Abstract The Quantum Image Representation (QIR) remains one of the most significant challenges in Quantum Image Processing (QIP) and Quantum Machine Learning (QML) with the resource constraints required by Noisy Intermediate-Scale Quantum (NISQ) hardware. Currently available pixel representation schemes, such as Flexible Representation of Quantum Images (FRQI) and Novel Enhanced Quantum Representation (NEQR), typically have circuit depth and the number of required qubits that grow with image resolution, rendering them impractical for large-scale images. To alleviate these limitations, we propose the Qubit-Efficient and Resolution-Independent Quantum Image Representation (QRISP), a compact, feature-aware encoding framework that is resource-efficient while preserving discriminative information for classification. The proposed approach divides an image into a user-configurable number of non-overlapping blocks, stores complementary statistical descriptors such as mean intensity, local variance, dominant gradient orientation, and calculates the same descriptors using a series of parameterized rotation gates in a quantum feature register; a position register is used to store block indices, and a lightweight entanglement layer is used to store the feature correlations. One of the major features of QRISP is the resolution-independent quantum circuit structure of quantum resources, which depend on the block configuration rather than the image size, allowing flexible processing and trade-offs between representation fidelity and qubit complexity. Experimental results with the MNIST and Fashion-MNIST datasets for the case of Quantum Support Vector Machine (QSVM) and Quantum Neural Network (QNN) pipelines show significant improvement in the number of gates and depth of the circuits, as well as in the time for computing the kernel, without compromising the classification results from FRQI and NEQR, with respect to which their performance is competitive. This shows their potential for scalable, NISQ-oriented quantum image processing.
Abstract The Quantum Image Representation (QIR) remains one of the most significant challenges in Quantum Image Processing (QIP) and Quantum Machine Learning (QML) with the resource constraints required by Noisy Intermediate-Scale Quantum (NISQ) hardware. Currently available pixel representation schemes, such as Flexible Representation of Quantum Images (FRQI) and Novel Enhanced Quantum Representation (NEQR), typically have circuit depth and the number of required qubits that grow with image resolution, rendering them impractical for large-scale images. To alleviate these limitations, we propose the Qubit-Efficient and Resolution-Independent Quantum Image Representation (QRISP), a compact, feature-aware encoding framework that is resource-efficient while preserving discriminative information for classification. The proposed approach divides an image into a user-configurable number of non-overlapping blocks, stores complementary statistical descriptors such as mean intensity, local variance, dominant gradient orientation, and calculates the same descriptors using a series of parameterized rotation gates in a quantum feature register; a position register is used to store block indices, and a lightweight entanglement layer is used to store the feature correlations. One of the major features of QRISP is the resolution-independent quantum circuit structure of quantum resources, which depend on the block configuration rather than the image size, allowing flexible processing and trade-offs between representation fidelity and qubit complexity. Experimental results with the MNIST and Fashion-MNIST datasets for the case of Quantum Support Vector Machine (QSVM) and Quantum Neural Network (QNN) pipelines show significant improvement in the number of gates and depth of the circuits, as well as in the time for computing the kernel, without compromising the classification results from FRQI and NEQR, with respect to which their performance is competitive. This shows their potential for scalable, NISQ-oriented quantum image processing.
