Graph neural networks (GNNs) are a powerful framework for learning representations from graph-structured data, but their direct implementation on near-term quantum hardware remains challenging due to circuit depth, multi-qubit interactions, and qubit scalability constraints. In this work, we introduce a hybrid quantum graph learning architecture designed explicitly for unsupervised learning in the noisy intermediate-scale quantum (NISQ) regime. Our approach combines a variational quantum feature extraction layer with an edge-local and qubit-efficient quantum message-passing mechanism inspired by the Quantum Alternating Operator Ansatz (QAOA) framework. The message-passing operation is decomposed into pairwise interactions along graph edges using standard single- and two-qubit gates. For a graph with $N$ nodes and $n$-qubit feature registers, this reduces the number of qubits required at one time from $Nn$ to at most $2n$. We train the model using the Deep Graph Infomax objective to perform unsupervised node representation learning. The external class labels are not used during graph construction or training and are used only to evaluate the learned embeddings. Experiments on the Cora citation network and the Phase 3 release of the 1000 Genomes Project show that the quantum edge interaction contributes to the quality of the learned node representations.
Graph neural networks (GNNs) are a powerful framework for learning representations from graph-structured data, but their direct implementation on near-term quantum hardware remains challenging due to circuit depth, multi-qubit interactions, and qubit scalability constraints. In this work, we introduce a hybrid quantum graph learning architecture designed explicitly for unsupervised learning in the noisy intermediate-scale quantum (NISQ) regime. Our approach combines a variational quantum feature extraction layer with an edge-local and qubit-efficient quantum message-passing mechanism inspired by the Quantum Alternating Operator Ansatz (QAOA) framework. The message-passing operation is decomposed into pairwise interactions along graph edges using standard single- and two-qubit gates. For a graph with N nodes and n-qubit feature registers, this reduces the number of qubits required at one time from Nn to at most 2n. We train the model using the Deep Graph Infomax objective to perform unsupervised node representation learning. The external class labels are not used during graph construction or training and are used only to evaluate the learned embeddings. Experiments on the Cora citation network and the Phase 3 release of the 1000 Genomes Project show that the quantum edge interaction contributes to the quality of the learned node representations.
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.
Graph neural networks (GNNs) have demonstrated strong capabilities in graph representation learning but still face limitations in efficiency and scalability. Quantum GNNs (QGNNs) offer a promising alternative. However, existing approaches often fail to fully exploit edge information, require substantial quantum resources, and insufficiently account for permutation invariance in graph learning. To address these challenges, this article proposes a permutation-invariant quantum GNN (PIQGNN). The proposed model introduces a low-qubit-cost quantum encoding strategy that jointly embeds node features, edge features, and graph topology into entangled quantum states using only n qubits, where n denotes the number of nodes, while explicitly enforcing permutation invariance. Furthermore, a symmetry-aware variational quantum neural network (QNN) is designed to enable end-to-end permutation-invariant learning. Its hyperparameters are optimized via Bayesian optimization to alleviate barren plateau (BP) effects and enhance training stability. Experimental results on multiple graph binary classification benchmark datasets demonstrate that, compared with classical GNNs, PIQGNN achieves competitive performance with a significantly reduced number of trainable parameters. Compared with existing QGNNs, PIQGNN attains higher accuracy with lower quantum resource requirements and exhibits stronger robustness under noisy conditions. These results indicate that PIQGNN provides an efficient, scalable, and noise-resilient quantum framework for graph learning, highlighting its practical potential in the noisy intermediate-scale quantum (NISQ) era.
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.
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) 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.