The convergence of quantum computing and machine learning offers significant potential for processing complex data distributions. However, the realization of this potential in the Noisy Intermediate-Scale Quantum (NISQ) era is constrained by physical hardware limitations, particularly restricted qubit counts and system noise. This thesis addresses the challenge of the ”Representation Bottleneck” by establishing a framework for resource-efficient quantum representation learning. The research demonstrates that effective learning on near-term devices can be achieved by optimizing circuit architectures and objective functions to align with hardware constraints. First, to address resource limitations in high-dimensional visual recognition, we propose the Multi-Gate Quantum Convolutional Neural Network (MG-QNN). By employing a Multi-Gate strategy, this architecture optimizes the utilization of quan tum resources within the circuit design. Empirical evaluations on face recognition benchmarks indicate that this approach maintains competitive recognition accuracy while reducing the qubit requirement compared to standard quantum convolutional methods. Second, extending the framework to non-Euclidean data, we introduce the Single-Qubit Graph Neural Network (sQGNN). Utilizing Discrete-Time Quantum Walks, this method encodes graph topologies and relational patterns onto a single qubit. This approach circumvents the need for multi-qubit entangling gates, thereby reducing the computational overhead and noise sensitivity typically associated with processing graph-structured data. Third, in the domain of generative modeling, we present the Single-Qubit Quan tum Convolutional Variational Autoencoder (QCVAE). Addressing the difficulty of generative tasks on constrained devices, this model integrates the Information Bottleneck principle with efficient data re-uploading techniques. The study demonstrates that a single qubit possesses sufficient expressivity to model and reconstruct image distributions effectively when guided by appropriate information theoretic constraints. Finally, to resolve the fundamental limitations of classical loss functions in quantum learning, we establish the Hilbert-Schmidt Information Bottleneck (HSIB). We identify that standard Euclidean metrics often fail to respect the geometric structure of the Hilbert space. The HSIB framework employs the Hilbert Schmidt distance as a tractable geometric measure, providing a learning objective that maximizes information retention while adhering to the intrinsic geometry of quantum states. Collectively, these contributions illustrate that practical quantum machine learning advantage in the NISQ era does not rely solely on scaling hardware, but on the strategic design of resource-efficient architectures and geometrically valid metrics.
The convergence of quantum computing and machine learning offers significant potential for processing complex data distributions. However, the realization of this potential in the Noisy Intermediate-Scale Quantum (NISQ) era is constrained by physical hardware limitations, particularly restricted qubit counts and system noise. This thesis addresses the challenge of the ”Representation Bottleneck” by establishing a framework for resource-efficient quantum representation learning. The research demonstrates that effective learning on near-term devices can be achieved by optimizing circuit architectures and objective functions to align with hardware constraints. First, to address resource limitations in high-dimensional visual recognition, we propose the Multi-Gate Quantum Convolutional Neural Network (MG-QNN). By employing a Multi-Gate strategy, this architecture optimizes the utilization of quan tum resources within the circuit design. Empirical evaluations on face recognition benchmarks indicate that this approach maintains competitive recognition accuracy while reducing the qubit requirement compared to standard quantum convolutional methods. Second, extending the framework to non-Euclidean data, we introduce the Single-Qubit Graph Neural Network (sQGNN). Utilizing Discrete-Time Quantum Walks, this method encodes graph topologies and relational patterns onto a single qubit. This approach circumvents the need for multi-qubit entangling gates, thereby reducing the computational overhead and noise sensitivity typically associated with processing graph-structured data. Third, in the domain of generative modeling, we present the Single-Qubit Quan tum Convolutional Variational Autoencoder (QCVAE). Addressing the difficulty of generative tasks on constrained devices, this model integrates the Information Bottleneck principle with efficient data re-uploading techniques. The study demonstrates that a single qubit possesses sufficient expressivity to model and reconstruct image distributions effectively when guided by appropriate information theoretic constraints. Finally, to resolve the fundamental limitations of classical loss functions in quantum learning, we establish the Hilbert-Schmidt Information Bottleneck (HSIB). We identify that standard Euclidean metrics often fail to respect the geometric structure of the Hilbert space. The HSIB framework employs the Hilbert Schmidt distance as a tractable geometric measure, providing a learning objective that maximizes information retention while adhering to the intrinsic geometry of quantum states. Collectively, these contributions illustrate that practical quantum machine learning advantage in the NISQ era does not rely solely on scaling hardware, but on the strategic design of resource-efficient architectures and geometrically valid metrics.
Amidst the rapidly evolving landscape of information technology, the convergence of quantum computing and machine learning—referred to as quantum machine learning—offers promising potential to enhance classical algorithms. However, significant challenges remain in both hardware and software implementation during the Noisy Intermediate-Scale Quantum (NISQ) era, including imperfect qubits, architectural constraints, and high noise levels. In response to these obstacles, this research introduces a novel solution: Quantum Convolutional Variational Autoencoders (QCVAE), designed to operate with only a single qubit. This innovative approach efficiently utilizes a single qubit to manage large-scale data, making it particularly well-suited for quantum computers with limited resources. Simulation results demonstrate the robustness of QCVAE in handling image data, and its deployment on a real quantum computer showcases the model’s practical viability. Additionally, the proposed approach leverages the information bottleneck principle to optimize quantum embeddings, effectively mitigating the impact of prevalent quantum noise. By addressing these core challenges, QCVAE presents a compelling solution for advancing quantum computing applications within the constraints of current NISQ technology.
