Variational quantum algorithms are gaining attention as an early application of noisy intermediate-scale quantum (NISQ) devices. One of the main problems of variational methods lies in the phenomenon of , present in the optimization of variational parameters. Adding geometric inductive bias to the quantum models has been proposed as a potential solution to mitigate this problem, leading to a new field called geometric quantum machine learning. In this work, an equivariant architecture for variational quantum classifiers is introduced to create a label-invariant model for image classification with C 4 rotational label symmetry. The equivariant circuit is benchmarked against two different architectures, and it is experimentally observed that the geometric approach boosts the model's performance. Finally, a classical equivariant convolution operation is proposed to extend the quantum model for the processing of larger images, employing the resources available in NISQ devices.
Variational quantum algorithms are gaining attention as an early application of noisy intermediate-scale quantum (NISQ) devices. One of the main problems of variational methods lies in the phenomenon of , present in the optimization of variational parameters. Adding geometric inductive bias to the quantum models has been proposed as a potential solution to mitigate this problem, leading to a new field called geometric quantum machine learning. In this work, an equivariant architecture for variational quantum classifiers is introduced to create a label-invariant model for image classification with C 4 rotational label symmetry. The equivariant circuit is benchmarked against two different architectures, and it is experimentally observed that the geometric approach boosts the model's performance. Finally, a classical equivariant convolution operation is proposed to extend the quantum model for the processing of larger images, employing the resources available in NISQ devices.
Quantum Neural Networks (QNNs) are suggested as one of the quantum algorithms which can be efficiently simulated with a low depth on near-term quantum hardware in the presence of noises. However, their performance highly relies on choosing the most suitable architecture of Variational Quantum Algorithms (VQAs), and the problem-agnostic models often suffer issues regarding trainability and generalization power. As a solution, the most recent works explore Geometric Quantum Machine Learning (GQML) using QNNs equivariant with respect to the underlying symmetry of the dataset. GQML adds an inductive bias to the model by incorporating the prior knowledge on the given dataset and leads to enhancing the optimization performance while constraining the search space. This work proposes equivariant Quantum Convolutional Neural Networks (EquivQCNNs) for image classification under planar p4m symmetry, including reflectional and 90° rotational symmetry. We present the results tested in different use cases, such as phase detection of the 2D Ising model and classification of the extended MNIST dataset, and compare them with those obtained with the non-equivariant model, proving that the equivariance fosters better generalization of the model.
Abstract Variational algorithms require architectures that naturally constrain the optimization space to run efficiently. Geometric quantum machine learning achieves this goal by encoding group structure into parameterized quantum circuits to include the symmetries of a problem as an inductive bias. However, constructing such circuits is challenging as a concrete guiding principle has yet to emerge. In this paper, we propose the use of spin networks , a form of directed tensor network invariant under a group transformation, to devise SU(2) equivariant quantum circuit ansätze—circuits possessing spin-rotation symmetry. By changing to the basis that block diagonalizes the SU(2) group action, these networks provide a natural building block for constructing parameterized equivariant quantum circuits. We prove that our construction is mathematically equivalent to other known constructions, such as those based on twirling and generalized permutations, but more direct to implement on quantum hardware. The efficacy of our constructed circuits is tested by solving the ground state problem of SU(2) symmetric Heisenberg models on the one-dimensional triangular lattice and the Kagome lattice. Our results highlight that our equivariant circuits boost the performance of quantum variational algorithms, indicating broader applicability to other real-world problems.
Abstract Machine learning is among the most widely anticipated use cases for near-term quantum computers, however there remain significant theoretical and implementation challenges impeding its scale up. In particular, there is an emerging body of work which suggests that generic, data agnostic quantum machine learning (QML) architectures may suffer from severe trainability issues, with the gradient of typical variational parameters vanishing exponentially in the number of qubits. Additionally, the high expressibility of QML models can lead to overfitting on training data and poor generalisation performance. A promising strategy to combat both of these difficulties is to construct models which explicitly respect the symmetries inherent in their data, so-called geometric quantum machine learning (GQML). In this work, we utilise the techniques of GQML for the task of image classification, building new QML models which are equivariant with respect to reflections of the images. We find that these networks are capable of consistently and significantly outperforming generic ansatze on complicated real-world image datasets, bringing high-resolution image classification via quantum computers closer to reality. Our work highlights a potential pathway for the future development and implementation of powerful QML models which directly exploit the symmetries of data.
Quantum computing is an emerging computing field that is expected to make a huge impact on several scopes of science and technology. In this paper, we investigate the role of quantum computing in image classification, as an important branch of machine learning with widely used applications in healthcare, military, and IR4.0. In particular, we systemically compare the performance of two well-known classical image classification systems, i.e., Support Vector Machine (SVM) and Convolutions Neural Network (CNN), with equivalent quantum image classification algorithms, i.e., Quantum Support Vector Machine (Q-SVM) and Quantum Convolutional Neural Network (Q-CNN). Both quantum and classical algorithms are implemented on available Noisy-Intermediate Scale Quantum (NISQ) devices using MNIST dataset. Performance of models were compared regarding accuracy and training time. The results show that classical algorithms outperform the quantum algorithms for the given tasks. However, we observe that large-scale fault-tolerant quantum computing can effectively perform image classification tasks in the future.
Noisy Intermediate-Scale Quantum (NISQ) devices have led to the creation of hybrid quantum-classical algorithms, which have provided an innovative design to improve classical machine learning. This article focuses on a review of Hybrid Quantum-Classical Neural Networks (H-QCNNs) in image classification, which is an emerging area that attempts to exploit the representational ability of parameterized quantum circuits (PQCs) and the proven feature extraction capabilities of classical deep learning. We empirically examine the current tendencies in architecture, such as quanvolutional networks, sequential models, and variational quantum classifiers, and critically assess their performance on standard and custom data. The literature analysis shows a large performance difference between noiseless simulation and execution on real hardware, indicating the highly problematic aspects of scaling beyond binary tasks, quantum noise, and a lack of standardized benchmarking. Moreover, we mention such innovative contributions as the small H-QNN model that offers comparable accuracy, yet meets strict NISQ requirements. Last but not least, the current review offers a systematic taxonomy of H-QCNN architectures, a comparative study of methodology options, and a clear roadmap to future research to reach a workable quantum advantage in computer vision. It is a resource to the beginners as well as a reference to the professionals working in the field, so the field would be moved to more powerful, scalable, and hardware-conscious ways of implementation.
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.