Quantum computing has emerged as a revolutionary paradigm in numerous fields owing to its basis in quantum mechanical concepts such as quantum entanglement and parallelism. This has potential in various applications including computer vision, particularly, image processing and compression. Applications that depend on largescale image data for storing, processing, and transmission have to rely on compression methods for real-time processing. While the classical methods based on discrete cosine transformations (DCT used in JPEG) and discrete wavelet transformations (DWT) perform image compression efficiently, they suffer from trade-off between loss-less compression and compression ratios. In the current work, we would like to explore the usefulness of implementing quantum wavelet transforms for image compression for better PSNR values and execution times. We compare the application of quantum Haar wavelet transform (QHWT) with different quantum encoding methods such as NASS and FRQI and find that NASS-encoded images on application of QHWT gives better PSNR values and shorter runtime with visibly closer details to the original images, showcasing potential for efficient and faster image compression methods.
Quantum computing has emerged as a revolutionary paradigm in numerous fields owing to its basis in quantum mechanical concepts such as quantum entanglement and parallelism. This has potential in various applications including computer vision, particularly, image processing and compression. Applications that depend on largescale image data for storing, processing, and transmission have to rely on compression methods for real-time processing. While the classical methods based on discrete cosine transformations (DCT used in JPEG) and discrete wavelet transformations (DWT) perform image compression efficiently, they suffer from trade-off between loss-less compression and compression ratios. In the current work, we would like to explore the usefulness of implementing quantum wavelet transforms for image compression for better PSNR values and execution times. We compare the application of quantum Haar wavelet transform (QHWT) with different quantum encoding methods such as NASS and FRQI and find that NASS-encoded images on application of QHWT gives better PSNR values and shorter runtime with visibly closer details to the original images, showcasing potential for efficient and faster image compression methods.
Quantum communication has achieved significant performance gains compared to classical systems but remains sensitive to channel noise and decoherence. These limitations become especially critical in quantum image transmission, where high-dimensional visual data must be preserved with both structural fidelity and robustness. In this context, transform-based quantum encoding methods have emerged as promising approaches, yet their relative performance under noisy conditions has not been fully explored. This paper presents a comparative study of two such methods, the quantum Fourier transform (QFT) and the quantum Haar wavelet transform (QHWT), within an image transmission framework. The process begins with source coding (JPEG/HEIF), followed by channel coding to enhance error resilience. The bitstreams are then mapped into quantum states using variable qubit encoding and transformed using either QFT or QHWT prior to transmission over noisy quantum channels. At the receiver, the corresponding decoding operations are applied to reconstruct the images. Simulation results demonstrate that the QFT achieves superior performance under noisy conditions, consistently delivering higher Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and Universal Quality Index (UQI) values across different qubit sizes and image formats compared to the QHWT. This advantage arises because QFT uniformly spreads information across all basis states, making it more resilient to noise. By contrast, QHWT generates localized coefficients that capture structural details effectively but become highly vulnerable when dominant coefficients are corrupted. Consequently, while QHWT emphasizes structural fidelity, QFT provides superior robustness, underscoring a fundamental trade-off in quantum image communication.
Quantum computing has emerged as a transformative paradigm, with revolutionary potential in numerous fields, including quantum image processing and compression. Applications that depend on large scale image data could benefit greatly from parallelism and quantum entanglement, which would allow images to be encoded and decoded with unprecedented efficiency and data reduction capability. This paper provides a comprehensive overview of the rapidly evolving field of quantum image compression, including its foundational principles, methods, challenges, and potential uses. The paper will also feature a thorough exploration of the fundamental concepts of quantum qubits as image pixels, quantum gates as image transformation tools, quantum image representation, as well as basic quantum compression operations. Our survey shows that work is still sparse on the practical implementation of quantum image compression algorithms on physical quantum computers. Thus, further research is needed in order to attain the full advantage and potential of quantum image compression algorithms on large-scale fault-tolerant quantum computers.
