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.
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.
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.
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.
Given the recent prominence of Noisy Intermediate Scale Quantum (NISQ) devices, hybrid quantum-classical neural networks have recently drawn a lot of excitement as a potential solution to improving learning efficiency. Our current paper describes a Hybrid Quantum-Classical Convolutional Neural Network (HQCNN) which is defined as a pretrained backbone of ResNet-18 and a small quantum-enhanced feature-transformation layer of Qiskit. The convolutional high-dimensional features are reduced to the classical eight-dimensional one, which in turn is encoded into a four-qubit parameterized quantum circuit. The resultant quantum expectation values are combined with the compressed features to come up with a hybridized representation of twelve dimensions, used to classify multi-class dataset. Experimental analysis of CIFAR10 data has shown that the suggested HQCNN achieves a test accuracy of 94.74% and improves class-wise precision, recall, and F1-scores than a number of existing hybrid models while using a significantly smaller number of latent features. More investigation into the quantum module indicates that it is predictable about scalability to batch, resistant to perturbations in features, and efficiently performed by evaluating circuit vectors. These results indicate that compact and expressive representations of images that can be helpful in the NISQ era can be acquired using hybrid architectures, thus providing a practical way to forward the benefits of quantum to modern deep-learning pipelines.
Classical convolutional neural networks (CNNs) have achieved notable success in image classification but face challenges in scalability, interpretability, and computational cost. With the growing availability of Noisy Intermediate-Scale Quantum (NISQ) devices, hybrid quantum-classical models offer a promising alternative by leveraging quantum parallelism and entanglement. In this work, we present a hybrid Quantum Convolutional Neural Network (QCNN) that integrates quantum convolutional layers into classical image classification pipeline for the MNIST dataset. Our architecture features a modular, low-depth Quantum Kernel Convolution (QKC) design suitable for near-term hardware. We implement the system using Qiskit and evaluate in terms of classification accuracy, circuit efficiency, and integration feasibility. Our results demonstrate that (i) the hybrid QCNN achieves similar accuracy to classical models while reducing the number of classical parameters, and (ii) quantum layers can successfully perform dimensionality reduction through entanglement-based pooling. This study highlights the potential of hybrid QCNN as a practical quantum-enhanced model for real-world image recognition tasks.
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.
In the last decade, quantum computing (QC) has shown its great potential in advancing research in many fields. Here we introduce a new quantum-classical neural network, by combining quantum computing and classical computing in a hybrid neural network (HNN) that can be trained to perform image classification. The HNN on the basis of the classic convolutional neural network (CNN) with quantum circuit is considered for image classification problem. The various configurations of HNN were investigated where QC with different number of qubits were used and compared. The HNN configurations were trained, validated, and tested on the more complex CIFAR10 and CIFAR100 datasets in addition to our previous attempts on the simpler MNIST, notMNIST, MNIST Fashion datasets. Performance of HNN was compared for multiclass classification on these datasets for different number of classes (from 2 to 10) using QCs with correspondent number of qubits (from 2 to 4). The metrics measured (accuracy and loss) during these experiments support our assumption about feasibility of HNN application for multiclass classification problems.