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IEEE Transactions on Quantum Engineering

Hybrid Quantum Capsule Network: Quantum Transformation Circuit as Vote Transformation in Image Classification

Ridho Nur Rohman Wijaya, Budi Setiyono, Dwi Ratna Sulistyaningrum

Published Jan 1, 2026• 0 citations
Publisher

Abstract

A capsule network (CapsNet) provides a richer hierarchical representation than conventional neural networks through vector-shaped capsules and intercapsule routing. However, most CapsNet designs still rely on classic matrix-multiplication-based vote transformations, which limit the formation of the prediction vector to linear mappings in Euclidean space. In this article, we propose the hybrid quantum capsule network (HQCapsNet), an architecture that replaces classical vote transformations with a quantum transformation circuit (QTC) based on a parameterized quantum circuit (PQC). We introduce a QTC in two schemes: classwise QTC and fully connected QTC. Furthermore, the routing agreement mechanism is extended via hybrid quantum routing, leveraging various quantum similarity metrics. The evaluation was conducted on several binary image classification datasets, with MNIST, TMNIST, and MNIST-M used as the primary datasets. The experimental analysis included benchmarking of quantum embedding variations, the PQC ansatz, qubit-count analysis, circuit depth, and routing iterations. The experimental results show that the fully connected QTC is the best configuration, achieving consistent accuracy improvements over the classwise QTC, with the most significant improvement from 92.86% to 97.62% on the MNIST-M dataset. Compared to the classical CapsNet, the HQCapsNet also achieves higher performance across all primary datasets, achieving 99.95% accuracy on MNIST and competing with quantum–classical models on comparable split data. These results indicate that integrating quantum computing at the voting transformation step is a promising approach to improving CapsNet’s representation and generalization capabilities.

