Quantum machine learning offers a practical opportunity to leverage near-term quantum devices without requiring quantum inference at deployment. We propose a quantum-classical hybrid knowledge distillation framework in which a variational quantum circuit, equipped with a Quantum Fourier Transform-inspired positional encoding, acts as a soft-label teacher for a compact classical student. Rather than serving as a standalone classifier, the quantum model is used offline to generate structured probability distributions that encode global spectral information and uncertainty. These quantum-derived soft labels are distilled into a lightweight classical network using a hybrid loss that combines hard and soft supervision. Experiments on MNIST demonstrate that students trained with quantum soft labels exhibit consistent and statistically meaningful robustness improvements to Gaussian noise and in-plane rotations compared to classical distillation baselines, while maintaining strong clean accuracy and calibration. These results highlight a distinct role for NISQ-era quantum models as supervisory signal generators, enabling quantum-informed learning within fully classical deployment pipelines.
Quantum machine learning offers a practical opportunity to leverage near-term quantum devices without requiring quantum inference at deployment. We propose a quantum-classical hybrid knowledge distillation framework in which a variational quantum circuit, equipped with a Quantum Fourier Transform-inspired positional encoding, acts as a soft-label teacher for a compact classical student. Rather than serving as a standalone classifier, the quantum model is used offline to generate structured probability distributions that encode global spectral information and uncertainty. These quantum-derived soft labels are distilled into a lightweight classical network using a hybrid loss that combines hard and soft supervision. Experiments on MNIST demonstrate that students trained with quantum soft labels exhibit consistent and statistically meaningful robustness improvements to Gaussian noise and in-plane rotations compared to classical distillation baselines, while maintaining strong clean accuracy and calibration. These results highlight a distinct role for NISQ-era quantum models as supervisory signal generators, enabling quantum-informed learning within fully classical deployment pipelines.
The rapid advancement of machine learning (ML) and the growing need for computational power have led to the exploration of quantum computing, which offers significant potential for faster complex calculations. However, Quantum Machine Learning (QML) faces challenges due to the limited number of qubits and noise of quantum circuits, particularly with Noisy Intermediate-Scale Quantum (NISQ) devices. These challenges severely limit the current capacity to train accurate and stable Quantum Machine Learning Models. In this paper, we propose a novel framework for QML that employs the knowledge distillation method to harness the power of well-trained classical machine learning (CML) models and enhance the training performance of QML models. In this framework, we utilize the well-trained CML as a teacher model to assist the training of the student QML model using the knowledge distillation method. By distilling knowledge from the robust CML model, our framework can potentially address the problem of the barren plateau which hinders effective model training. Knowledge distillation is well suited for this framework through the transfer of knowledge without parameter sharing. Through empirical tests, our framework has demonstrated not only an increase in the accuracy of QML models but also a notable improvement in training stability.
Abstract Quantum computing has emerged as a promising paradigm for addressing computational tasks intractable for classical systems, leveraging quantum mechanical principles such as superposition and entanglement to efficiently explore high-dimensional solution spaces. In recent years, hybrid quantum-classical approaches have gained increasing attention as a means to exploit the representational power of quantum systems while preserving the practicality of classical machine learning frameworks. This paper presents a study on quantum-enhanced model compression via feature-based knowledge distillation, in which a large classical neural network (the teacher) transfers knowledge to a substantially smaller hybrid student model. The proposed hybrid quantum-classical student architecture incorporates a parameterized quantum circuit (PQC) implemented in Qiskit, employing a linear $$\varvec{R_y}$$ angle-encoding feature map followed by an EfficientSU2 variational ansatz, with features bounded through a $$\varvec{\tanh (\cdot )\times \frac{\pi }{2}}$$ scaling to ensure stable gradient propagation. Gradient computation is performed via Reverse-Mode (adjoint) differentiation through the StatevectorEstimator primitive, which provides exact, shot-noise-free gradients at the cost of a single forward–backward pass per optimization step. The hybrid student is compared against a parameter-matched purely classical student under strict 1:1 parameter parity across a six-task binary benchmark spanning MNIST and Fashion-MNIST, as well as a four-class multi-class benchmark, totaling eleven classification experiments. A hardware validation experiment is additionally conducted on the IQM Garnet 20-qubit quantum processor using the Parameter-Shift Rule. The results indicate that the hybrid student outperforms its classical counterpart in five of six binary tasks (83%) and in the two hardest multi-class configurations, with advantages most pronounced in high-confusion regimes where compact classical classifiers approach the limits of their expressive capacity. On real quantum hardware, accuracy decreases from 99.04% in noiseless simulation to 80.50%, reflecting the impact of gate noise, readout errors, and transpilation overhead. While the hybrid model demonstrates improved parameter efficiency and expressive capacity, it incurs higher computational overhead and exhibits greater epoch-to-epoch training variability relative to classical baselines. We discuss practical limitations related to noise, scalability, and current hardware constraints, and identify directions for future work including hardware-efficient gradient estimation and advanced error mitigation protocols. Overall, our findings suggest that variational quantum circuits can serve as compact yet expressive components within neural compression schemes, with their representational advantage most effectively realized in binary and high-ambiguity classification scenarios.
