Abstract Quantum image processing requires color representations that are compact in quantum registers and recoverable from finite-shot measurement statistics. Existing quantum image representations often emphasize storage efficiency, whereas the geometric organization of color information and its effect on reconstruction remain less explored. Here we propose a Bloch-sphere-based quantum color space that maps discrete RGB values to single-qubit state parameters (θ , φ). Colors are organized by maximum–minimum channel subgroups: each subgroup is assigned to a latitude band, and channel-permutation trajectories are encoded by the azimuthal angle. The construction also induces a canonical grayscale subspace. Finite-shot measurement counts are converted into angle estimates and decoded through a deterministic region-of-point/lookup-table (RoP/LUT) rule. In Qiskit Aer simulations, MNIST grayscale reconstruction achieves an average mean squared error (MSE) of 3.90 and peak signal-to-noise ratio (PSNR) of 42.44 dB. On CIFAR-10, the 64 3 RGB grid achieves the best reconstruction performance, with MSE 81.29, PSNR 29.84 dB, and structural similarity (SSIM) 0.9313. Shot-wise experiments show that pixel-wise validation benefits from increased measurement budgets, whereas position-register full-image encoding is limited by sparse per-position measurement counts.
Abstract Quantum image processing requires color representations that are compact in quantum registers and recoverable from finite-shot measurement statistics. Existing quantum image representations often emphasize storage efficiency, whereas the geometric organization of color information and its effect on reconstruction remain less explored. Here we propose a Bloch-sphere-based quantum color space that maps discrete RGB values to single-qubit state parameters (θ , φ). Colors are organized by maximum–minimum channel subgroups: each subgroup is assigned to a latitude band, and channel-permutation trajectories are encoded by the azimuthal angle. The construction also induces a canonical grayscale subspace. Finite-shot measurement counts are converted into angle estimates and decoded through a deterministic region-of-point/lookup-table (RoP/LUT) rule. In Qiskit Aer simulations, MNIST grayscale reconstruction achieves an average mean squared error (MSE) of 3.90 and peak signal-to-noise ratio (PSNR) of 42.44 dB. On CIFAR-10, the 64 3 RGB grid achieves the best reconstruction performance, with MSE 81.29, PSNR 29.84 dB, and structural similarity (SSIM) 0.9313. Shot-wise experiments show that pixel-wise validation benefits from increased measurement budgets, whereas position-register full-image encoding is limited by sparse per-position measurement counts.
We present a systematic empirical study of quantum amplitude encoding applied to the reconstruction of a full-colour photographic image via Discrete Cosine Transform (DCT) coefficients. A 256x256 RGB photograph is compressed by retaining the K lowest-frequency DCT coefficients per channel in zigzag scan order, whose magnitudes are loaded into an n-qubit quantum state using Qiskit's StatePreparation gate. We conduct a comprehensive sweep of n from 4 to 16 qubits at shot counts from 200,000 to 16,000,000, recording PSNR and SSIM at every combination. A principal finding is the PSNR dome: image quality peaks at intermediate n and falls as n increases further. We derive an optimality condition n* approximately log2(S/50). A unified RGB formulation encoding all three colour channels as a single 18-qubit amplitude state (K=262,144) is introduced, achieving PSNR=29.07 dB at 8M shots. All experiments run on the Qiskit Aer sampling simulator.
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.
Abstract Color images (i.e. RGB) contain rich visual information essential for object recognition, spatial context analysis, and decision-making across fields such as medical imaging, remote sensing, and computer vision. Processing such data efficiently requires significant computational resources, which can be addressed by the parallelism and speed of quantum computing. Representing RGB image data within quantum states enables efficient and scalable processing compared to classical methods. In recent years, various quantum image representation techniques have been developed based on probabilistic and basis state encoding. Probabilistic encoding methods are efficient for representing quantum binary images but face challenges in accurately reconstructing RGB images. This is due to the randomness introduced by measurement. To overcome this limitation, several basis state encoding approaches have been proposed. These methods map classical pixel values directly to quantum basis states. Thus enabling accurate grayscale and RGB image representation. However, they often require a larger number of qubits and complex gate operations, leading to higher circuit preparation costs. So, there exists substantial potential for quantum probabilistic RGB image representation using randomized measurements. Hence, our objective is to develop a probabilistic quantum image representation, capable of representing RGB images using fewer qubits. This method aims to reconstruct the classical image with high accuracy using randomized measurements, thereby addressing the major limitations of probabilistic methods. To balance image quality with resource efficiency, we propose an Improved Probabilistic Quantum Image Representation (IPQIR) method based on equal superposition states. This approach utilizes a quantum circuit with Hadamard Gate to encode classical pixel values into equal superposition states. The original image is then reconstructed by performing multiple quantum measurements and applying expectation value estimation to average the outcomes. To align with existing research in quantum image representation, quantum state tomography and different applications are utilized as standard evaluation methods to assess the effectiveness of the proposed algorithm. The tomography achieved a fidelity of 97.51%. In addition, various parametric and non-parametric statistical tests were performed to verify the accuracy of the reconstructed classical image. The high Pearson (0.9983) and Spearman (0.9959) correlation coefficients indicate a nearly perfect linear and monotonic relationship between the original and reconstructed images.
