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.
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.
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.
The comparative evaluation between classical and quantum reinforcement learning (QRL) paradigms was conducted to investigate their convergence behavior, robustness under observational noise, and computational efficiency in a benchmark control environment. The study employed a multilayer perceptron (MLP) agent as a classical baseline and a parameterized variational quantum circuit (VQC) as a quantum counterpart, both trained on the CartPole-v1 environment over 500 episodes. Empirical results demonstrated that the classical MLP achieved near-optimal policy convergence with a mean return of 498.7 +/- 3.2, maintaining stable equilibrium throughout training. In contrast, the VQC exhibited limited learning capability, with an average return of 14.6 +/- 4.8, primarily constrained by circuit depth and qubit connectivity. Noise robustness analysis further revealed that the MLP policy deteriorated gracefully under Gaussian perturbations, while the VQC displayed higher sensitivity at equivalent noise levels. Despite the lower asymptotic performance, the VQC exhibited significantly lower parameter count and marginally increased training time, highlighting its potential scalability for low-resource quantum processors. The results suggest that while classical neural policies remain dominant in current control benchmarks, quantum-enhanced architectures could offer promising efficiency advantages once hardware noise and expressivity limitations are mitigated.
Abstract Variational Quantum Computing (VQC) faces fundamental scalability barriers, primarily due to the presence of barren plateaus and its sensitivity to quantum noise. To address these challenges, we introduce TensorHyper-VQC, a novel tensor-train (TT)-guided hypernetwork framework that significantly improves the robustness and scalability of VQC. Our framework fully delegates the generation of quantum circuit parameters to a classical TT network, effectively decoupling optimization from quantum hardware. This innovative parameterization mitigates gradient vanishing, enhances noise resilience through structured low-rank representations, and facilitates efficient gradient propagation. Grounded in Neural Tangent Kernel and statistical learning theory, our rigorous theoretical analyses establish strong guarantees on approximation capability, optimization stability, and generalization performance. Extensive empirical results across quantum dot classification, Max-Cut optimization, and molecular quantum simulation tasks demonstrate that TensorHyper-VQC consistently achieves superior performance and robust noise tolerance, including hardware-level validation on a 156-qubit IBM Heron processor. These results position TensorHyper-VQC as a scalable and noise-resilient framework for advancing practical quantum machine learning on near-term devices.
Abstract Variational quantum circuits (VQCs) are a central paradigm for quantum machine learning, yet their practical deployment is limited by poor trainability, sensitivity to noise, and the lack of input-adaptive parameterization. In this work, we introduce TensorDual-VQC, a tensor-structured operator-learning framework that models variational quantum computation as an input-conditioned mapping that jointly governs quantum state encoding and circuit parameter generation. The proposed approach employs a shared low-rank Tensor-Train (TT) backbone with dual output heads, inducing a coupled representation that constrains the hypothesis space to a structured low-dimensional manifold. Under standard smoothness and low-rank assumptions, we show that the approximation behavior is governed by the TT-rank rather than the ambient parameter dimension, and that shared latent structure can enable more compact representations than decoupled parameterizations in structured regimes. We further analyze trainability through the induced Neural Tangent Kernel, showing that the multi-branch gradient structure enriches the span of gradient features and can improve kernel conditioning under mild non-degeneracy conditions. In addition, we relate robustness to quantum noise to the intrinsic effective dimension of the tensor parameter manifold, providing a first-order scaling characterization of output variance under stochastic perturbations. We evaluate TensorDual-VQC on quantum dot classification, quantum simulation, and combinatorial optimization tasks under both simulated noise and real quantum hardware. Across all settings, the proposed framework achieves higher accuracy, faster convergence, and greater stability than standard VQCs and hypernetwork-based baselines when quantum resources are matched. These results suggest that structured operator learning with shared low-rank representations provides a principled and practical approach to scalable, noise-resilient quantum learning in the NISQ regime.
Quantum machine learning (QML) is promising for potential speedups and improvements in conventional machine learning (ML) tasks (e.g., classification/regression). The search for ideal QML models is an active research field. This includes identification of efficient classical-to-quantum data encoding scheme, construction of parametric quantum circuits (PQC) with optimal expressivity and entanglement capability, and efficient output decoding scheme to minimize the required number of measurements, to name a few. However, most of the empirical/numerical studies lack a clear path towards scalability. Any potential benefit observed in a simulated environment may diminish in practical applications due to the limitations of noisy quantum hardware (e.g., under decoherence, gate-errors, and crosstalk). We present a scalable quantum-classical hybrid deep neural network (DeepQMLP) architecture inspired by classical deep neural network architectures. In DeepQMLP, stacked shallow Quantum Neural Network (QNN) models mimic the hidden layers of a classical feed-forward multi-layer perceptron network. Each QNN layer produces a new and potentially rich representation of the input data for the next layer. This new representation can be tuned by the parameters of the circuit. Shallow QNN models experience less decoherence, gate errors, etc. which make them (and the network) more resilient to quantum noise. We present numerical studies on a variety of classification problems to show the trainability of DeepQMLP. We also show that DeepQMLP performs reasonably well on unseen data and exhibits greater resilience to noise over QNN models that use a deep quantum circuit. DeepQMLP provided up to 25.3% lower loss and 7.92% higher accuracy during inference under noise than QMLP.
Abstract Quantum Machine Learning (QML) offers tremendous potential but is currently limited by the availability of qubits. We introduce an innovative approach that utilizes pre-trained neural networks to enhance Variational Quantum Circuits (VQC). This technique effectively separates approximation error from qubit count and removes the need for restrictive conditions, making QML more viable for real-world applications. Our method significantly improves parameter optimization for VQC while delivering notable gains in representation and generalization capabilities, as evidenced by rigorous theoretical analysis and extensive empirical testing on quantum dot classification tasks. Moreover, our results extend to applications such as human genome analysis, demonstrating the broad applicability of our approach. By addressing the constraints of current quantum hardware, our work paves the way for a new era of advanced QML applications, unlocking the full potential of quantum computing in fields such as machine learning, materials science, medicine, mimetics, and various interdisciplinary areas.