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Connection Science

Modified transfer learning based variational quantum circuit for MNIST image classification

Meshal Alharbi

Published Feb 5, 2026• 0 citations
Publisher

Abstract

Handwritten digit recognition (HWR) is a technology designed to enable mobile devices and computers to interpret handwritten inputs, encompassing both online and offline sources, such as images, scanned documents and digitised content. Various sectors, including insurance, banking, retail, healthcare and logistics, have increasingly adopted HWR. Despite the use of methods such as optical characteristic recognition (OCR), connectionist temporal classification (CTC) and machine learning (ML), their accuracy is compromised by interpretational limitations and significant error probabilities, leading to unreliable results. In order to address these shortcomings, this study advocates the collaborative use of deep ResNet and Inception models, combined with a variational quantum circuit (VQC) for HWR. The investigation utilises the MNIST dataset, which comprises 60,000 training set images and 10,000 testing set images of handwritten digits, each with a size of 28 × 28 pixels. Two selected samples, namely, Sample-1 (1, 0) and Sample-2 (3, 6), are drawn from this dataset. The hybrid approach of ResNet-Inception, which integrates a quantum encoding layer and VQC, is designed to enhance computational precision and digit recognition. ResNet improves accuracy through residual blocks with skip connections that mitigate vanishing and exploding gradients, while VQC enhances efficiency for high-velocity, large-scale datasets. The framework is evaluated using accuracy, precision, recall, and F1-score.

