedding correlation matrix, thereby concentrating eigenvalues in dominant eigenmodes that preserve global structural patterns. This entropy minimization creates direct information pathways between distant but functionally related nodes, effectively bypassing multi-hop bottlenecks. We evaluate QGNN on both standard benchmarks (Cora, Citeseer, PPI, Electronic Circuits) and the Long Range Graph Benchmark (LRGB) suite, which features graphs with average diameters up to 56.99 (Peptides). On LRGB datasets, QGNN achieves substantial improvements: 37.6% relative MAE reduction on Peptides-struct compared to GCN, 4.0% improvement over Graph Transformers (GraphGPS), and notably, 97% better performance than GCN on node pairs separated by 7+ hops. Despite these gains, QGNN requires only 20-30% additional computational overhead compared to standard GCN, while being 5-6 × faster than Graph Transformer approaches. Our results establish entropy-based regularization as a principled and efficient approach for long-range dependency modeling in graphs.
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.
Graph Neural Networks (GNNs) are now one of the key tools to model relational and non-Euclidean data in multiagent systems, infrastructure networks and even molecular modeling applications. Nevertheless, in very dense or noisy graph topologies, classical message-passing architectures may experience scalability and representational degeneration, especially due to over-smoothing and insufficient higher-order dependency information. The recent developments in quantum machine learning indicate that hybrid quantum-classical models can also provide an alternative feature representation by projecting relational data to parameterized quantum circuits. This article presents a Quantum-Enhanced Graph Neural Network (QGNN) architecture that extends variational quantum circuits with graph learning pipelines, based on classical learning. Parameters are represented as parameterized qubits, and relational dependencies are represented as structured entanglement mappings. We benchmark the regimes where quantum-enhanced relational encoding proves to be more robust and stable through the swarm coordination, molecular property prediction, and financial transaction network. We also elaborate on the issue of scalability, hardware issues, and practical aspects of near-term hybrid implementations and give a critical view of the changing role of quantum methods in computational intelligence systems.
Graph Neural Networks (GNNs) are now one of the key tools to model relational and non-Euclidean data in multiagent systems, infrastructure networks and even molecular modeling applications. Nevertheless, in very dense or noisy graph topologies, classical message-passing architectures may experience scalability and representational degeneration, especially due to over-smoothing and insufficient higher-order dependency information. The recent developments in quantum machine learning indicate that hybrid quantum-classical models can also provide an alternative feature representation by projecting relational data to parameterized quantum circuits. This article presents a Quantum-Enhanced Graph Neural Network (QGNN) architecture that extends variational quantum circuits with graph learning pipelines, based on classical learning. Parameters are represented as parameterized qubits, and relational dependencies are represented as structured entanglement mappings. We benchmark the regimes where quantum-enhanced relational encoding proves to be more robust and stable through the swarm coordination, molecular property prediction, and financial transaction network. We also elaborate on the issue of scalability, hardware issues, and practical aspects of near-term hybrid implementations and give a critical view of the changing role of quantum methods in computational intelligence systems.
Calculating the von Neumann entanglement entropy from experimental data is challenging due to its dependence on the complete wavefunction, forcing reliance on approximations like classical mutual information (MI). We propose a machine learning approach using a graph neural network for predicting the von Neumann entropy from experimentally accessible bitstrings. We tested this approach on a Rydberg ladder system and achieved a mean absolute error of 3.7×10−33.7 \times 10^{-3}3.7×10−3 when testing it inside of its training range on a dataset with entropy ranging from 0 to 1.9, we also evaluated the mean absolute percentage error on the data that have its entropy larger than 0.01 of the maximum entropy(so we can avoid the areas of our phase space with near zero entropy) and got a relative error of 1.72%, outperforming MI-based bounds. When tested beyond this range, the model still delivers reasonable results. Furthermore, we demonstrate that fine tuning the model with a small dataset significantly improves its performance on data outside its original training range.
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.
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.