Matrix Product States have been extensively explored as a powerful tool for simulating quantum states in image classification task. However, most research has focused on classical simulations or computations involving high-dimensional unitaries, and significant challenges still exist in the practical preparation of Matrix Product States on quantum computers. This paper proposes a novel and practically feasible quantum variational algorithm based on Matrix Product States for image classification task. We design a hardware-efficient quantum circuit with several adjustable entangling operators to prepare the local tensors in Matrix Product States and integrate minimal residuals to ensure computational stability. We demonstrate that our algorithm can reduce the parameter complexity from growing exponentially with the system size to a linear scale. To validate the effectiveness of this quantum variational algorithm, we conducted experiments on the MNIST dataset, achieving accuracies of 99.95% and 95.96% for binary and ten-class classification tasks, which outperforms other related quantum algorithms. This work advances the practical application of quantum machine learning in resource-constrained environments of quantum computing.
Matrix Product States have been extensively explored as a powerful tool for simulating quantum states in image classification task. However, most research has focused on classical simulations or computations involving high-dimensional unitaries, and significant challenges still exist in the practical preparation of Matrix Product States on quantum computers. This paper proposes a novel and practically feasible quantum variational algorithm based on Matrix Product States for image classification task. We design a hardware-efficient quantum circuit with several adjustable entangling operators to prepare the local tensors in Matrix Product States and integrate minimal residuals to ensure computational stability. We demonstrate that our algorithm can reduce the parameter complexity from growing exponentially with the system size to a linear scale. To validate the effectiveness of this quantum variational algorithm, we conducted experiments on the MNIST dataset, achieving accuracies of 99.95% and 95.96% for binary and ten-class classification tasks, which outperforms other related quantum algorithms. This work advances the practical application of quantum machine learning in resource-constrained environments of quantum computing.
Abstract Image classification, a pivotal task in multiple industries, faces computational challenges due to the burgeoning volume of visual data. This research addresses these challenges by introducing two quantum machine learning models that leverage the principles of quantum mechanics for effective computations. Our first model, a hybrid quantum neural network with parallel quantum circuits, enables the execution of computations even in the noisy intermediate-scale quantum era, where circuits with a large number of qubits are currently infeasible. This model demonstrated a record-breaking classification accuracy of 99.21% on the full MNIST dataset, surpassing the performance of known quantum–classical models, while having eight times fewer parameters than its classical counterpart. Also, the results of testing this hybrid model on a Medical MNIST (classification accuracy over 99%), and on CIFAR-10 (classification accuracy over 82%), can serve as evidence of the generalizability of the model and highlights the efficiency of quantum layers in distinguishing common features of input data. Our second model introduces a hybrid quantum neural network with a Quanvolutional layer, reducing image resolution via a convolution process. The model matches the performance of its classical counterpart, having four times fewer trainable parameters, and outperforms a classical model with equal weight parameters. These models represent advancements in quantum machine learning research and illuminate the path towards more accurate image classification systems.
Image classification is a fundamental task in deep learning, and recent advances in quantum computing have generated significant interest in quantum neural networks. Traditionally, Convolutional Neural Networks (CNNs) are employed to extract image features, while Multilayer Perceptrons (MLPs) handle decision making. However, parameterized quantum circuits offer the potential to capture complex image features and define sophisticated decision boundaries. In this paper, we present a novel Hybrid Quantum–Classical Neural Network (H-QNN) for image classification, and demonstrate its effectiveness using the MNIST dataset. Our model combines quantum computing with classical supervised learning to enhance classification accuracy and computational efficiency. In this study, we detail the architecture of the H-QNN, emphasizing its capability in feature learning and image classification. Experimental results demonstrate that the proposed H-QNN model outperforms conventional deep learning methods in various training scenarios, showcasing its effectiveness in high-dimensional image classification tasks. Additionally, we explore the broader applicability of hybrid quantum–classical approaches in other domains. Our findings contribute to the growing body of work in quantum machine learning, and underscore the potential of quantum-enhanced models for image recognition and classification.