DOI
10.1080/09540091.2026.2624939

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Handwritten digit recognition (HWR) is a technology designed to enable mobile devices and computers to interpret handwritten inputs, encompassing both online and offline sources, such as images, scanned documents and digitised content. Various sectors, including insurance, banking, retail, healthcare and logistics, have increasingly adopted HWR. Despite the use of methods such as optical characteristic recognition (OCR), connectionist temporal classification (CTC) and machine learning (ML), their accuracy is compromised by interpretational limitations and significant error probabilities, leading to unreliable results. In order to address these shortcomings, this study advocates the collaborative use of deep ResNet and Inception models, combined with a variational quantum circuit (VQC) for HWR. The investigation utilises the MNIST dataset, which comprises 60,000 training set images and 10,000 testing set images of handwritten digits, each with a size of 28 × 28 pixels. Two selected samples, namely, Sample-1 (1, 0) and Sample-2 (3, 6), are drawn from this dataset. The hybrid approach of ResNet-Inception, which integrates a quantum encoding layer and VQC, is designed to enhance computational precision and digit recognition. ResNet improves accuracy through residual blocks with skip connections that mitigate vanishing and exploding gradients, while VQC enhances efficiency for high-velocity, large-scale datasets. The framework is evaluated using accuracy, precision, recall, and F1-score.
Handwritten digit recognition in regional scripts, such as Devanagari, is crucial for multilingual document digitization, educational tools, and the preservation of cultural heritage. The script's complex structure and limited annotated datasets pose significant challenges to conventional models. This paper introduces the first hybrid quantum-classical architecture for Devanagari handwritten digit recognition, combining a convolutional neural network (CNN) for spatial feature extraction with a 10-qubit variational quantum circuit (VQC) for quantum-enhanced classification. Trained and evaluated on the Devanagari Handwritten Character Dataset (DHCD), the proposed model achieves a state-of-the-art test accuracy for quantum implementation of 99.80% and a test loss of 0.2893, with an average per-class F1-score of 0.9980. Compared to equivalent classical CNNs, our model demonstrates superior accuracy with significantly fewer parameters and enhanced robustness. By leveraging quantum principles such as superposition and entanglement, this work establishes a novel benchmark for regional script recognition, highlighting the promise of quantum machine learning (QML) in real-world, low-resource language settings.
A digital recognition paradigm integrating a hybrid quantum-traditional neural network is developed for numerical recognition, whereby quantum computing and conventional neural networks may collaborate. This model integrates parameterized quantum circuits within a convolutional framework to attain a combination of embedding and direct output. The input from the convolutional fully connected layer functions as the control parameter for the quantum layer and is subjected to a sequence of transformations for feature processing. This structure's potential is evidenced by digit recognition on the MNIST dataset for digital applications. The approach employs transfer learning, integrating convolutional and deep image feature extraction using hybrid networks, thereby mitigating the overfitting problem associated with a singular convolutional network on limited sample datasets. The findings demonstrate the model's efficacy, utility, and superior generalization capability. The recognition rates of the direct output hybrid network and the embedded hybrid network on the MNIST dataset increased by 0.0398 and 0.0211, respectively, in comparison to a convolutional network. Following transfer learning and feature fusion, the recognition rates of the hybrid model on small sample datasets exceed those of a singular network, achieving 83%, so validating the model's learning and generalization proficiency for digital applications.
The recognition of handwritten digits holds a significant place in the field of information processing. Recognizing such characters accurately from images is a complex task because of the vast differences in people's writing styles. Furthermore, the presence of various image artifacts such as blurring, intensity variations, and noise adds to the complexity of this process. The existing algorithm, convolution neural network (CNN) is one of the prominent algorithms in deep learning to handle the above problems. But there is a difficulty in handling input data that differs significantly from the training data, leading to decreased accuracy and performance. In this work, a method is proposed to overcome the aforementioned limitations by incorporating a quantum convolutional neural network algorithm (QCNN). QCNN is capable of performing more complex operations than classical CNNs. It can achieve higher levels of accuracy than classical CNNs, especially when working with noisy or incomplete data. It has the potential to scale more efficiently and effectively than classical CNNs, making them better suited for large-scale applications. The effectiveness of the proposed model is demonstrated on the modified national institute of standards and technology (MNIST) dataset and achieved an average accuracy of 91.08%.
The expressivity and scalability of fixed feature embeddings and shallow quantum circuits for Quantum Support Vector Machines (QSVMs) are restricted due to the limitations of near-term hardware. In this work, we propose a novel QSVM framework consisting of Low-Rank Adaptation (LoRA)-modified VisionTransformer embeddings as well as trainable variational quantum circuits. The architecture enhances the representational power by the joint optimization of embedding and circuit parameters. Empirical evaluation on distilled benchmark datasets shows significant performance gains, with up to 38.7% absolute accuracy improvement on MNIST (61.3% to 100.0%). The model also achieves 91% to 100% test accuracies on Fashion-MNIST, KMNIST and CIFAR-10 datasets with only 200 training samples for each dataset. The results show that the performance improvements are due to the joint design between the feature embeddings and the quantum circuits, rather than just the quantum kernels. Cross-dataset evaluations and circuit-depth analyses provide experimental evidence that the approach is suitable for scalable quantum machine learning in image classification tasks.
Introduction: Image classification stands as a pivotal undertaking within the domain of computer vision technology. Primarily, this task entails the processes of image augmentation and segmentation, which are executed by various neural network architectures, including multi-layer neural networks, artificial neural networks, and perceptron networks. These image classifiers employ distinct hyperparameters for the prediction and identification of objects. Nevertheless, these neural networks exhibit susceptibility to issues such as overfitting and a lack of interpretability when confronted with low-quality images. Objective: These limitations can be mitigated through the adoption of Quantum Computing (QC) methodologies, which offer advantages such as rapid execution speed, inherent parallelism, and superior resource utilization. Method: This approach aims to ameliorate the challenges posed by conventional Machine Learning (ML) methods. Convolutional Neural Networks (CNNs) are instrumental in reducing the number of parameters while preserving the quality of dataset images. They also possess the capability to automatically discern salient features and maintain robustness in noisy environments. Consequently, a novel approach known as Deep Revamped Quantum CNN (DRQCNN) has been developed and implemented for the purpose of categorizing images contained within the Fashion MNIST dataset, with a particular emphasis on achieving heightened accuracy rates. Results: In order to assess its efficacy, this proposed method is systematically compared with the traditional Artificial Neural Network (ANN). DRQCNN leverages quantum circuits as convolutional filters with a weight adjustment mechanism for multi-dimensional vectors. Conclusions: This innovative approach is designed to enhance image classification accuracy and overall system effectiveness. The efficacy of the proposed system is evaluated through the analysis of key performance metrics, including F1-score, precision, accuracy, and recall
Accurate and computationally efficient classification of brain tumors from MRI scans is critical for deployment in resource-constrained clinical settings, where conventional deep CNN architectures-despite achieving strong accuracy-often require large parameter counts that limit scalability. This work proposes a hybrid quantum-classical deep learning framework that combines a classical convolutional feature extractor with a variational quantum circuit (VQC) for multi-class tumor classification. Spatial features extracted by the CNN backbone will be dimensionality-reduced and encoded into quantum states using angle encoding; a parameterized quantum circuit will then process these features in a higher-dimensional Hilbert space, leveraging superposition and entanglement to capture non-linear feature correlations. Measurement outputs from the quantum layer will be passed to a classical fully connected layer for classification into glioma, meningioma, pituitary tumor, and no-tumor categories. The proposed framework will be evaluated on a publicly available benchmark MRI dataset and benchmarked against state-of-the-art classical CNN architectures in terms of accuracy, precision, recall, F1-score, and parameter efficiency. This study aims to demonstrate that quantum-enhanced layers can achieve competitive classification performance while substantially reducing trainable parameters, offering a practical direction for efficient, quantum-assisted medical image analysis.