Amidst the rapidly evolving landscape of information technology, the convergence of quantum computing and machine learning—referred to as quantum machine learning—offers promising potential to enhance classical algorithms. However, significant challenges remain in both hardware and software implementation during the Noisy Intermediate-Scale Quantum (NISQ) era, including imperfect qubits, architectural constraints, and high noise levels. In response to these obstacles, this research introduces a novel solution: Quantum Convolutional Variational Autoencoders (QCVAE), designed to operate with only a single qubit. This innovative approach efficiently utilizes a single qubit to manage large-scale data, making it particularly well-suited for quantum computers with limited resources. Simulation results demonstrate the robustness of QCVAE in handling image data, and its deployment on a real quantum computer showcases the model’s practical viability. Additionally, the proposed approach leverages the information bottleneck principle to optimize quantum embeddings, effectively mitigating the impact of prevalent quantum noise. By addressing these core challenges, QCVAE presents a compelling solution for advancing quantum computing applications within the constraints of current NISQ technology.
Abstract The arrival of noisy intermediate-scale quantum (NISQ) devices defines an era in which quantum utility is fundamentally constrained by finite coherence times, limited qubit counts, gate infidelities, restricted connectivity, and measurement noise. Within this regime, hybrid quantum-classical frameworks have emerged as the dominant operational paradigm, particularly for quantum machine learning (QML). This review identifies a fundamental trade-off between expressivity, trainability, and noise resilience that governs the performance and scalability of NISQ-era QML systems. To contextualize these challenges, we introduce the resource-constrained iterative routing framework, a hardware-aware conceptual architecture that integrates topology-aware classical compression and distributed quantum orchestration to maintain circuit depths within device-dependent limits while routing representations toward symmetry-constrained Hilbert subspaces to mitigate noise-induced barren plateaus. Furthermore, we shift the discussion of quantum advantage away from asymptotic fault-tolerant complexity toward the notion of operational NISQ advantage based on finite-resource scaling, trainability preservation, and sampling complexity. We evaluate the practical resource efficiency of variational quantum algorithms, quantum kernel methods, and quantum neural networks across superconducting, trapped-ion, neutral-atom, and photonic platforms. The review also examines reproducibility challenges, emphasizing benchmarking against optimized classical baselines, and discusses strategies for managing the sampling overhead of error mitigation alongside distributed execution and quantum circuit compilation. Ultimately, NISQ in Practice positions hybrid QML as a physically constrained computational paradigm while outlining a pathway from contemporary noisy workflows toward early fault-tolerant quantum architectures.
In the last decade, quantum computing has showcased its unique mechanism across diverse fields, highlighting significant potential for data-driven applications requiring substantial computational resources. Within this landscape, quantum machine learning emerges as a promising frontier, poised to harness the unique advantages of quantum computing for machine learning tasks. Nonetheless, the current generation of quantum hardware, typified by noisy intermediate-scale quantum (NISQ) devices, grapples with severe resource constraints, particularly in terms of qubit availability. While quantum computing offers tantalizing capabilities such as superposition and entanglement, which can be strategically leveraged to optimize the performance of quantum neural networks, the challenge remains in mitigating the resource limitations while upholding high recognition accuracy. To address this imperative, we introduce a pioneering face recognition method christened the Multi-Gate Quantum Convolutional Neural Network (MG-QCNN). This innovation is engineered to surmount the resource bottleneck endemic to NISQ devices while preserving exceptional recognition accuracy. Our empirical investigations conducted on benchmark datasets, including the Yale face dataset and the ORL face database, illuminate the remarkable potential of this approach. Specifically, our proposed variational quantum circuit architecture consistently achieves an impressive average accuracy of 96%, which is better than the 95% of the classic CNN. Our model underscores the efficacy of quantum convolution operations in the extraction of feature maps, exhibiting a transformative stride toward unlocking the full potential of quantum-enhanced face recognition, and compared with other quantum models, our method has more advantages in accuracy and efficiency.
Quantum convolutional neural networks (QCNNs) are emerging as promising models in quantum machine learning, particularly for image classification and computer vision tasks. Recent developments include hybrid classical–quantum architectures, advanced quantum encoding methods, and novel circuit designs that improve data processing on Noisy Intermediate-Scale Quantum (NISQ) devices. However, practical implementation remains challenging due to circuit complexity, gate count, qubit connectivity, and hardware noise, which limit scalability and performance. Consequently, quantum circuit optimization has become essential for reducing resource requirements and improving classification accuracy. This study presents a systematic literature review of 40 research papers published between 2014 and 2025. The review covers QCNNs together with closely related quantum neural network (QNN) models and quantum circuit optimization studies, since circuit-optimization techniques are frequently developed for QNNs more broadly rather than for QCNN architectures in isolation. Within this scope, it examines network architectures, encoding strategies, application domains, and optimization techniques, with particular attention to heuristic and metaheuristic approaches such as genetic algorithms and evolutionary strategies. The findings highlight growing trends in hybrid quantum–classical integration, the widespread adoption of metaheuristic optimization, and the importance of multi-objective frameworks adapted to quantum hardware constraints. Finally, the review identifies key research gaps and future directions for practical QCNN deployment on near-term quantum devices.
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.