DOI
10.1109/tqe.2026.3709247

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A capsule network (CapsNet) provides a richer hierarchical representation than conventional neural networks through vector-shaped capsules and intercapsule routing. However, most CapsNet designs still rely on classic matrix-multiplication-based vote transformations, which limit the formation of the prediction vector to linear mappings in Euclidean space. In this article, we propose the hybrid quantum capsule network (HQCapsNet), an architecture that replaces classical vote transformations with a quantum transformation circuit (QTC) based on a parameterized quantum circuit (PQC). We introduce a QTC in two schemes: classwise QTC and fully connected QTC. Furthermore, the routing agreement mechanism is extended via hybrid quantum routing, leveraging various quantum similarity metrics. The evaluation was conducted on several binary image classification datasets, with MNIST, TMNIST, and MNIST-M used as the primary datasets. The experimental analysis included benchmarking of quantum embedding variations, the PQC ansatz, qubit-count analysis, circuit depth, and routing iterations. The experimental results show that the fully connected QTC is the best configuration, achieving consistent accuracy improvements over the classwise QTC, with the most significant improvement from 92.86% to 97.62% on the MNIST-M dataset. Compared to the classical CapsNet, the HQCapsNet also achieves higher performance across all primary datasets, achieving 99.95% accuracy on MNIST and competing with quantum–classical models on comparable split data. These results indicate that integrating quantum computing at the voting transformation step is a promising approach to improving CapsNet’s representation and generalization capabilities.
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.
The growing complexity and scale of image processing tasks challenge classical convolutional neural networks (CNNs) with high computational costs. Hybrid quantum-classical convolutional neural networks (HQCNNs) show potential to improve performance by accelerating processing speed, enhancing classification accuracy, and reducing model parameters, though studies have primarily focused on the RGB color space. However, the effectiveness of HQCNNs in non-RGB color spaces, such as Lab, YCrCb, and HSV, remains largely unexplored. We propose an HQCNN to evaluate image classification across diverse color spaces. The HQCNN integrates parameterized quantum circuits (PQCs) with a classical CNN, leveraging quantum entanglement and trainable gates to enhance expressiveness across varied color representations. We assess performance on MNIST, CIFAR-10, EuroSAT, and SAT-4 datasets. Experimental results demonstrate that the HQCNN outperforms the classical CNN across all tested color spaces for the ten-class MNIST task, achieving a best accuracy of 94.3%94.3\%94.3% in Lab compared to 92.8%92.8\%92.8% in RGB for the CNN, with superior performance on other datasets in various color spaces. These findings highlight the potential of non-RGB color spaces and optimized PQC designs to improve classification performance. We provide new insights for advancing hybrid quantum-classical computer vision through optimized PQC architectures and diverse color space applications.
Hybrid quantum classical neural networks integrate parameterized quantum circuits (PQCs) with established deep learning architectures, but their performance depends strongly on the choice of quantum circuit architecture, a choice that remains largely manual. Most existing approaches rely on hand-designed or fixed circuit ansätze, requiring circuit structure, gate composition, and qubit connectivity to be specified in advance with no guarantee that they suit the task. This limitation is especially acute in image classification, where quantum circuits must transform features extracted by classical networks while remaining compact enough for practical training, requirements that generic, task-agnostic ansätze are unlikely to satisfy simultaneously. We extend EXAQC, an evolutionary framework for automated quantum circuit discovery, to image classification. EXAQC evolves PQCs as intermediate processing modules while retaining classical feature-extraction and prediction layers. On MNIST, Fashion-MNIST, and CIFAR-10, EXAQC achieves 98.42%, 90.62%, and 85.47% accuracy, respectively, while using comparable gate counts to other quantum architecture-search methods. Against classical networks, evolved hybrid models maintain comparable accuracy with substantially fewer trainable parameters, reaching 85.68% on CIFAR-10 with over 25×\times× fewer parameters than a 10-layer CNN. Encoding choice also matters: rotation-based encodings (RX, RY, U3) outperform amplitude encoding by 22-25 points on CIFAR-10. These results demonstrate that automated circuit discovery yields compact quantum modules that can replace larger classical components in vision architectures while retaining competitive accuracy.
Quantum machine learning is emerging as a strategy to solve real-world problems. As a quantum computing model, parameterized quantum circuits provide an approach for constructing quantum machine learning algorithms, which may either realize computational acceleration or achieve better algorithm performance than classical algorithms. Based on the parameterized quantum circuit, we propose a hybrid quantum-classical convolutional neural network (HQCCNN) model for image classification that comprises both quantum and classical components. The quantum convolutional layer is designed using a parameterized quantum circuit. It is used to perform linear unitary transformation on the quantum state to extract hidden information. In addition, the quantum pooling unit is used to perform pooling operations. After the evolution of the quantum system, we measure the quantum state and input the measurement results into a classical fully connected layer for further processing. We demonstrate its potential by applying HQCCNN to the MNIST dataset. Compared to a convolutional neural network in a similar architecture, the results reveal that HQCCNN has a faster training speed and higher testing set accuracy than a convolutional neural network.
This paper proposes and evaluate Hybrid Quantum Convolutional Neural Networks (HQCNNs) that integrate Structured Variational Quantum Circuits (SVQCs) into classical convolutional networks for image classification. Prior quanvolutional architectures often rely on unstructured variational circuits, leading to barren-plateau training landscapes, unpredictable convergence, and poor scaling of expressivity as qubit count grows. Moreover, simplistic data-encoding schemes can either fail to capture spatial correlations or demand impractically deep circuits, while arbitrary entanglement patterns obscure the relationship between circuit design and learning capacity. To address these challenges, we design four HQCNN architectures with progressively increased quantum encoding precision, entanglement topology, and classical post-processing depth. Each HQCNN replaces the convolutional layer with a quanvolutional layer: local image patches are encoded into small qubit registers via an Enhanced Novel Enhanced Quantum Representation (ENEQR), then processed by the SVQCs, and then measured to produce quantum feature maps. The four versions vary in quantum structure: Version 1 uses a simple linear 5-qubit chain (q=2), Version 2 adds wrap-around entanglement (closed-loop topology), Version 3 augments the classical head with a deeper batch-normalized multilayer perceptron, and Version 4 increases encoding fidelity to q=4 (7 qubits per patch). All models end-to-end using the Adam optimizer and cross-entropy loss on the MNIST dataset for 10 epochs using a PennyLane simulator. Version 4 achieves the best test accuracy (96% on MNIST). Fourier spectrum analysis reveals that richer entanglement and higher-fidelity encoding broaden the circuits’ harmonic spectrum, correlating with enhanced representational capacity and improved classification performance. These results confirm that carefully structured quantum layers and enhanced encoding can enrich feature representations and boost accuracy, albeit with increased simulation overhead and training complexity.
Accurate classification of microscopic blood cells is still a critical task in medical image analysis, where subtle variations and limited data can challenge conventional deep learning models. As such, we investigate in this work the potential of Hybrid Quantum-Classical Neural Networks (HQNNs) to enhance feature representation and improve classification performance in this domain. We propose a modular architecture combining a pre-trained ResNet-50 backbone with a low-dimensional latent bottleneck and a variational quantum circuit, enabling a direct comparison between quantum-enhanced and purely classical transformation mechanisms. To isolate the contribution of the quantum component, we evaluate three architectures: a HQNN model, a Classical Matched Model with an additional nonlinear transformation layer of comparable capacity, and a baseline model without an intermediate transformation stage. Experiments conducted on two publicly available blood cell datasets, namely the Blood Cell Images dataset and the PBC dataset, demonstrate that HQNNs consistently achieve superior or more balanced performance across evaluation metrics. In the Blood Cell Images Dataset, the proposed approach improves macro F1-score by up to 3.7% compared to classical baselines, while improving the F1-score from 98.54% to 98.69% in the more challenging 8-class scenario with near-saturated performance. Additional evaluation on IBM quantum hardware shows that the model remains robust under noise, with only a modest performance degradation relative to simulated results. These results indicate that quantum feature transformations can enhance discriminative representations, particularly in challenging classification scenarios, and highlight the practical potential of HQNN models for medical imaging tasks.