Graph representation learning has been extensively studied, and recent models can well incorporate both node features and graph structures. Despite these progress, the inherent scalability challenge for classical computers of processing graph data and solving the downstream tasks (many are NP-hard) is still a bottleneck for existing classical graph learning models. On the other hand, quantum computing is known a promising direction for its theoretically verified scalability as well as the increasing evidence for the access to physical quantum machine in near-term. Different from many existing classical-quantum hybrid machine learning models on graphs, in this paper we take a more aggressive initiative for developing a native quantum paradigm for (attributed) graph representation learning, which to our best knowledge, has not been fulfilled in literature yet. Specifically, our model adopts the well-established theory and technique in quantum computing e.g. quantum random walk, and adapt it to the attributed graph. Then the node attribute quantum state sequence is fed into a quantum recurrent network to obtain the final node embedding. Experimental results on three public datasets show the effectiveness of our quantum model which also outperforms a classical learning approach GraphRNA notably in terms of efficiency even on a classical computer. Though it is still restricted to the classical loss-based learning paradigm with gradient descent for model parameter training, while our computing scheme is compatible with quantum computing without involving classical computers. This is in fact largely in contrast to many hybrid quantum graph learning models which often involve many steps and modules having to be performed on classical computers.
Graph representation learning has been extensively studied, and recent models can well incorporate both node features and graph structures. Despite these progress, the inherent scalability challenge for classical computers of processing graph data and solving the downstream tasks (many are NP-hard) is still a bottleneck for existing classical graph learning models. On the other hand, quantum computing is known a promising direction for its theoretically verified scalability as well as the increasing evidence for the access to physical quantum machine in near-term. Different from many existing classical-quantum hybrid machine learning models on graphs, in this paper we take a more aggressive initiative for developing a native quantum paradigm for (attributed) graph representation learning, which to our best knowledge, has not been fulfilled in literature yet. Specifically, our model adopts the well-established theory and technique in quantum computing e.g. quantum random walk, and adapt it to the attributed graph. Then the node attribute quantum state sequence is fed into a quantum recurrent network to obtain the final node embedding. Experimental results on three public datasets show the effectiveness of our quantum model which also outperforms a classical learning approach GraphRNA notably in terms of efficiency even on a classical computer. Though it is still restricted to the classical loss-based learning paradigm with gradient descent for model parameter training, while our computing scheme is compatible with quantum computing without involving classical computers. This is in fact largely in contrast to many hybrid quantum graph learning models which often involve many steps and modules having to be performed on classical computers.
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.
Learning of network embedding with vector-based node representation has attracted wide attention over the decade. It differs from the general setting of graph node embedding whereby the node attributes are also considered and yet may incur privacy issues. In this paper, we depart from the classic CPU/GPU architecture to consider the well-established network alignment problem based on network embedding, and develop a quantum machine learning approach with a low qubit cost for its near-future applicability on Noisy Intermediate-Scale Quantum (NISQ) devices. Specifically, our model adopts the discrete-time quantum walk (QW) and conducts the QW on the tailored merged network to extract structure information from the two aligning networks without the need for quantum state preparation which otherwise requires high quantum gate cost. Then the quantum states from QW are fed to a quantum embedding ansatz (i.e., parameterized circuit) to learn the latent representation of each node. The key part of our approach is to connect these two quantum modules to achieve a pure quantum paradigm without involving classical modules. To our best knowledge, there has not been any classic-quantum hybrid approach to network embedding, let alone a pure quantum paradigm being free from the bottleneck of communication between classic devices and quantum devices, which is still an open problem. Experimental results on two real-world datasets show the effectiveness of our quantum embedding approach in comparison with classical embedding approaches. Our model is readily and efficiently implemented in Python with a full-amplitude simulation of the QW and the quantum circuit. Therefore, our model can be readily deployed on an existing NISQ device with all the circuits provided, and only 13 qubits are needed in the experiments, which is rarely attained in existing quantum graph learning works.
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.
