Abstract Hybrid quantum–classical learning has emerged as a promising paradigm for leveraging near-term quantum devices in practical machine learning tasks. However, many existing hybrid architectures rely on tightly coupled end-to-end training schemes that are difficult to optimize, sensitive to quantum noise, and strongly dependent on specific encoder designs. In this work, we introduce Quantum LEGO Learning, a modular framework for hybrid artificial intelligence that decomposes learning into reusable classical and quantum blocks with explicitly separated roles. Within this framework, a pre-trained classical neural network acts as a frozen feature extractor, while a variational quantum circuit (VQC) serves as the only trainable, adaptive module that operates on structured latent representations. This design enables stable optimization, reduces parameter coupling between classical and quantum components, and supports architecture-agnostic integration across different classical backbones. We develop a block-wise theoretical analysis that decomposes the learning behavior of the hybrid model into components of approximation, estimation, optimization, and noise-induced error. The analysis shows that once expressive classical representations are fixed, the overall model's approximation capability depends primarily on the classical feature block, while the trainable quantum module governs the complexity of downstream adaptation. We further derive optimization and noise-resilience bounds demonstrating how freezing the classical block suppresses the propagation of noisy gradients during training. To validate the proposed framework, we conduct systematic experiments on quantum dot classification and genome transcription factor binding site prediction using multiple frozen feature extractors, including ResNet and tensor-train network backbones, combined with both quantum and classical adaptive heads. Experimental results from noiseless simulations, realistic quantum-noise models, and IBM Heron quantum hardware demonstrate stable optimization, robustness to noise, and improved performance of VQC-based adaptive heads under matched parameter budgets. These results suggest that modular hybrid architectures provide a practical and scalable pathway for quantum-enhanced learning in the NISQ regime.
Abstract Hybrid quantum–classical learning has emerged as a promising paradigm for leveraging near-term quantum devices in practical machine learning tasks. However, many existing hybrid architectures rely on tightly coupled end-to-end training schemes that are difficult to optimize, sensitive to quantum noise, and strongly dependent on specific encoder designs. In this work, we introduce Quantum LEGO Learning, a modular framework for hybrid artificial intelligence that decomposes learning into reusable classical and quantum blocks with explicitly separated roles. Within this framework, a pre-trained classical neural network acts as a frozen feature extractor, while a variational quantum circuit (VQC) serves as the only trainable, adaptive module that operates on structured latent representations. This design enables stable optimization, reduces parameter coupling between classical and quantum components, and supports architecture-agnostic integration across different classical backbones. We develop a block-wise theoretical analysis that decomposes the learning behavior of the hybrid model into components of approximation, estimation, optimization, and noise-induced error. The analysis shows that once expressive classical representations are fixed, the overall model's approximation capability depends primarily on the classical feature block, while the trainable quantum module governs the complexity of downstream adaptation. We further derive optimization and noise-resilience bounds demonstrating how freezing the classical block suppresses the propagation of noisy gradients during training. To validate the proposed framework, we conduct systematic experiments on quantum dot classification and genome transcription factor binding site prediction using multiple frozen feature extractors, including ResNet and tensor-train network backbones, combined with both quantum and classical adaptive heads. Experimental results from noiseless simulations, realistic quantum-noise models, and IBM Heron quantum hardware demonstrate stable optimization, robustness to noise, and improved performance of VQC-based adaptive heads under matched parameter budgets. These results suggest that modular hybrid architectures provide a practical and scalable pathway for quantum-enhanced learning in the NISQ regime.
Hybrid quantum-classical learning models increasingly integrate neural networks with variational quantum circuits (VQCs) to exploit complementary inductive biases. However, many existing approaches rely on tightly coupled architectures or task-specific encoders, limiting conceptual clarity, generality, and transferability across learning settings. In this work, we introduce Quantum LEGO Learning, a modular and architecture-agnostic learning framework that treats classical and quantum components as reusable, composable learning blocks with well-defined roles. Within this framework, a pre-trained classical neural network serves as a frozen feature block, while a VQC acts as a trainable adaptive module that operates on structured representations rather than raw inputs. This separation enables efficient learning under constrained quantum resources and provides a principled abstraction for analyzing hybrid models. We develop a block-wise generalization theory that decomposes learning error into approximation and estimation components, explicitly characterizing how the complexity and training status of each block influence overall performance. Our analysis generalizes prior tensor-network-specific results and identifies conditions under which quantum modules provide representational advantages over comparably sized classical heads. Empirically, we validate the framework through systematic block-swap experiments across frozen feature extractors and both quantum and classical adaptive heads. Experiments on quantum dot classification demonstrate stable optimization, reduced sensitivity to qubit count, and robustness to realistic noise.
