quantum graph neural networks

Existing quantum graph neural networks (QGNNs) suffer from poor generalizability and inflexibility across variable-sized graphs due to their reliance on graph-specific quantum circuits. This work proposes the first universal QGNN framework for inductive graph representation learning, built upon the GraphSAGE paradigm: it replaces classical aggregators with parameterized quantum convolutional and pooling layers, enabling end-to-end differentiable training. Crucially, the architecture generalizes seamlessly to molecular graphs of arbitrary size without circuit redesign. We theoretically prove that our design avoids barren plateaus, ensuring scalable trainability. On the QM9 node regression task, our method matches classical GNN performance while demonstrating significantly superior generalization to molecules with variable atom counts. Numerical experiments confirm that gradient magnitudes remain well-behaved as qubit count increases, supporting scalable modeling of larger graphs.

本文通过实现和评估两种量子图卷积网络模型（SGC和LGC），在解决大规模图数据学习的内存限制问题上，展示了量子方法的有效性和竞争力。

Classical polynomial approximations for Laplacian spectral filtering in graph neural networks (GNNs) incur high computational overhead and limit scalability. Method: This paper proposes a learnable quantum spectral filter embedded in a quantum-classical hybrid GNN architecture. Leveraging parameterized quantum Fourier circuits, the method encodes the geometric structure of the graph Laplacian into quantum circuit connectivity and directly learns the frequency-domain filtering function within an exponentially compressed parameter space—using only 1–100 trainable quantum parameters—bypassing classical approximation entirely. The model integrates quantum Fourier transforms, low-dimensional approximations of the Laplacian eigenspace, and a classical prediction head to enable efficient graph signal convolution and pooling. Results: On the TUDataset benchmark, the approach achieves graph classification performance competitive with or superior to state-of-the-art GNNs, while significantly improving spectral filtering efficiency and scalability.

To address poor scalability and challenging crosstalk suppression in large-scale superconducting quantum circuit parameter design, this paper proposes a graph neural network (GNN)-based “three-level scaling” optimization framework. The method introduces a novel supervised–unsupervised co-training paradigm: a medium-scale circuit is used to supervise the training of an evaluator, while an unsupervised designer generalizes the optimization to large-scale circuits. It is the first approach to jointly optimize single- and two-qubit gate frequencies—modeled as node and edge attributes on a circuit graph, respectively. Evaluated on an 870-qubit circuit, the framework reduces error rates by 49% compared to the state-of-the-art algorithm (achieving a 51% error reduction) and accelerates design time from 90 minutes to 27 seconds. The method achieves high accuracy, ultra-low latency, and strong scalability, establishing a new paradigm for automated superconducting quantum chip design.

This work addresses the problem of efficiently approximating multi-qubit unitary matrices with quantum circuits. We propose a scalable, Lie-group-theoretic parametrization framework. Methodologically, we replace the conventional Pauli-string basis with a recursively defined block basis as generators; employ the exponential map combined with structured parameterized quantum circuits to achieve compact unitary representations; and introduce a linear-scale recursive construction scheme—where an (n+1)-qubit unitary circuit is built incrementally from an n-qubit circuit by adding only a constant number of CNOT and single-qubit gates. Our approach achieves O(n) depth and width scaling, markedly enhancing scalability, training efficiency, and hardware compatibility. The resulting framework provides a novel paradigm for large-scale quantum algorithm compilation and quantum neural network design.

This work proposes a scalable quantum graph neural network that establishes, for the first time, a rigorous correspondence with the Weisfeiler–Leman (WL) hierarchy. By employing variational quantum circuits to implement permutation-equivariant message passing, the model explicitly aligns with a specified WL test level, thereby offering theoretical guarantees on expressivity. To address key limitations of existing approaches—namely, weak connections to classical message-passing schemes and insufficient theoretical foundations regarding trainability and scalability—the architecture integrates a low-complexity readout mechanism and a pretraining strategy generalizable across graph sizes. Empirical evaluations on simulations up to 56 qubits demonstrate the model’s ability to distinguish graph structures indistinguishable by classical methods, while achieving superior performance in molecular property prediction and the traveling salesman problem.

This work addresses the challenges of deploying graph neural networks on noisy intermediate-scale quantum (NISQ) devices, where large circuit depth, complex many-body interactions, and poor scalability hinder practical implementation. The authors propose a fully quantum graph convolutional architecture that leverages an edge-local message-passing mechanism to reduce qubit requirements from O(Nn) to O(n), utilizing only hardware-native single- and two-qubit gates to significantly enhance scalability. Built upon the Quantum Alternating Operator Ansatz (QAOA), the framework integrates variational quantum feature extraction with the Deep Graph Infomax objective for unsupervised training. Experiments on the Cora citation network and a large-scale genomic SNP dataset demonstrate performance comparable to existing quantum and hybrid models, confirming its feasibility on real NISQ hardware.

This work addresses the computational inefficiency of classical graph neural networks (GNNs) in large-scale dense wireless networks and the limited scalability of existing purely quantum message-passing models due to qubit constraints. To overcome these challenges, the authors propose the Scalable Quantum Message-passing GNN (SQM-GNN), which decomposes a large graph into subgraphs and employs shared parameterized quantum circuits across subgraphs to circumvent hardware limitations. By integrating both node and edge features, SQM-GNN fully captures the structural characteristics of wireless networks. The model adopts a hybrid quantum-classical architecture that balances expressive power with computational efficiency. Evaluated on device-to-device (D2D) power control tasks, SQM-GNN significantly outperforms classical GNNs and heuristic baselines, demonstrating its practical potential for wireless resource management.

This study addresses the lack of systematic comparison between classical and quantum-inspired node embedding approaches under unified experimental conditions. For the first time, it systematically evaluates three classes of embedding methods—classical baselines, variational quantum circuit embeddings, and quantum-inspired embeddings—in graph classification tasks, while strictly controlling backbone architectures, data splits, optimization strategies, and evaluation metrics. The experiments reveal that quantum-inspired embeddings achieve superior performance and greater training stability on structurally dense datasets, such as discretized QM9 and certain TU benchmarks, yet underperform classical methods on attribute-sparse social graphs. These findings highlight a critical trade-off between inductive bias and training stability, providing an empirical foundation for advancing quantum graph representation learning.

This work investigates the efficient representation and optimization of stochastic neural networks on gate-model quantum computers. By systematically mapping stochastic neurons to quantum circuits, the authors construct a variety of quantum neural network architectures, including fully connected networks, Hopfield networks, restricted Boltzmann machines, autoencoders, and convolutional neural networks. These models are trained using a combination of the Kiefer–Wolfowitz algorithm and simulated annealing. Notably, the proposed quantum networks are innovatively employed as oracles within Grover’s search algorithm, yielding the first Grover-based quantum generative AI model. The study demonstrates the feasibility and effectiveness of this approach for quantum generative tasks, establishing a novel pathway toward quantum-enhanced generative modeling.