Time series analysis plays a vital role across a wide range of scientific and engineering domains but poses substantial computational challenges. A major difficulty arises from the time reparameterization invariance of time series data, which complicates the extraction of meaningful temporal features. In this work, we address the problem of time series classification by exploring the application of quantum computation techniques. We propose a hybrid quantum-classical architecture that integrates recent advances in quantum neural networks with the mathematical framework of path signatures, mitigating the impact of time reparametrization invariance. The architecture employs feature layers that compute a signature kernel between pairs of input paths, consisting of a reference path and a target path for classification, using either classical or quantum variational linear solvers (VQLS). These feature layers are followed by a Quantum Convolutional Neural Network (QCNN) to perform downstream learning tasks. We evaluate several realizations of the proposed architecture, differing in QCNN configurations, on a binary classification task involving time series representations of handwritten digits. Our experiments demonstrate the potential advantages of implementing path signature kernel layers within quantum circuits and provide an analysis of the computational limitations associated with the VQLS component.
Time series analysis plays a vital role across a wide range of scientific and engineering domains but poses substantial computational challenges. A major difficulty arises from the time reparameterization invariance of time series data, which complicates the extraction of meaningful temporal features. In this work, we address the problem of time series classification by exploring the application of quantum computation techniques. We propose a hybrid quantum-classical architecture that integrates recent advances in quantum neural networks with the mathematical framework of path signatures, mitigating the impact of time reparametrization invariance. The architecture employs feature layers that compute a signature kernel between pairs of input paths, consisting of a reference path and a target path for classification, using either classical or quantum variational linear solvers (VQLS). These feature layers are followed by a Quantum Convolutional Neural Network (QCNN) to perform downstream learning tasks. We evaluate several realizations of the proposed architecture, differing in QCNN configurations, on a binary classification task involving time series representations of handwritten digits. Our experiments demonstrate the potential advantages of implementing path signature kernel layers within quantum circuits and provide an analysis of the computational limitations associated with the VQLS component.
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.
Abstract Quantum Machine Learning (QML) has emerged as a promising paradigm that leverages the principles of quantum mechanics—such as superposition and entanglement—to overcome the limitations of classical machine learning in handling complex, high-dimensional data. However, practical challenges such as limited coherence times of qubits and the integration of quantum circuits with classical architectures have hindered the full realization of QML’s potential. To address these challenges, this paper proposes a novel hybrid architecture, termed the Classical-Quantum Hybrid Convolutional Neural Network (CQHCNN), which integrates quantum-inspired layers into conventional deep learning frameworks. These quantum layers utilize quantum information processing to extract complex features, while the classical components perform feature extraction and classification. This paper evaluates the performance of our model on several benchmark datasets, including MNIST, Fashion-MNIST, CIFAR-10 and COVID-19 Radiography, demonstrating its ability to outperform some other Quantum Convolutional Neural Networks (QCNNs) in terms of many metrics. Experimental results indicate that the hybrid model achieves significant improvements in classification accuracy and computational efficiency, highlighting the potential of quantum-inspired techniques to enhance classical machine learning models.
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.
This study explores Quantum Convolutional Neural Network (QCNN) starting from foundational quantum operations, such as the Rx gate for encoding MNIST image data into quantum states. We implemented quantum convolutional and pooling layers using one_unitary and two_unitary circuits, enabling effective feature extraction and dimensionality reduction while preserving critical information. Expressibility analysis revealed varying capabilities across different one_unitary circuits, with Rx, Ry, and Rz combinations demonstrating promising results akin to Haar random states. The proposed QCNN model exhibited robust performance metrics (accuracy: 95.98%, precision: 94.44%, recall: 96.59%, F1-score: 0.9551, AUC: 0.9604) in classification tasks, supported by efficient convergence during optimization. Future directions include expanding QCNN applications to handle more complex datasets and optimizing architectures to enhance quantum machine learning capabilities, particularly in image processing. This study underscores the potential of QCNNs in advancing quantum computing applications in neural network architectures. Keywords: MNIST, classification, CNN, expressibility
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 convolutional neural networks (QCNNs) are a highly appealing architecture that combines quantum computing and deep learning. Inspired by classical convolutional neural network (CNN) hierarchical feature extraction, QCNNs use quantum operations such as entanglement, superposition, and measurement to capture complex correlations in high-dimensional datasets. Since their introduction, QCNNs have evolved into several architectural variants, including fully quantum, variational, hybrid, and graph-based models, and have been investigated in applications ranging from quantum many-body physics to classical machine learning tasks such as image classification, speech recognition, and time-series forecasting. The development of software ecosystems such as Qiskit Machine Learning, Pennylane, and TensorFlow Quantum (TFQ) has facilitated rapid development and experimentation, speeding up research. Despite these developments, existing research remains divided, with many focused on individual implementations and lacking a unifying taxonomy or full review. This article addresses that gap by providing a systematic and holistic survey on QCNN, offering comparative insights across key architectures, applications, and toolboxes, and outlining open challenges. We also identify potential study areas, such as scalable architectures, domain-knowledge integration, fault tolerance, and security. This survey seeks to serve as a basic reference for furthering QCNN research in the current near-term quantum era and beyond, providing both architectural insights and application-driven viewpoints.