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.
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.
The objective of this research is to develop a Hybrid Quantum-Classical Convolutional Neural Network (QC-CNN) framework that integrates parameterized quantum circuits (PQCs) within classical CNN architectures to enhance image classification performance.The proposed model leverages quantum principles such as superposition and entanglement for high-dimensional feature representation, achieving superior accuracy and reduced computational complexity.Experiments on MNIST and CIFAR-10 datasets demonstrated improved classification accuracy of 98.7% and 82.5%, respectively, surpassing traditional CNNs while reducing training time by 33% and parameters by 45%.Statistical analysis confirmed the significance of these improvements.Visualizations using t-SNE revealed enhanced class separability, and noise perturbation tests validated the model's robustness.The results highlight the hybrid QC-CNN's potential for efficient and scalable quantum-enhanced deep learning applications.Extended evaluations, including quantum-layer-depth analysis, robustness testing, and t-SNE visualization, empirically support the hybrid QC-CNN's effectiveness across varied scenarios.
Quantum machine learning on noisy intermediate-scale quantum (NISQ) devices often suffers from noise sensitivity, small-data overfitting, and miscalibrated predictive confidence. We propose an uncertainty-aware hybrid Bayesian quantum neural network (BQNN) that couples a Bayesian convolutional front-end with a parameterized quantum circuit (PQC), forming a three-stage pipeline: Bayesian feature extraction, quantum state evolution, and classical decision making. For 28 ×28 grayscale inputs, the front-end uses an 8-filter 3 ×3 Bayesian convolution followed by 2 ×2 max-pooling and a fully connected layer to produce a 10-dimensional embedding, which is mapped to four rotation angles and encoded on 4 qubits. Two parameterized quantum circuit designs are considered for the quantum classification layer. On MNIST and Fashion-MNIST, repeated experiments over five independent random seeds show that the proposed BQNN variants consistently outperform the corresponding QCNN baselines. On MNIST, BQNN-2 achieves a mean best test accuracy of 95.46 ± 0.36%, a mean final test accuracy of 95.44 ± 0.38%, and a mean final test loss of 0.169 ± 0.012. On Fashion-MNIST, BQNN-1 attains the best mean overall performance, with a mean best test accuracy of 87.59 ± 0.62%, a mean final test accuracy of 87.49 ± 0.73%, and a mean final test loss of 0.385 ± 0.017, while BQNN-2 exhibits slightly smaller run-to-run variation. Additional representative comparisons with QNN baselines under the same training configuration further suggest faster convergence and higher peak accuracy for BQNN. Using 30 Monte-Carlo forward passes, BQNN achieves better calibration (ECE 0.007-0.009) than QCNN (ECE 0.016-0.020), thereby reducing overconfident predictions. Additional robustness experiments under noisy mixed-state simulation further show that, under depolarizing noise, BQNN consistently preserves higher peak test accuracy than QCNN across both circuit variants on MNIST, demonstrating improved robustness in NISQ-like noisy settings.
Deep learning has achieved significant success in pattern recognition, with convolutional neural networks (CNNs) serving as a foundational architecture for extracting spatial features from images. Quantum computing provides an alternative computational framework, a hybrid quantum-classical convolutional neural networks (QCCNNs) leverage high-dimensional Hilbert spaces and entanglement to surpass classical CNNs in image classification accuracy under comparable architectures. Despite performance improvements, QCCNNs typically use fixed quantum layers without incorporating trainable quantum parameters. This limits their ability to capture non-linear quantum representations and separates the model from the potential advantages of expressive quantum learning. In this work, we present a hybrid quantum-classical-quantum convolutional neural network (QCQ-CNN) that incorporates a quantum convolutional filter, a shallow classical CNN, and a trainable variational quantum classifier. This architecture aims to enhance the expressivity of decision boundaries in image classification tasks by introducing tunable quantum parameters into the end-to-end learning process. Through a series of small-sample experiments on MNIST, F-MNIST, and MRI tumor datasets, QCQ-CNN demonstrates competitive accuracy and convergence behavior compared to classical and hybrid baselines. We further analyze the effect of ansatz depth and find that moderate-depth quantum circuits can improve learning stability without introducing excessive complexity. Additionally, simulations incorporating depolarizing noise and finite sampling shots suggest that QCQ-CNN maintains a certain degree of robustness under realistic quantum noise conditions. While our results are currently limited to simulations with small-scale quantum circuits, the proposed approach offers a potentially promising direction for hybrid quantum learning in near-term applications.
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.
Noisy-label learning in small-scale medical image classification is challenging and hinders the superiority of deep neural networks. Recent studies suggest that quantum neural networks (QNNs) have shown potential in limited-data regimes, yet their use for noisy-label learning remains under-explored. A key obstacle is QNNs' intrinsic "natural smoothness", which may regularize training but also obscure high-confidence samples needed for noise-transition estimation. We propose Supermartingale-based Label Transition (SLT), an anchor-free loss correction framework for robust QNN-based medical image classification under noisy labels. SLT models entropy reduction in predictive distributions as a supermartingale and uses its monotonic behavior to identify stable transition-matrix refinement steps. This enables dynamic transition updates while reducing noise-driven oscillations during QNN training. We further provide a convergence analysis showing that the proposed transition-refinement process reaches a steady state. Experiments on multiple public small-scale medical image datasets demonstrate that SLT consistently improves QNN-based classification and stably outperforms classic noise-label learning baselines under synthetic and real-world label noise.
Convolutional Neural Networks (CNNs) are extensively utilized for image classification due to their ability to exploit data correlations effectively. However, traditional CNNs encounter several challenges, including limitations in accuracy improvement, computational efficiency, explain ability, and generalization. As data dimensionality or model complexity increases, CNNs often become more difficult to train efficiently, leading to slower processing times. To overcome these challenges, Quantum Convolutional Neural Networks (QCNNs) offer a promising quantum-based approach to enhance existing models, particularly by improving training efficiency and reducing processing times. This paper provides a comparative analysis of classical CNNs and a novel quantum circuit architecture tailored for image-based tasks. The analysis emphasizes the adaptability and potential of quantum circuits to enhance feature extraction, recognition accuracy, and processing efficiency.We applied various QCNN architectures to the Chinese-MNIST dataset and compared their performance with traditional CNN models. Although QCNNs achieved slightly lower accuracy, they demonstrated significantly greater stability. These findings high- light QCNNs’ potential to overcome the computational limitations of conventional deep learning, offering a promising pathway for quantum-enhanced solutions in computer vision. Future work will focus on refining quantum circuit designs, developing hybrid quantum-classical models, and extending QCNN applications to larger and more diverse datasets.