Graphons are continuous functions hidden behind large-scale graphs. Traditional approaches to graphon learning either suffer from the resolution limitations of piecewise-constant functions or struggle to capture the high-frequency structures intrinsic to graphons. In this paper, we propose quantum graphon neural representation (QGNR), a quantum-enhanced machine learning method that enables arbitrarily high-resolution and high-frequency graphon modeling through Fourier series expressivity of data re-uploading quantum circuits. We further extend QGNR to conditional graphon learning, thereby allowing the handling of complex graph-related tasks. Numerical results demonstrate that QGNR outperforms classical state-of-the-art methods in graphon learning and excels in graph classification tasks across domains like molecular property prediction and social network analysis. Notably, QGNR attains superior performance while requiring up to 81.65% fewer variational parameters than the most advanced neural network-based baselines. This work pioneers the application of quantum machine learning to graphons, demonstrating promising quantum advantages in representational power and learning efficiency.
Graphons are continuous functions hidden behind large-scale graphs. Traditional approaches to graphon learning either suffer from the resolution limitations of piecewise-constant functions or struggle to capture the high-frequency structures intrinsic to graphons. In this paper, we propose quantum graphon neural representation (QGNR), a quantum-enhanced machine learning method that enables arbitrarily high-resolution and high-frequency graphon modeling through Fourier series expressivity of data re-uploading quantum circuits. We further extend QGNR to conditional graphon learning, thereby allowing the handling of complex graph-related tasks. Numerical results demonstrate that QGNR outperforms classical state-of-the-art methods in graphon learning and excels in graph classification tasks across domains like molecular property prediction and social network analysis. Notably, QGNR attains superior performance while requiring up to 81.65% fewer variational parameters than the most advanced neural network-based baselines. This work pioneers the application of quantum machine learning to graphons, demonstrating promising quantum advantages in representational power and learning efficiency.
Quantum computing holds significant potential for advancing machine learning, particularly in handling complex graph-structured data. This paper introduces Single-Qubit Quantum Graph Neural Networks (sQGNNs), a novel model that integrates quantum networks with quantum walk operations to improve generalization in graph learning tasks. By leveraging quantum walks, we demonstrated sQGNNs capture complex relational patterns and enhance network expressiveness beyond classical methods. Our results proved that quantum encoding efficiently represents high-dimensional graph data, preserving dependencies and optimizing memory use. Across benchmark datasets, sQGNNs demonstrate superior generalization and robustness against overfitting, achieving higher accuracy with reduced computational cost. Our results underscore sQGNNs’ promise for scalable, quantum-enhanced graph learning, establishing a foundation for future quantum-assisted machine learning applications.
This paper introduces a novel approach to graph neural networks (GNNs) – the 'Quantum Adaptive Graph Neural Network' – leveraging quantum self-adaptation to enhance both expressiveness and computational efficiency. Traditional GNNs often struggle with the inherent complexities of graph data and require substantial computational resources. We propose a new architecture that employs quantum mechanics to simulate graph structures, allowing the network to learn more robust representations. This approach, dubbed Quantum Adaptive Graph Neural Network (QAGNN), utilizes quantum machine learning algorithms to improve the network's ability to capture intricate relationships within the graph. The paper details the core mechanism, its mathematical foundations, and preliminary experimental results demonstrating significant improvements in various graph classification tasks compared to traditional GNNs. We present a comprehensive analysis of the QAGNN's performance and discuss potential future research directions.
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.
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.
At present, there are a large number of quantum neural network models to deal with Euclidean spatial data, while little research have been conducted on non-Euclidean spatial data. In this paper, we propose a novel quantum graph convolutional neural network (QGCN) model based on quantum parametric circuits and utilize the computing power of quantum systems to accomplish graph classification tasks in traditional machine learning. The proposed QGCN model has a similar architecture as the classical graph convolutional neural networks, which can illustrate the topology of the graph type data and efficiently learn the hidden layer representation of node features as well. Numerical simulation results on a graph dataset demonstrate that the proposed model can be effectively trained and has good performance in graph level classification tasks.
The large-scale structure (LSS) of the Universe, characterized by the distribution of clusters, filaments, walls, and voids, encodes fundamental information about cosmology and structure formation. Standard cosmological analyses, based on abundances as well as two-point and higher-order correlation functions, have been widely used to extract information from LSS. While powerful, these techniques can only access a subset of the full information content, leaving much of the encoded structure underexploited. This motivates the use of more flexible approaches capable of learning directly from the raw, graph-like nature of the cosmic web without relying on strong compression or dimensionality reduction. Recent advances in machine learning, particularly graph neural networks (GNNs), provide a natural framework for this task by capturing the non-Euclidean connectivity of cosmic structures. Building on these developments, recent progress in quantum machine learning (QML) offers an intriguing opportunity to further enhance representation power through quantum-enhanced models. In this work, we investigate the potential of quantum graph neural networks (QGNNs) as an alternative computational framework for analyzing LSS, focusing on structure identification and classification with an emphasis on distinguishing clusters and voids. Leveraging the hybrid quantum–classical paradigm implemented in PennyLane, we construct variational quantum circuits to encode graph representations of cosmological data and compare their performance against state-of-the-art classical GNNs. Our study evaluates the accuracy and expressivity of QGNNs relative to classical models, with particular attention to their ability to capture complex correlations in sparse, high-dimensional astrophysical datasets. Preliminary results indicate that QGNNs achieve comparable classification performance, while highlighting both the opportunities and current limitations of quantum-enhanced approaches in cosmological applications.