Recently, efforts have been made in the community to design new Graph Neural Networks (GNN), as limitations of Message Passing Neural Networks became more apparent. This led to the appearance of Graph Transformers using global graph features such as Laplacian Eigenmaps. In our paper, we introduce a GNN architecture where the aggregation weights are computed using the long-range correlations of a quantum system. These correlations are generated by translating the graph topology into the interactions of a set of qubits in a quantum computer. This work was inspired by the recent development of quantum processing units which enables the computation of a new family of global graph features that would be otherwise out of reach for classical hardware. We give some theoretical insights about the potential benefits of this approach, and benchmark our algorithm on standard datasets. Although not being adapted to all datasets, our model performs similarly to standard GNN architectures, and paves a promising future for quantum enhanced GNNs.
Recently, efforts have been made in the community to design new Graph Neural Networks (GNN), as limitations of Message Passing Neural Networks became more apparent. This led to the appearance of Graph Transformers using global graph features such as Laplacian Eigenmaps. In our paper, we introduce a GNN architecture where the aggregation weights are computed using the long-range correlations of a quantum system. These correlations are generated by translating the graph topology into the interactions of a set of qubits in a quantum computer. This work was inspired by the recent development of quantum processing units which enables the computation of a new family of global graph features that would be otherwise out of reach for classical hardware. We give some theoretical insights about the potential benefits of this approach, and benchmark our algorithm on standard datasets. Although not being adapted to all datasets, our model performs similarly to standard GNN architectures, and paves a promising future for quantum enhanced GNNs.
In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the topology of a graph onto interactions between qubits in a quantum computer. Our inspiration stems from the recent advancements in quantum processing units, which offer computational capabilities beyond the reach of classical hardware. We prove that some of these quantum features are theoretically more expressive for certain graphs than the commonly used relative random walk probabilities. Empirically, we show that the performance of state-of-the-art models can be improved on standard benchmarks and large-scale datasets by computing tractable versions of quantum features. Our findings highlight the potential of leveraging quantum computing capabilities to enhance the performance of transformers in handling graph data.
Transformers are increasingly employed for graph data, demonstrating competitive performance in diverse tasks. To incorporate graph information into these models, it is essential to enhance node and edge features with positional encodings. In this work, we propose novel families of positional encodings tailored for graph transformers. These encodings leverage the long-range correlations inherent in quantum systems, which arise from mapping the topology of a graph onto interactions between qubits in a quantum computer. Our inspiration stems from the recent advancements in quantum processing units, which offer computational capabilities beyond the reach of classical hardware. We prove that some of these quantum features are theoretically more expressive for certain graphs than the commonly used relative random walk probabilities. Empirically, we show that the performance of state-of-the-art models can be improved on standard benchmarks and large-scale datasets by computing tractable versions of quantum features. Our findings highlight the potential of leveraging quantum computing capabilities to potentially enhance the performance of transformers in handling graph data.
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 (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) 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.