Abstract Quantum Image Representation (QIR) is a fundamental concept in quantum image processing. It describes how classical images are converted into quantum states for processing on quantum computers. Researchers proposed several QIR models, with FRQI and NEQR being the most popular ones. These models show the possibilities of the quantum image encoding. Nevertheless, they are also limited in some way. Mostly, pixel intensity accuracy, the required number of qubits, and circuit complexity have trade-offs. Their application to Noisy Intermediate-Scale Quantum (NISQ) devices becomes challenging, the quantum resources being small in such devices, due to this. In the following paper, we introduce our own approach, which is the Intensity-Preserving Quantum image Representation (IP-QIR). The key aim of IP-QIR is to maintain the information about the grayscale intensities and decrease the amount of quantum resources. IP-QIR quantifies pixel intensities by a controlled rotation scheme. The measurement statistics of a single qubit hold the intensity information and the position qubits represent the spatial information. The strategy uses small patches of images rather than complete images to make it easy to implement. This will decrease the depth of circuit design and makes the approach less advanced to the near-term quantum hardware. IBM Qiskit simulations are used in assessing the performance of IP-QIR. The three types of grayscale images of which experiments are run are the synthetic image patches, SAR images and medical TB chest X-ray images. It is revealed that IP-QIR maintains the intensity information compared to the FRQI and NEQR. SAR and medical data can reach values of fidelity of 84.12\%. The other notable point is that the size of a 4 x 4 image patch only needs five qubits which are much lower than in NEQR. Meanwhile, good reconstruction accuracy is achieved. These findings demonstrate the fact that IP-QIR is an effective and realistic approach to quantum image representation on the NISQ-era quantum devices.
Quantum image representation (QIR) is the basic idea behind quantum image processing. It explains how a normal image is converted into quantum states so that it can be processed using quantum computers. The commonly used models for QIR are Flexible Representation of Quantum Images (FRQIs) and Novel Enhanced Quantum Representation (NEQR). Though these approaches highlight the potential of quantum-based image encoding, the limitation of practical applicability on Noisy Intermediate-Scale Quantum (NISQ) devices exists. In this paper, we propose an intensity-preserving quantum image representation (IP-QIR) scheme that aims to maintain accurate grayscale intensity information while significantly reducing quantum resource usage. The proposed method employs a controlled rotation-based encoding strategy, where pixel intensities are embedded into the measurement probability of a single intensity qubit, and spatial information is represented using position qubits. To further enhance feasibility on near-term quantum hardware, the framework operates on small image patches instead of full-resolution images, thereby reducing circuit depth and overall complexity. The performance of the proposed IP-QIR approach is evaluated through IBM Qiskit simulations on three types of grayscale images: synthetic image patches, synthetic aperture radar (SAR) images, and medical tuberculosis (TB) chest X-ray images. Experimental results demonstrate that IP-QIR achieves better intensity preservation than FRQIs and NEQR, with fidelity values reaching up to 84.12% for both SAR and medical datasets. In addition, IP-QIR represents a 4×4 image patch using only five qubits, which significantly reduces the qubit requirement when compared to NEQR, while still preserving high reconstruction accuracy.
Quantum Image Representation (QIR) has become a key component of Quantum Image Processing (QIP), enabling the encoding and manipulation of visual data within quantum computing environments.Its integration with Quantum Artificial Intelligence (QAI) and Quantum Machine Learning (QML) has attracted significant research interest due to the potential advantages of quantum parallelism and compact data representation.This survey reviews major QIR techniques, analyzes their encoding strategies and computational characteristics, and examines their opportunities, challenges, and future relevance in quantum AI and machine learning applications.A systematic review of 70 peer-reviewed journal and conference publications published between 1992 and 2025 was conducted.The selected studies were evaluated based on encoding mechanisms, qubit requirements, circuit complexity, retrieval capability, scalability, and suitability for quantum image processing and learning tasks.The review covers prominent QIR models, including FRQI, NEQR, MCQI, QPIE, GQIR, QRMW, and tensor-network-based representations.Comparative analysis reveals important trade-offs between qubit efficiency, encoding complexity, retrieval accuracy, and scalability.Amplitude-based approaches provide compact image encoding but suffer from probabilistic retrieval, whereas basis-state representations offer deterministic recovery at the expense of increased circuit complexity.QIR demonstrates significant potential in image classification, feature extraction, image compression, and hybrid quantum-classical learning frameworks.QIR provides a promising foundation for next-generation quantum-enhanced visual intelligence systems.However, practical implementation remains constrained by state preparation overhead, noise, decoherence, limited qubit availability, and the lack of standardized evaluation frameworks.Future research should focus on scalable encoding methods, fault-tolerant quantum architectures, benchmarking standards, and deeper integration with advanced QML models to accelerate the development of practical quantum image analytics.