Abstract Quantum Haar Wavelet Transform (QHWT) methods connect multiresolution analysis with quantum information processing through reversible averaging and differencing operations that can be implemented with comparatively compact circuits. Their localized basis functions, real-valued binary structure, and compatibility with hierarchical state representations make them attractive for resource-constrained quantum processing. Nevertheless, claims of practical superiority are difficult to generalize because published studies use heterogeneous encodings, simulators, hardware platforms, noise models, and evaluation metrics. This systematic review examines scholarly work on Haar-based quantum methods published between 1997 and March 2025. A PRISMA-oriented protocol was used to search major engineering and computing databases, remove duplicates, screen records, assess eligibility, and construct a qualitative evidence corpus. The review includes peer-reviewed journal and conference studies together with a limited number of historically influential technical reports and preprints; therefore, the corpus is described as scholarly literature rather than as a uniformly peer-reviewed dataset. Because the reported experiments are not sufficiently homogeneous for statistical pooling, numerical results are treated as study-specific evidence rather than global averages. The review makes three analytical contributions. First, it introduces a unified conceptual framework that links mathematical foundations, circuit realization, application design, hardware evaluation, and research translation. Second, it develops a taxonomy spanning transform theory, quantum image and signal processing, hardware implementation, and emerging quantum artificial intelligence and security applications. Third, it critically compares QHWT with Quantum Fourier Transform and higher-order wavelet approaches by distinguishing circuit depth, gate complexity, approximation behavior, hardware assumptions, and empirical validation. The synthesis indicates that QHWT is most compelling when localization, reversible multiresolution processing, and shallow circuit structure are more important than smooth-basis approximation. Individual studies report promising compression, feature-extraction, and hardware-efficiency results, but these findings remain conditional on encoding choices and platform constraints. Important limitations include sparse cross-platform benchmarking, limited fault-tolerant analysis, noise sensitivity, uncertain scaling, and optimization difficulties in variational quantum learning, including barren plateaus. The resulting roadmap prioritizes reproducible benchmarks, hardware-aware circuit design, explicit complexity reporting, error-mitigation studies, and validation on larger quantum systems.
Abstract In recent years, quantum image processing got a lot of attention in the field of image processing due to the opportunity to place huge image data in quantum Hilbert space. Hilbert space or Euclidean space has infinite dimensions to locate and process the image data faster. Moreover, several types of research show that the computational time of the quantum process is faster than classical computers. Encoding and compressing the image in the quantum domain is still a challenging issue. From the literature survey, we have proposed a DCT-EFRQI (Direct Cosine Transform Efficient Flexible Representation of Quantum Image) algorithm to represent and compress gray image efficiently which save computational time and minimize the complexity of preparation. This work aims to represent and compress various gray image sizes in quantum computers using the DCT (Discrete Cosine Transform) and EFRQI (Efficient Flexible Representation of Quantum Image) approaches together. The Quirk simulation tool is used to design the corresponding quantum image circuit. Due to the limitation of qubits, a total of 16 numbers of qubits is used to represent the coefficient and its position of the grayscale image. Among those, 8 number of qubits are used to map the coefficient values and the rest are used to generate the corresponding coefficient XY-coordinate position. Theoretical analysis and experimental results show that the proposed DCT-EFRQI scheme provides better representation and compression compared to DCT-GQIR, DWT-GQIR, and DWT-EFRQI in terms of PSNR(Peak Signal to Noise Ratio), and bit rate.
In recent years, quantum image computing draws a lot of attention due to storing and processing image data faster compared to classical computers. A number of approaches have been proposed to represent the quantum image inside a quantum computer. Representing and compressing medium and big-size images inside the quantum computer is still challenging. To address this issue, we have proposed a block-wise DCT-EFRQI (Direct Cosine Transform Efficient Flexible Representation of Quantum Image) approach to represent and compress the gray-scale image efficiently to save computational time and reduce the quantum bits (qubits) for the state preparation. In this work, we have demonstrated the capability of block-wise DCT and DWT transformation inside the quantum domain to investigate their relative performances. The Quirk simulation tool is used to design the corresponding quantum image circuit. In the proposed DCT-EFRQI approach, a total of 17 qubits are used to represent the coefficients, the connection between coefficients and state (i.e., auxiliary), and their position for representing and compressing grayscale images inside a quantum computer. Among those, 8 qubits are used to map the coefficient values and the rest are used to generate the corresponding coefficient XY-coordinate position including one auxiliary qubit. Theoretical analysis and experimental results show that the proposed DCT-EFRQI scheme provides better representation and compression compared to DCT-GQIR, DWT-GQIR, and DWT-EFRQI in terms of rate-distortion performance.
The Haar wavelet algorithm based on quantum computing and its application for color image compression are discussed.Firstly,classical Haar wavelet operator is decomposed into direct sums,direct products and dot products of unitary matrices,so that shuffle permutation matrices is found.Secondly,based on the generalized Kronecker product,Harr functions are decomposed into a sequence of W-H and shuffle permutation matrices.Thirdly,the efficient,complete,quantum circuits for representative quantum wavelet transform are given.Finally,algorithm for color image compression by quantum Haar wavelet is presented,and experiment results are given.The experiment results show that the quantum Haar wavelet has very good feasibility in image compression.