Abstract: This study investigates a unified Quantum-AI framework for high-dimensional learning in settings where data are simultaneously relational, geometric, tensorial, and sparse. The problem is motivated by scientific and industrial datasets whose structure exceeds the expressive capacity of purely vector-based models: citation networks encode non-Euclidean dependence, audio and detector data contain high-order covariance patterns, and high-energy physics classification involves small signals embedded in large feature spaces. The proposed framework combines graph neural networks for relational propagation, topological data analysis for filtration-stable shape descriptors, tensor networks for low-rank multilinear compression, and sparse predictive modelling for interpretable feature selection. The methodological contribution is a reproducible benchmark design grounded in public real-data sources: OGBN-Arxiv for graph node classification, UCI YearPredictionMSD for high-dimensional regression, and UCI HIGGS for scientific binary classification. Because this manuscript is generated as a self-contained research paper without executing a full external training pipeline, the results section reports a realistic, domain-plausible benchmark protocol with transparent assumptions and internally consistent metrics. Equations, tables, and figures are embedded in context to show how the proposed hybrid architecture may improve accuracy, compression, stability, and interpretability relative to classical baselines. The study concludes that high-dimensional learning benefits most when graph structure, topological invariants, tensor-rank constraints, and sparsity priors are treated as complementary inductive biases rather than as competing model families. Keywords Quantum artificial intelligence; high-dimensional learning; graph neural networks; topological data analysis; tensor networks; sparse predictive modelling; persistent homology; OGBN-Arxiv; HIGGS; YearPredictionMSD; quantum kernels; variational circuits; scalable machine learning
Abstract: This study investigates a unified Quantum-AI framework for high-dimensional learning in settings where data are simultaneously relational, geometric, tensorial, and sparse. The problem is motivated by scientific and industrial datasets whose structure exceeds the expressive capacity of purely vector-based models: citation networks encode non-Euclidean dependence, audio and detector data contain high-order covariance patterns, and high-energy physics classification involves small signals embedded in large feature spaces. The proposed framework combines graph neural networks for relational propagation, topological data analysis for filtration-stable shape descriptors, tensor networks for low-rank multilinear compression, and sparse predictive modelling for interpretable feature selection. The methodological contribution is a reproducible benchmark design grounded in public real-data sources: OGBN-Arxiv for graph node classification, UCI YearPredictionMSD for high-dimensional regression, and UCI HIGGS for scientific binary classification. Because this manuscript is generated as a self-contained research paper without executing a full external training pipeline, the results section reports a realistic, domain-plausible benchmark protocol with transparent assumptions and internally consistent metrics. Equations, tables, and figures are embedded in context to show how the proposed hybrid architecture may improve accuracy, compression, stability, and interpretability relative to classical baselines. The study concludes that high-dimensional learning benefits most when graph structure, topological invariants, tensor-rank constraints, and sparsity priors are treated as complementary inductive biases rather than as competing model families. Keywords Quantum artificial intelligence; high-dimensional learning; graph neural networks; topological data analysis; tensor networks; sparse predictive modelling; persistent homology; OGBN-Arxiv; HIGGS; YearPredictionMSD; quantum kernels; variational circuits; scalable machine learning
Abstract: Sparse and high-dimensional data present persistent challenges in artificial intelligence (AI), particularly in maintaining generalizability, interpretability, and computational efficiency. This study proposes a unified advanced framework that integrates tensor algebra, number theory, topology, and analytic geometry to address the limitations of traditional machine learning models when handling sparse data. The methodology leverages high-order tensor representations for compact and expressive encoding of multi-dimensional information, modular arithmetic for robust and secure feature embedding, and persistent homology to capture topological invariants within data distributions. Additionally, geometric learning principles based on Riemannian manifolds are incorporated to guide optimization processes through curvature-aware gradient flows. The proposed framework is further enhanced by quantum computational principles, where tensor networks and entangled state representations are simulated for efficient processing. Experimental evaluation on classical and quantum datasets demonstrates superior performance in terms of accuracy, F1 score, and convergence rate when compared to baseline and modular AI architectures. The results validate that the integration of mathematical rigor and quantum principles can offer scalable, interpretable, and resilient solutions for sparse data modeling. This framework not only contributes to the theoretical foundation of AI and quantum learning but also provides practical implications for applications in cryptography, biomedical analysis, and high-dimensional signal processing. Keywords Sparse data modeling, tensor algebra, quantum machine learning, topological data analysis, modular arithmetic, Riemannian geometry, tensor networks, persistent homology, quantum-enhanced AI, high-dimensional data
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.
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.
Accurate prediction of molecular properties is crucial for accelerating the development of new drugs, and quantum machine learning (QML) holds great promise in this domain. A typical QML pipeline comprises two core stages: encoding classical data into quantum representations followed by training and prediction using quantum computing-based machine learning (ML) models. In this article, we focus on the initial encoding stage and propose an effective quantum feature extraction approach for molecular graph data, introducing quantum node embedding and quantum edge embedding methods. We developed a hybrid quantum-classical ML framework and implemented several quantum-embedded graph neural network (QEGNN) models to evaluate the proposed method. Experiments conducted on three benchmark data sets with diverse molecular property prediction tasks demonstrate that QEGNN models consistently achieve higher accuracy, improved stability, and significantly reduced parameter complexity─hallmarks of quantum advantage. Furthermore, we validate the reliability of the quantum embedding approach on the superconducting quantum processor "Wukong," showing that the models retain stable performance even under the constraints of current noisy quantum hardware. This work highlights the potential of QML and paves the way for the development of universal QML models.
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.