Quantum image processing (QIP) has become one of the most significant fields in quantum computing (QC); it merges quantum mechanics with image processing to improve classical image-processing speed, which involves various operations to advance quantum image representation (QIR). Accordingly, we introduce two new QIRs: The first is based on the wavelength and bit plane, called the quantum image representation bit plane (QIRBP), and the second is based on the wavelength and adjacency pixels, which is called the quantum image representation wavelength correlation (QIRWC). The QIRBP model uses $ b+2n+6 $ quantum bit (qubits) to store a digital color image of size $ {2}^{n}\times {2}^{n} $. In contrast, the QIRWC needs $ 2b+4n+8 $ qubits to store a digital color image of size $ {2}^{n}\times {2}^{n} $ and to entangle the wavelength between two neighboring pixels. While the QIRWC approach is more complex, it is also more efficient on the basis of the transformation data. The complexity arises from the level of information being transmitted. In this work, two new representation methods (QIRBP and QIRWC) are proposed to overcome existing QIR weaknesses by enhancing storage efficiency, enabling compact high-resolution representation, improving data transformation through wavelength correlation and pixel adjacency, reducing noise, achieving greater versatility, and advancing scalable QIR. To prove the efficiency of the proposed methods, they were analyzed and compared with other efficient quantum image representations, outlining their similar and different aspects.
Quantum image processing (QIP) has become one of the most significant fields in quantum computing (QC); it merges quantum mechanics with image processing to improve classical image-processing speed, which involves various operations to advance quantum image representation (QIR). Accordingly, we introduce two new QIRs: The first is based on the wavelength and bit plane, called the quantum image representation bit plane (QIRBP), and the second is based on the wavelength and adjacency pixels, which is called the quantum image representation wavelength correlation (QIRWC). The QIRBP model uses b+2n+6 quantum bit (qubits) to store a digital color image of size 2n×2n. In contrast, the QIRWC needs 2b+4n+8 qubits to store a digital color image of size 2n×2n and to entangle the wavelength between two neighboring pixels. While the QIRWC approach is more complex, it is also more efficient on the basis of the transformation data. The complexity arises from the level of information being transmitted. In this work, two new representation methods (QIRBP and QIRWC) are proposed to overcome existing QIR weaknesses by enhancing storage efficiency, enabling compact high-resolution representation, improving data transformation through wavelength correlation and pixel adjacency, reducing noise, achieving greater versatility, and advancing scalable QIR. To prove the efficiency of the proposed methods, they were analyzed and compared with other efficient quantum image representations, outlining their similar and different aspects.
Quantum image processing, as a convergence of quantum computing and image processing, necessitates extensive research into quantum image representations (QIRs), which are among the most significant topics shaping the field of quantum computing (QC) due to their potential opportunities and challenges. This study introduces a novel QIR model based on the hue, saturation, and intensity (HSI) colour model. Our model advances image encoding by uniquely integrating an adjacency matrix to capture spatial pixel relationships with a Fourier transform (FT) representation for pixel intensity. Based on the HSI color space, AFQIRHSI uses a dual-entanglement structure; one state links the adjacency and intensity information, while another efficiently encodes hue and saturation. Named the adjacency Fourier quantum image representation of HSI (AFQIRHSI), this model utilises [Formula: see text] qubits to store a colour digital image of size [Formula: see text]. AFQIRHSI enhances storage capacity by factors of four and two compared to earlier models, such as QIRHSI and EQIRHSI. In this paper, we also present several quantum image operations, including complement colour transformation [Formula: see text], global colour transformation [Formula: see text], quantum image retrieval [Formula: see text], and quantum image detection (QED). Comparative analyses of various quantum image representations are provided, highlighting their similarities and differences. AFQIRHSI offers a robust foundation for advanced quantum image processing applications, particularly in medical imaging and AI-based image classification.
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.
Abstract The quantum image representation based on bit-planes (BRQI) is a widely used model in quantum image processing. It utilizes both the superposition and entanglement properties to store the position and color information of an image effectively, but the time complexity is still high(O(2qn22n)). Here, we propose an improved BRQI model, which still uses log2 q + 1 qubits to represent the color information, and has a low time complexity(O(qn22n)). When storing the value of bit-plane, it can use only one controlled operation to store the values of two adjacent bit-planes at the same time, makes the time and space complexity significantly reduced. Moreover, we design a corresponding quantum image compression algorithm. Simulation experimental results show that the compression efficiency of this model is also better than that of the widely used models NEQR and BRQI, and the time complexity of quantum image representation is further reduced. Hence, our findings will be helpful for further developing the quantum image representation and compression algorithm.
Quantum Image Processing (QIP)is an exciting new field showing a lot of promise as a powerful addition to the arsenal of Image Processing techniques. Representing image pixel by pixel using classical information requires an enormous amount of computational resources. Hence, exploring methods to represent images in a different paradigm of information is important. In this work, we study the representation of images in Quantum Information. The main motivation for this pursuit is the ability of storing N bits of classical information in only log(2N) quantum bits (qubits). The promising first step was the exponentially efficient implementation of the Fourier transform in quantum computers as compared to Fast Fourier Transform in classical computers. In addition, images encoded in quantum information could obey unique quantum properties like superposition or entanglement.
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.
RGB multi channel representation is proposed for images on quantum computers (MCQI) that captures information about colors (RGB channels) and their corresponding positions in an image in a normalized quantum state. The proposed representation makes it possible to store the RGB information about an image simultaneously by using 2n+3 qubits for encoding 2n× 2npixel images, whereas pixel-wise processing is necessary in many other quantum image representations, e.g., qubit lattice, grid qubit, and quantum lattice. Simulation of storage and retrieval of MCQI images using human facial images demonstrated that 15 qubits are required for encoding 64 × 64 colored images, and encoded information is retrieved by measurement. Perspectives of designing quantum image operators are also discussed based onMCQI representation, e.g., channel of interest, channel swapping, and restrict version of color transformation.