Hyperdimensional Computing (HDC) is a brain-inspired computational paradigm that utilizes high-dimensional vector spaces to represent, bind, and process information efficiently. Its robustness, scalability, and adaptability make HDC particularly effective for machine learning tasks such as classification and pattern recognition. In this work, we introduce Quantum-StateHD (QSHD), a novel approach that leverages random quantum states as encoding mechanisms for high-dimensional spaces within the HDC framework. Quantum states, with their inherent properties of high-dimensionality, near-orthogonality, and probabilistic distributions, provide a natural substrate for constructing robust representations. Quantum-StateHD encodes classical data into the coefficients of random quantum states and seamlessly integrates these representations into the HDC pipeline. Experimental results on several benchmark classification datasets demonstrate that Quantum-StateHD achieves competitive or superior performance compared to traditional state-of-the-art HDC methods, showcasing its potential for robust and efficient high-dimensional information processing. This study bridges the gap between quantum information science and HDC, offering a promising direction for hybrid quantum-classical machine learning architectures.
Hyperdimensional Computing (HDC) is a brain-inspired computational paradigm that utilizes high-dimensional vector spaces to represent, bind, and process information efficiently. Its robustness, scalability, and adaptability make HDC particularly effective for machine learning tasks such as classification and pattern recognition. In this work, we introduce Quantum-StateHD (QSHD), a novel approach that leverages random quantum states as encoding mechanisms for high-dimensional spaces within the HDC framework. Quantum states, with their inherent properties of high-dimensionality, near-orthogonality, and probabilistic distributions, provide a natural substrate for constructing robust representations. Quantum-StateHD encodes classical data into the coefficients of random quantum states and seamlessly integrates these representations into the HDC pipeline. Experimental results on several benchmark classification datasets demonstrate that Quantum-StateHD achieves competitive or superior performance compared to traditional state-of-the-art HDC methods, showcasing its potential for robust and efficient high-dimensional information processing. This study bridges the gap between quantum information science and HDC, offering a promising direction for hybrid quantum-classical machine learning architectures.
Hyperdimensional Computing (HDC) is a robust computational framework inspired by human cognition characterized by simple and efficient operations within high-dimensional vector spaces. Quantum-enhanced Hyperdimensional Computing (QeHDC) extends classical HDC by leveraging quantum mechanical properties to enhance computational efficiency. In this paper, we propose a novel Quantum HDC framework featuring a one-pass training method, leveraging sinusoidal and quantum encoding to project classical data into quantum amplitude states efficiently. Our framework introduces an innovative reference-state-based quantum binding operation realized via quantum circuits. Furthermore, we propose a density-matrix-based superclass generation strategy employing eigenvalue decomposition to extract critical quantum state features effectively, enabling a more accurate and robust class representation. Experimental evaluations conducted on standard benchmark datasets demonstrate our approach's superior performance, robustness to noise, and computational feasibility compared to traditional classical and existing quantum-enhanced approaches. The results highlight the practical benefits and potential of Quantum HDC for quantum-enhanced classification tasks and pave the way for future advancements in quantum-inspired computational paradigms.
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.
A significant challenge in quantum computing (QC) is developing learning models that truly align with quantum principles, as many current approaches are complex adaptations of classical frameworks. In this work, we introduce Quantum Hyperdimensional Computing (QHDC), a fundamentally new paradigm. We demonstrate that the core operations of its classical counterpart, Hyperdimensional Computing (HDC), a brain-inspired model, map with remarkable elegance and direct correspondence onto the native operations of a QC. This suggests HDC is exceptionally well-suited for a quantum-native implementation. We establish a direct, resource-efficient mapping: (i) hypervectors are mapped to quantum states, (ii) the bundling operation is implemented as a quantum-native averaging process using a Linear Combination of Unitaries (LCU) and Oblivious Amplitude Amplification (OAA), (iii) the binding operation is realized via quantum phase oracles, (iv) the permutation operation is implemented using the Quantum Fourier Transform (QFT), and (v) vector similarity is calculated using quantum state fidelity measurements based on the Hadamard Test. We present the first-ever implementation of this framework, validated through symbolic analogical reasoning and supervised classification tasks. The viability of QHDC is rigorously assessed via a comparative analysis of results from classical computation, ideal quantum simulation, and execution of a 156-qubit IBM Heron r3 quantum processor. Our results validate the proposed mappings and demonstrate the versatility of the framework, establishing QHDC as a physically realizable technology. This work lays the foundation for a new class of quantum neuromorphic algorithms and opens a promising avenue for tackling complex cognitive and biomedical problems intractable for classical systems.
Quantum state tomography (QST) is a fundamental technique for characterizing quantum systems, but it often suffers from significant experimental challenges, including high measurement complexity and resource demands. This paper explores the potential of hyperdimensional computing (HDC) as a viable alternative to traditional QST. HDC leverages high-dimensional vectors to represent and manipulate quantum states, allowing for the development of algorithms that exploit inherent correlations to reconstruct quantum state information with reduced measurement requirements. The core claim is that HDC offers a potentially efficient and scalable approach to QST. This work details the theoretical framework, outlining key algorithms and highlighting the advantages of utilizing HDC for quantum state characterization. The focus is on demonstrating the feasibility of this approach through conceptual design, emphasizing the reduced complexity compared to conventional QST methods. We propose a framework for representing quantum states within HDC vectors and present a simplified reconstruction algorithm.
This paper explores a novel approach to quantum state teleportation leveraging hyperdimensional computing (HDC). Traditional quantum state teleportation protocols face limitations due to qubit fidelity requirements and the complexity associated with distributing entangled qubits over long distances. We propose utilizing HDC – high-dimensional vectors characterized by near-orthogonal components – to represent and transmit quantum states. Our method significantly reduces the need for direct qubit entanglement, offering a potentially scalable and robust alternative. The core mechanism involves encoding the quantum state information into the high-dimensional vector components and subsequently extracting the state at the destination. We detail the mathematical framework underpinning this approach, focusing on vector projections, inner products, and state reconstruction. The results demonstrate a viable path towards distributed quantum state teleportation, addressing the key challenges of fidelity and entanglement distribution. We provide a detailed analysis of the computational complexity and potential advantages of this HDC-based teleportation scheme.
This paper presents a quantum algorithm for efficiently decoding hypervectors, a crucial process in extracting atomic elements from hypervectors - an essential task in Hyperdimensional Computing (HDC) models for interpretable learning and information retrieval. HDC employs high-dimensional vectors and efficient operators to encode and manipulate information, representing complex objects from atomic concepts. When one attempts to decode a hypervector that is the product (binding) of multiple hypervectors, the factorization becomes prohibitively costly with classical optimization-based methods and specialized recurrent networks, an inherent consequence of the binding operation. We propose HDQF, an innovative quantum computing approach, to address this challenge. By exploiting parallels between HDC and quantum computing and capitalizing on quantum algorithms' speedup capabilities, HDQF encodes potential factors as a quantum superposition using qubit states and bipolar vector representation. This yields a quadratic speedup over classical search methods and effectively mitigates Hypervector Factorization capacity issues.