Quantum image processing is an emerging topic in the field of quantum information and technology. In this paper, we propose a new quantum image representation of RGB images with deterministic image retrieval, which is an improvement over all the similar existing representations in terms of using minimum resource. We use two entangled quantum registers constituting of total 7 qutrits to encode the color channels and their intensities. Additionally, we generalize the existing encoding methods by using both qubits and qutrits to encode the pixel positions of a rectangular image. This hybrid-qudit approach aligns well with the current progress of NISQ devices in incorporating higher dimensional quantum systems than qubits. We then describe the image encoding method using higher-order qubit-qutrit gates, and demonstrate the decomposition of these gates in terms of simpler elementary gates. We use the Google Cirq's quantum simulator to verify the image preparation in both the ideal noise-free scenario and in presence of realistic noise modelling. We show that the complexity of the image encoding process is linear in the number of pixels. Lastly, we discuss the image compression and some basic RGB image processing protocols using our representation.
Quantum image processing is a new and exciting subdiscipline of quantum computation that aims to extend classical image processing applications on a quantum computer.The research starts with a proposal of a representation of images on a quantum computer, named Multi-Channel Representation for Quantum Images (MCQI).This representation encodes the positions and their corresponding colors in the images as a normalized quantum state.For an n by n sized image, 2n qubits and 3 qubits are used to carry the position and color respectively.The preparation procedure of a quantum image is discussed by the multi-channel polynomial preparation, which turns the initial quantum states to the MC-QI quantum states.The image retrieval procedure by quantum measurement is proposed which converts the quantum states to classical images.Furthermore, based on MCQI, some categories of possible processing transformations are suggested.By considering the structure of MCQI representation, the Channel of Interest (CoI), the Channel Swapping (CS), the Color Space Transformation (CST), and Alpha Blending (αB) quantum image processing operators are discussed using unitary transformations with low complexity.All the 4 operators are used to process the information about color in the images.Their complexity are analyzed in terms of the number of basic quantum gates which are needed to build the transformations, and they can be built by 9, 3, 287, 28 basic quantum gates, respectively.Some strategies for designing new transformations from known ones are proposed as well.These strategies can be used to design further algorithms for image processing.Based on the MCQI representation and the four image processing operators, a quantum measurement based double-key double-domain watermarking strategy for multichannel quantum images (MC-WaQI) is developed.In these application, a revised of the original MCQI representation and some restricted versions of the transformations are considered.The research provides the foundation to design other quantum image processing algorithms and can be extend to the following areas:• MCQI representation can be used to build quantum image database,• new frequency operations on quantum images based on quantum Fourier quantum discrete cosine, and quantum wavelet transformations,• building the special effect on color quantum movie,• image data transmission by quantum communication.
To address the limitations of existing models that predominantly represent data in Cartesian coordinate systems and RGB color representations, this paper proposes YCrCbQPI (A Quantum Polar Coordinate Color Image Representation Model Based on YCrCb Color Space, YCrCb-QPI). This model integrates luminance and chrominance separation properties of YCrCb with the geometric invariance of logarithmic polar coordinates. Through a differentiated quantum encoding strategy, more qubits are allocated to critical luminance information while less sensitive chrominance information is assigned simplified encoding. Corresponding quantum state preparation circuits are also designed. Theoretical analysis indicates that compared to traditional RGB polar coordinate models, this model achieves significant savings in color information encoding resources while maintaining comparable visual fidelity. Furthermore, the model inherently possesses the rotation and scaling invariance of polar coordinates, establishing a robust foundation for developing efficient quantum image processing algorithms.