Learning with softmax cross-entropy on one-hot labels often leads to overconfident predictions and poor robustness under noise or perturbations. Label smoothing mitigates this by redistributing some confidence uniformly, but treats all samples equally, ignoring intra-class variability. We propose a hybrid quantum–classical framework that leverages quantum non-determinism to refine data labels into probabilistic ones, offering more nuanced, human-like uncertainty representations than label smoothing or Bayesian approaches. A variational quantum circuit (VQC) encodes inputs into multi-qubit quantum states, using entanglement and superposition to capture subtle feature correlations. Measurement via the Born rule extracts probabilistic soft labels that reflect input-specific uncertainty. These labels are then used to train a classical convolutional neural network (CNN) with soft-target cross-entropy loss. On MNIST and Fashion-MNIST, our method improves robustness—achieving up to 50% higher accuracy under noise—while maintaining competitive clean-data accuracy. It also enhances model calibration and interpretability, as CNN outputs better reflect quantum-derived uncertainty. This work introduces Quantum Probabilistic Label Refining, which bridges quantum measurement and classical deep learning to enable robust training via refined, correlation-aware labels, without architectural changes or adversarial techniques.
While Quantum Neural Networks (QNNs) offer the potential for resource-efficient image classification, practical implementations are hindered by qubit instability and finite availability, causing them to often underperform classical counterparts. This performance disparity constitutes a critical research gap. We propose a novel hybrid classical-quantum knowledge distillation approach to bridge this gap. Our method utilizes a pre-trained classical CNN (AlexNet) as a teacher to guide the training of a quantum student model by minimizing the Kullback-Leibler (KL) divergence (DKL) between their output distributions. The quantum student model employs an architecture designed to facilitate intricate feature interactions using iterated CNOT gates. This technique substantially improves quantum model accuracy, demonstrating gains of 0.34% (6-class, 3 qubits) and 0.28% (8-class, 3 qubits) on the MNIST dataset, and 0.74% (8-class, 4 qubits). Our contribution lies in operationalizing a knowledge distillation paradigm for applied Quantum Machine Learning (QML), enabling the effective transfer of robust knowledge from established classical architectures to resource-constrained quantum models, thereby enhancing faster convergence and accelerating practical QML deployment.
Distributed quantum machine learning faces significant challenges due to heterogeneous client data and variations in local model structures, which hinder global model aggregation. To address these challenges, we propose a knowledge distillation framework for variational quantum convolutional neural networks on heterogeneous data. The framework features a quantum gate number estimation mechanism based on client data, which guides the construction of resource-adaptive VQCNN circuits. Particle swarm optimization is employed to efficiently generate personalized quantum models tailored to local data characteristics. During aggregation, a knowledge distillation strategy integrating both soft-label and hard-label supervision consolidates knowledge from heterogeneous clients using a public dataset, forming a global model while avoiding parameter exposure and privacy leakage. Theoretical analysis shows that proposed framework benefits from quantum high-dimensional representation, offering advantages over classical approaches, and minimizes communication by exchanging only model indices and test outputs. Extensive simulations on the PennyLane platform validate the effectiveness of the gate number estimation and distillation-based aggregation. Experimental results demonstrate that the aggregated global model achieves accuracy close to fully supervised centralized training. These results shown that proposed methods can effectively handle heterogeneity, reduce resource consumption, and maintain performance, highlighting its potential for scalable and privacy-preserving distributed quantum learning.
While hybrid quantum–classical architectures and knowledge distillation have each been explored independently in medical imaging and model compression, no prior work has unified these domains within a single framework. This study addresses this gap by investigating the integration of quantum–classical neural networks with knowledge distillation for medical image analysis, with a focus on circuit behavior, parameter efficiency, and diagnostic performance. The framework (QuantumMedKD) employs classical CNN architectures (ResNet-50, EfficientNet-B0, Xception) as teacher models, transferring learned representations to parameter-efficient quantum student networks via parameterized quantum circuits across qubit configurations (3-8), demonstrated through pneumonia detection from pediatric chest radiographs. Experimental validation reveals remarkable parameter efficiency, requiring only 24-36 trainable parameters compared to millions for classical counterparts, achieving compression ratios exceeding 1 0 5 while maintaining competitive diagnostic performance. Optimal configurations achieve 84.00% accuracy (EfficientNet-B0, 6-qubit) and 73.33% (Xception, 4-qubit), with knowledge distillation providing statistically significant improvements ( p -vallues < 0.001, Cohen’s d > 2.0). Medical evaluation confirms diagnostic capability with sensitivity 81.4%, specificity 73.9%, and AUC 0.89, establishing quantum–classical knowledge transfer viability for resource-constrained healthcare deployment. QuantumMedKD reveals essential principles and proof-of-concept for quantum-enhanced healthcare AI systems within and beyond the noisy intermediate-scale quantum (NISQ) era for high efficiency and deployability, paving the way for future advancements in the field.