Graph Neural Networks (GNN) and Transformer-based architectures have achieved remarkable progress in graph learning, yet they still struggle to capture both global structural dependencies and model the dynamic information propagation. In this paper, we propose CTQWformer, a hybrid graph learning framework that integrates continuous-time quantum walks (CTQW) with GNN. CTQWformer employs a trainable Hamiltonian that fuses graph topology and node features, enabling physically grounded modeling of quantum walk dynamics that captures rich and intricate graph structure information. The extracted CTQW-based representations are incorporated into two complementary modules:(i) a Graph Transformer module that embeds final-time propagation probabilities as structural biases in the self-attention mechanism, and (ii) a Graph Recurrent Module that captures temporal evolution patterns with bidirectional recurrent networks. Extensive experiments on benchmark graph classification datasets demonstrate that CTQWformer outperforms graph kernel and GNN-based methods, demonstrating the potential of integrating quantum dynamics into trainable deep learning frameworks for graph representation learning. To the best of our knowledge, CTQWformer is the first hybrid CTQW-based Transformer, integrating CTQW-derived structural bias with temporal evolution modeling to advance graph learning.
In recent years, quantum computing, as a potential way to break the bottleneck of Moore's Law, has gradually shown its unique advantages in the field of machine learning. Not only can it bring exponential or polynomial acceleration in some specific tasks, it also provides entirely new ways of representing and processing information. Focusing on the core theme of application and method innovation of quantum machine learning in structured data, this thesis systematically studies the theoretical models and practical applications of quantum computing in many sub-fields such as agricultural remote sensing, graph neural networks, and hyperdimensional computing, and explores the adaptability, scalability, and effectiveness of quantum models in real-world tasks. Firstly, in the cropland classification and yield prediction task, this study identifies that traditional neural networks tend to underperform when facing imbalanced and small-sample remote sensing data, often misclassifying minority crop types. To address this, we propose a quantum-classical hybrid recognition framework that integrates quantum feature mapping with classical neural networks. After incorporating quantum feature encoding, we observe a significant improvement in classification performance, especially in cases involving subtle field boundaries and heterogeneous textures. The quantum-enhanced model demonstrates superior accuracy, robustness, and generalization compared to its classical counterpart, validating the advantage of leveraging quantum representations in real-world agricultural datasets. The second part focuses on the learning of graph structure data and proposes to embed the Continuous Time Quantum Walk (CTQW) into the Graph Neural Network (GNN) architecture. This method not only preserves the global interference characteristic of quantum states but also realizes the efficient modeling of graph topology through the spectral graph methods. Experiments show that the proposed method is superior to many classical graph learning models in tasks such as node classification and graph structure inference. The third and fourth components of this thesis collectively explore quantum approaches to hyperdimensional computing (HDC), establishing a progressive transition from native quantum-state-based implementation to quantum-enhanced HDC strategies. Initially, we investigate the intrinsic mathematical correspondence between quantum states and high-dimensional hypervectors, and propose a novel quantum-state-based high-dimensional encoding method. This method is realized through quantum circuits capable of generating hypervectors with controllable entropy, thereby implementing essential HDC operations, such as classification and memory reconstruction, on real quantum hardware. This marks the first successful migration of core HDC mechanisms into a fully quantum-native framework. Building upon this foundation, we further propose the first quantum-enhanced HDC strategy, which does not rely solely on quantum-native implementations but rather utilizes key quantum features to boost the efficiency and expressivity of conventional HDC systems. Specifically, we introduce mechanisms such as quantum-reference-state-based binding, using density matrices to represent superclass states, and quantum state tomography for robust feature extraction. These innovations significantly enhance the resilience and performance of HDC under high-noise and high-dimensional sensing environments. The resulting models achieve superior accuracy and robustness across a variety of multi-class classification tasks, demonstrating the practical benefits of integrating quantum computation into the broader HDC paradigm. In this thesis, experimental validation is carried out in multiple real and simulation environments, including Qiskit and Paddle Quantum platforms, and a complete closed loop was achieved from theoretical derivation, quantum circuit design to end-to-end experimental evaluation. The results show that quantum methods can expand the expressive power of classical models and become an important tool to deal with large-scale, structured data problems in the future. The work in this thesis provides methodological support for quantum machine learning from theory to application, and also expands the research boundaries of high-dimensional computation and graph learning in the quantum background.