Hybrid quantum-classical computing offers a promising pathway to harness quantum advantages while mitigating the hardware limitations of noisy intermediate-scale quantum (NISQ) devices. This work proposes a modular hybrid architecture that combines classical preprocessing, quantum-enhanced feature mapping through parameterized quantum circuits (PQCs), and adaptive classical optimization. The framework is designed to improve robustness and generalization of machine learning models in noisy environments, addressing critical issues such as overfitting, noise sensitivity, and hardware-induced errors. Experimental evaluations were conducted on benchmark datasets, including Iris, reduced-dimension MNIST, synthetic noisy XOR, Wine Quality, and Breast Cancer Wisconsin. The proposed model was tested under multiple noise models, such as Gaussian, salt-and-pepper, Poisson, and quantum-specific errors (bit-flip, phase-flip, and depolarizing), using 5-fold cross-validation and repeated trials for statistical rigor. Key performance metrics included Classification Accuracy (CA), Robustness Index (RI), and Training Stability (TS), with results reported as mean ± standard deviation and supported by paired t-tests (p < 0.05). Results demonstrate that the hybrid model consistently outperforms classical support vector machines (SVM) and standalone variational quantum classifiers (VQC) in noisy conditions, achieving smaller accuracy degradation and higher stability. The combination of quantum- enhanced feature mapping, optimizer synergy, and modular design is shown to be central to its resilience.
Abstract Variational Quantum Circuits (VQCs) offer a novel pathway for quantum machine learning, yet their practical application is hindered by inherent limitations such as constrained linear expressivity, optimization challenges, and acute sensitivity to quantum hardware noise. This work introduces VQC-MLPNet, a scalable and robust hybrid quantum-classical architecture designed to overcome these obstacles. By innovatively employing quantum circuits to dynamically generate parameters for classical Multi-Layer Perceptrons (MLPs) via amplitude encoding and parameterized quantum operations, VQC-MLPNet substantially expands representation capabilities and augments training stability. We provide rigorous theoretical guarantees via statistical learning techniques and Neural Tangent Kernel analysis, explicitly deriving upper bounds on approximation, uniform deviation, and optimization errors. These theoretical insights demonstrate exponential improvements in representation capacity relative to quantum circuit depth and the number of qubits, providing clear computational advantages over standalone quantum circuits and existing hybrid quantum architectures. Our theoretical claims are empirically corroborated through extensive experiments, including the classification of semiconductor quantum-dot charge states and the prediction of genomic transcription factor binding sites, demonstrating resilient performance even under realistic IBM quantum noise simulations. This research establishes a theoretically sound and practically robust framework, advancing the frontiers of quantum-enhanced learning for unconventional computing paradigms in the Noisy Intermediate-Scale Quantum era and beyond.
The development of quantum computers has been the stimulus that enables the realization of Quantum Machine Learning (QML), an area that integrates the calculational framework of quantum mechanics with the adaptive properties of classical machine learning. This article suggests a broad architecture that allows the connection between classical data pipelines and quantum algorithms, hybrid quantum-classical models emerge as a promising route to scalable and near-term quantum benefit. At the core of this paradigm lies the Classical-Quantum (CQ) paradigm, in which the qubit states of high-dimensional classical data are encoded using sophisticated classical encoding strategies which encode the data in terms of amplitude and angle of rotation, along with superposition mapping. These techniques allow compression of information exponentially into Hilbert space representations, which, together with reduced sample complexity, allows greater feature expressivity. We also examine variational quantum circuits, quantum gates expressed as trainable variables that run with classical optimizers to overcome decoherence, noise, and gate-depth constraints of the existing Noisy Intermediate-Scale Quantum (NISQ) devices. Experimental comparisons with a Quantum Naive Bayes classifier prove that even small quantum circuits can approximate probabilistic inference with competitive accuracy compared to classical benchmarks, and have much better robustness to noisy data distributionsThis model does not only explain the algorithmic and architectural design of QML, it also offers a roadmap to the implementation of quantum kernels, variational algorithms, and hybrid feedback loops into practice, including optimization, computer vision, and medical diagnostics. The results support the idea that hybrid architectures with strong data encoding and adaptive error protection are key to moving QML out of theory to practice.
One key step in performing quantum machine learning (QML) on noisy intermediate-scale quantum (NISQ) devices is the dimension reduction of the input data prior to their encoding. Traditional principle component analysis (PCA) and neural networks have been used to perform this task; however, the classical and quantum layers are usually trained separately. A framework that allows for a better integration of the two key components is thus highly desirable. Here we introduce a hybrid model combining the quantum-inspired tensor networks (TN) and the variational quantum circuits (VQC) to perform supervised learning tasks, which allows for an end-to-end training. We show that a matrix product state based TN with low bond dimensions performs better than PCA as a feature extractor to compress data for the input of VQCs in the binary classification of MNIST dataset. The architecture is highly adaptable and can easily incorporate extra quantum resource when available.
Quantum transfer learning combines pretrained classical deep learning models with quantum circuits to reuse expressive feature representations while limiting the number of trainable parameters. In this work, we introduce a family of compact quantum transfer learning architectures that attach variational quantum classifiers to frozen convolutional backbones for image classification. We instantiate and evaluate several classical-quantum hybrid models implemented in PennyLane and Qiskit, and systematically compare them with a classical transfer-learning baseline across heterogeneous image datasets. To ensure a realistic assessment, we evaluate all approaches under both ideal simulation and noisy emulation using noise models calibrated from IBM quantum hardware specifications, as well as on real IBM quantum hardware. Experimental results show that the proposed quantum transfer learning architectures achieve competitive and, in several cases, superior accuracy while consistently reducing training time and energy consumption relative to the classical baseline. Among the evaluated approaches, PennyLane-based implementations provide the most favorable trade-off between accuracy and computational efficiency, suggesting that hybrid quantum transfer learning can offer practical benefits in realistic NISQ era settings when feature extraction remains classical.