Convolutional neural networks rely on linear filtering operations that can be reformulated efficiently in suitable transform domains. At the same time, advances in quantum computing have shown that certain structured linear transforms can be implemented with shallow quantum circuits, opening the door to hybrid quantum-classical approaches for enhancing deep learning models. In this work, we introduce WTHaar-Net, a convolutional neural network that replaces the Hadamard Transform used in prior hybrid architectures with the Haar Wavelet Transform (HWT). Unlike the Hadamard Transform, the Haar transform provides spatially localized, multi-resolution representations that align more closely with the inductive biases of vision tasks. We show that the HWT admits a quantum realization using structured Hadamard gates, enabling its decomposition into unitary operations suitable for quantum circuits. Experiments on CIFAR-10 and Tiny-ImageNet demonstrate that WTHaar-Net achieves substantial parameter reduction while maintaining competitive accuracy. On Tiny-ImageNet, our approach outperforms both ResNet and Hadamard-based baselines. We validate the quantum implementation on IBM Quantum cloud hardware, demonstrating compatibility with near-term quantum devices.
Convolutional neural networks rely on linear filtering operations that can be reformulated efficiently in suitable transform domains. At the same time, advances in quantum computing have shown that certain structured linear transforms can be implemented with shallow quantum circuits, opening the door to hybrid quantum-classical approaches for enhancing deep learning models. In this work, we introduce WTHaar-Net, a convolutional neural network that replaces the Hadamard Transform used in prior hybrid architectures with the Haar Wavelet Transform (HWT). Unlike the Hadamard Transform, the Haar transform provides spatially localized, multi-resolution representations that align more closely with the inductive biases of vision tasks. We show that the HWT admits a quantum realization using structured Hadamard gates, enabling its decomposition into unitary operations suitable for quantum circuits. Experiments on CIFAR-10 and Tiny-ImageNet demonstrate that WTHaar-Net achieves substantial parameter reduction while maintaining competitive accuracy. On Tiny-ImageNet, our approach outperforms both ResNet and Hadamard-based baselines. We validate the quantum implementation on IBM Quantum cloud hardware, demonstrating compatibility with near-term quantum devices.
In this paper, we propose a novel Hadamard Transform (HT)-based neural network layer for hybrid quantum-classical computing. It implements the regular convolutional layers in the Hadamard transform domain. The idea is based on the HT convolution theorem which states that the dyadic convolution between two vectors is equivalent to the element-wise multiplication of their HT representation. Computing the HT is simply the application of a Hadamard gate to each qubit individually, so the HT computations of our proposed layer can be implemented on a quantum computer. Compared to the regular Conv2D layer, the proposed HT-perceptron layer is computationally more efficient. Compared to a CNN with the same number of trainable parameters and 99.26\% test accuracy, our HT network reaches 99.31\% test accuracy with 57.1\% MACs reduced in the MNIST dataset; and in our ImageNet-1K experiments, our HT-based ResNet-50 exceeds the accuracy of the baseline ResNet-50 by 0.59\% center-crop top-1 accuracy using 11.5\% fewer parameters with 12.6\% fewer MACs.
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.
The integration of quantum computing principles with classical deep learning architectures has emerged as a promising direction for advancing image recognition systems beyond the limitations of purely classical convolutional neural networks (CNNs). This study proposes and analyzes a hybrid quantum–classical deep learning framework based on quanvolutional neural network (QNN) principles, where quantum circuits are embedded within convolutional feature extraction layers to enhance representation capability. The research investigates how quantum-enhanced filters, particularly quanvolutional layers, contribute to improved feature diversity, non-linear transformation capacity, and classification accuracy in image recognition tasks. Building upon established convolutional architectures and quantum machine learning theories, the proposed framework integrates quantum random circuit encoding with classical deep neural networks to evaluate performance gains in comparison to conventional CNN models. The study further incorporates theoretical insights from hybrid quantum-classical learning systems, emphasizing the role of parameterized quantum circuits in feature mapping and optimization stability. The methodology is grounded in NISQ-era quantum computing constraints and leverages hybrid optimization strategies to ensure computational feasibility. Experimental evaluation demonstrates that quanvolution-based models can provide improved robustness in feature extraction, particularly in high-dimensional image spaces, while maintaining competitive computational efficiency. However, scalability limitations and noise sensitivity in quantum circuits remain key challenges. Overall, this work contributes to the growing field of quantum-enhanced machine learning by providing a structured performance analysis of hybrid quanvolutional architectures and highlighting their potential role in next-generation intelligent visual recognition systems.
The emergence of deep vision models such as convolutional neural networks and vision transformers has revolutionized computer vision, enabling significant advancements in image classification, object detection, and segmentation. In parallel, the rapid development of quantum computing has spurred interest in quantum machine learning (QML), which integrates the strengths of quantum computation with the representational power of deep learning. In QML, parameterized quantum circuits offer the potential to capture complex image features, define complex decision boundaries, and provide other computational advantages. This paper investigates hybrid quantum-classical vision architectures, with a focus on hybrid quantum-classical convolutional neural networks and hybrid quantum-classical vision transformers. These hybrid models explore both quantum pre-processing and post-processing of data, respectively, where quantum circuits are strategically integrated into the data pipeline to enhance model performance. Our results suggest that these hybrid models can enhance accuracy and computational efficiency in vision-related tasks, even with the constraints of current noisy intermediate-scale quantum devices.
Abstract Quantum Neural Networks (QNNs) present a promising research direction in image recognition, demonstrating significant potential for various applications. However, QNNs with a fixed circuit topology structure are prone to encountering the barren plateaus during training when processing exponential number of qubits, which limit their performance and scalability. In this paper, a novel Hybrid Quantum-Classical Inception-inspired Convolutional Neural Networks (HQCNN) is proposed. The HQCNN enhances feature learning capability and mitigates the barren plateau issue by integrating quantum convolutional kernels with diverse circuit topologies across multiple channels. The architecture employs an amplitude encoding layer to map multi-channel classical data into quantum states, followed by diverse quantum convolutional kernels that extract feature representations. Furthermore, Hadamard gates are used to intergrate multi-channel features and incorporate quantum pooling to reduce feature dimensionality, with a fully connected layer mapping the quantum-enhancing features into class labels for classification tasks. Finally, by analyzing the influence of the circuit structures and quantum gate combinations on the models' performance, the optimal HQCNN architecture is constructed. Experimental results demonstrate that HQCNN achieves 98.5% accuracy on the MNIST-4 classification task and 92.5% accuracy on the MNIST-10 classification task, which indicates that the proposed model outperforms state-of-the-art HQCNN models and classical CNN in image classification with about 10% parameters. This study provides an effective approach for alleviating the barren plateau issue and designing multi-channel quantum convolutional neural networks for processing big classic data with fewer quantum resources.
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.