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.
Abstract Quantum image representation constitutes a foundational component of quantum image processing; however, its practical deployment on Noisy Intermediate-Scale Quantum (NISQ) hardware is fundamentally constrained by the cost of quantum state preparation. Existing representations such as the Flexible Representation of Quantum Images (FRQI) and the Novel Enhanced Quantum Representation (NEQR) rely on uniform, full-resolution encoding strategies that incur rapidly increasing gate counts and circuit depths, leading to severe decoherence and error accumulation on near-term devices. These limitations are particularly pronounced for heterogeneous and information-sparse modalities such as medical Magnetic Resonance Imaging (MRI) and Synthetic Aperture Radar (SAR), where uniform pixel-wise encoding introduces substantial redundant state preparation. To address these constraints, we propose Adaptive Hybrid Quantum Image Representation (AHQIR), a saliency-driven selective quantum state-preparation framework designed for efficient encoding of medical and SAR imagery under NISQ limitations. AHQIR departs from global encoding by employing a classical adaptive preprocessing stage to identify diagnostically significant regions in MRI and dominant backscatter structures in SAR images using a statistical thresholding criterion, thereby restricting quantum encoding to a salient pixel subset S. The quantum realization of AHQIR integrates Perception-Aided Encoding (PE) and Coherent-Size Encoding (CE) mechanisms, which condition state preparation on salient pixel coordinates and eliminate the requirement for power-of-two image padding. As a result, circuit depth and multi-qubit gate count scale with the number of salient pixels rather than total image size, enabling physically realizable circuits within current coherence limits. This selective and intentionally lossy design sacrifices global pixel-level fidelity in non-salient regions in order to preserve semantic and structural fidelity within regions of interest. AHQIR is evaluated against multiple state-of-the-art quantum image encoding schemes, including FRQI and NEQR, across Brain Tumor MRI and real-world SAR datasets. Experimental results demonstrate substantial reductions in gate count and improved robustness under realistic noise models, while maintaining reconstruction errors below clinically and analytically relevant thresholds for salient regions. These findings indicate that saliency-aware, selective state preparation offers a practical and scalable pathway for quantum.
In order to leverage quantum computers for machine learning tasks such as image classification, consideration is required. Noisy Intermediate-Scale Quantum (NISQ) computers have limitations that include noise, scalability, read-in and read-out times, and gate operation times. Therefore, strategies should be devised to mitigate the impact complex datasets that can have on the overall efficiency of a quantum machine learning pipeline. This may otherwise lead to excessive resource demands or noise. We apply a classical feature extraction using a ResNet10-inspired convolutional autoencoder to reduce dataset dimensionality and extract abstract, meaningful features before feeding them into a quantum layer. The chosen quantum layer is a quantum-enhanced support vector machine (QSVM), as SVMs typically do not require large sample sizes to identify patterns in data and have short-depth quantum circuits, which limits the impact of noise. The autoencoder is trained to extract meaningful features through image reconstruction, aiming to minimize the mean squared error across a training set of images. We use three datasets to illustrate the pipeline: HTRU-1, MNIST, and CIFAR-10. We include a quantum-enhanced one-class support vector machine (QOCSVM) for the highly unbalanced HTRU-1 set, with classical machine learning results for comparison. HTRU-2 is also included to serve as a benchmark for a dataset with meaningful features. The autoencoder achieved near-perfect reconstruction and high accuracy for MNIST, while CIFAR-10 showed poorer performance due to image complexity, and HTRU-1 struggled due to the imbalance in the dataset. The varying performance across datasets highlights the need to balance dimensionality reduction and prediction performance using quantum methods.