Image classification plays a vital role in large-scale data analysis, especially in object recognition tasks using advanced Deep Learning (DL) frameworks. However, the growing complexity and computational demands of modern DL models have introduced challenges related to scalability and efficiency. Quantum Computing (QC) has emerged as a promising alternative, capable of addressing these limitations by leveraging the principles of Quantum Machine Learning (QML). However, many existing QML models require a large number of qubits, which poses limitations within the current Noisy Intermediate-Scale Quantum (NISQ) era. This work introduces a novel Adaptive Quantum Convolutional Neural Network (AQCNN) designed for efficient and scalable image classification within the constraints of NISQ devices. Addressing the limitations of existing QML approaches, particularly the high qubit requirements, AQCNN incorporates a resource-efficient quantum convolutional layer that performs localized quantum filtering using parameterized quantum circuits. A classical preprocessing layer encodes input features to reduce qubit load, followed by quantum embedding and hybrid quantum-classical layers that optimize feature extraction and classification performance. The model leverages an adaptive quantum convolution strategy, minimizing quantum gate depth and circuit complexity while preserving critical spatial hierarchies in image data. Evaluated on benchmark datasets, AQCNN achieved 95.88% accuracy on MNIST and 95.68% on FMNIST, outperforming comparable QML architectures. Additionally, the model supports scalable execution through parallel quantum circuit arrays, enabling practical deployment on current quantum hardware. This architecture demonstrates a significant advance in quantum-assisted image classification, balancing performance with qubit and gate efficiency. The integration of adaptive quantum convolution and hybrid processing not only enhances classification accuracy but also provides a viable path forward for deploying QML solutions under realistic hardware constraints.
One key step in performing quantum machine learning (QML) on noisy intermediate-scale quantum (NISQ) devices is the dimension reduction of the input data prior to their encoding. Traditional principle component analysis (PCA) and neural networks have been used to perform this task; however, the classical and quantum layers are usually trained separately. A framework that allows for a better integration of the two key components is thus highly desirable. Here we introduce a hybrid model combining the quantum-inspired tensor networks (TN) and the variational quantum circuits (VQC) to perform supervised learning tasks, which allows for an end-to-end training. We show that a matrix product state based TN with low bond dimensions performs better than PCA as a feature extractor to compress data for the input of VQCs in the binary classification of MNIST dataset. The architecture is highly adaptable and can easily incorporate extra quantum resource when available.
Abstract We introduce a hybrid model combining a quantum-inspired tensor network and a variational quantum circuit to perform supervised learning tasks. This architecture allows for the classical and quantum parts of the model to be trained simultaneously, providing an end-to-end training framework. We show that compared to the principal component analysis, a tensor network based on the matrix product state with low bond dimensions performs better as a feature extractor for the input data of the variational quantum circuit in the binary and ternary classification of MNIST and Fashion-MNIST datasets. The architecture is highly adaptable and the classical-quantum boundary can be adjusted according to the availability of the quantum resource by exploiting the correspondence between tensor networks and quantum circuits.
Image classification is a core task in the field of computer vision, with significant implications for applications such as medical imaging and autonomous driving. Classical neural network architectures face numerous challenges when dealing with high-dimensional and complex data, particularly in terms of feature extraction and data processing capabilities, limiting their performance in certain applications. Quantum computing offers promising new approaches to processing high-dimensional complex data, most notably through Parameterized Quantum Circuits (PQC) as quantum hybrid neural networks for image classification. In this paper, we propose a hybrid neural network featuring a specific PQC structure designed to generate entanglement in accordance with sample images. This PQC structure utilizes the adjacency matrix of the corresponding graph of the sample image, embedding adjacency relationships among nodes into the entanglement module, thereby generating entanglement aligned with the features of specific images. Numerical results validate the effectiveness of our PQC model across various image classification tasks, enhancing the efficiency of feature learning and representation. Our model demonstrates significant advantages in classification accuracy and learning efficiency on classical datasets. Our research not only advances the theoretical understanding of hybrid quantum networks but also paves the way for practical implementations in real-world scenarios.