This research paper explores the application of singular value decomposition (SVD) in quantum image processing (QIP), specifically focusing on the computation of eigenvalues using variational quantum algorithms. SVD is a powerful mathematical tool in image processing, used for tasks such as image compression, noise reduction, and feature extraction. In this study, we propose quantum variational singular value decomposition (QVSVD) based on the variational quantum deflation (VQD) algorithm to determine the eigenvalues that contributes in calculating the singular values of the image matrix and eventually doing the SVD. This facilitates the extraction of eigenvalues with exponential speedup on real hardware compared to classical methods. We detail the implementation of this quantum algorithm within the framework of QIP, highlighting its advantages in terms of computational efficiency and accuracy on a Fault-Tolerant Quantum Computing (FTQC). Furthermore, we present a comparative analysis of the quantum and the classical method of SVD, demonstrating the accuracy of the image data. The simulation results validate the theoretical advantages of using quantum algorithms for SVD in image processing. This work not only underscores the potential of quantum computing in enhancing image processing techniques but also sets the stage for future research in the field, exploring more complex image processing tasks and other quantum algorithms. Our findings suggest that quantum image processing can offer unprecedented capabilities, paving the way for advancements in various applications such as medical imaging, remote sensing, and multimedia processing.
This research paper explores the application of singular value decomposition (SVD) in quantum image processing (QIP), specifically focusing on the computation of eigenvalues using variational quantum algorithms. SVD is a powerful mathematical tool in image processing, used for tasks such as image compression, noise reduction, and feature extraction. In this study, we propose quantum variational singular value decomposition (QVSVD) based on the variational quantum deflation (VQD) algorithm to determine the eigenvalues that contributes in calculating the singular values of the image matrix and eventually doing the SVD. This facilitates the extraction of eigenvalues with exponential speedup on real hardware compared to classical methods. We detail the implementation of this quantum algorithm within the framework of QIP, highlighting its advantages in terms of computational efficiency and accuracy on a Fault-Tolerant Quantum Computing (FTQC). Furthermore, we present a comparative analysis of the quantum and the classical method of SVD, demonstrating the accuracy of the image data. The simulation results validate the theoretical advantages of using quantum algorithms for SVD in image processing. This work not only underscores the potential of quantum computing in enhancing image processing techniques but also sets the stage for future research in the field, exploring more complex image processing tasks and other quantum algorithms. Our findings suggest that quantum image processing can offer unprecedented capabilities, paving the way for advancements in various applications such as medical imaging, remote sensing, and multimedia processing.
Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although these algorithms are promising, the required quantum subroutines and resources are too costly on near-term quantum devices. In this work, we propose a variational quantum algorithm for singular value decomposition (VQSVD). By exploiting the variational principles for singular values and the Ky Fan Theorem, we design a novel loss function such that two quantum neural networks (or parameterized quantum circuits) could be trained to learn the singular vectors and output the corresponding singular values. Furthermore, we conduct numerical simulations of VQSVD for random matrices as well as its applications in image compression of handwritten digits. Finally, we discuss the applications of our algorithm in recommendation systems and polar decomposition. Our work explores new avenues for quantum information processing beyond the conventional protocols that only works for Hermitian data, and reveals the capability of matrix decomposition on near-term quantum devices.
Classical data analysis requires computational efforts that become intractable in the age of Big Data. An essential task in time series analysis is the extraction of physically meaningful information from a noisy time series. One algorithm devised for this very purpose is singular spectrum decomposition (SSD), an adaptive method that allows for the extraction of narrow-banded components from non-stationary and non-linear time series. The main computational bottleneck of this algorithm is the singular value decomposition (SVD). Quantum computing could facilitate a speedup in this domain through superior scaling laws. We propose quantum SSD by assigning the SVD subroutine to a quantum computer. The viability for implementation and performance of this hybrid algorithm on a near term hybrid quantum computer is investigated. In this work, we show that by employing randomized SVD, we can impose a qubit limit on one of the circuits to improve scalibility. Using this, we efficiently perform quantum SSD on simulations of local field potentials recorded in brain tissue, as well as GW150914, the first detected gravitational wave event.
Quantum image processing uses quantum computing, which implements the concepts of entanglement and superposition to increase efficiency, scalability, and revolutionary promise in demanding image processing ap plications. In this research paper, a comprehensive frame work for quantum image processing (QIP) is presented, which includes innovative quantum algorithms for pattern recognition, image improvement, and representation. The system presents advanced quantum encoding models for effective image data manipulation and storage. In addition, it discusses the quantum image-based algorithms that give better results than classical techniques in terms of speed and accuracy for image enhancement tasks such as edge recognition, contrast adjustment, and noise reduction. Researchers have developed quantum-based feature ex traction and classification methods for pattern recognition, which demonstrate enhanced scalability and accuracy for complex visual data. It has various applications in satellite data processing, secure visual data transmission, and medical imaging highlighted by simulations and theoretical analysis that confirm the proposed approaches.
Quantum algorithms have emerged as a transformative approach to address the computational challenges of high-dimensional image processing tasks. This research investigates the integration of quantum computing principles, such as Quantum Fourier Transform (QFT) and Quantum Principal Component Analysis (QPCA), to optimize processes like edge detection, noise reduction, and image segmentation. These quantum-enhanced techniques promise significant improvements in computational efficiency and accuracy compared to classical methods, especially when handling complex visual data in real-time applications like medical imaging, satellite imagery, and autonomous systems. Additionally, the study explores hybrid quantum-classical architectures to bridge current limitations in noisy intermediate-scale quantum (NISQ) devices, ensuring resource optimization and scalability. The potential of quantum algorithms to provide faster, more precise solutions is evaluated alongside challenges like error mitigation and algorithmic stability. This research highlights the future role of quantum computing in revolutionizing image processing, paving the way for breakthroughs in computer vision and artificial intelligence.
The integration of quantum computing into image processing represents a significant advancement in computational technology, offering transformative capabilities that enhance performance, efficiency, and accuracy. This chapter explores hybrid quantum-classical algorithms, focusing on how quantum subroutines can be integrated into classical image processing workflows. A comparative analysis of various quantum image encoding techniques highlights their strengths and limitations, paving the way for optimized applications across diverse fields. Key advantages of quantum-enhanced image processing, such as improved speed in high-resolution data analysis and superior optimization methods, are discussed in relation to real-world applications, including medical imaging and computer vision. The chapter anticipates future developments in quantum technology, emphasizing the need for interdisciplinary collaboration to unlock the full potential of quantum computing in digital image applications. By addressing the critical gaps in current methodologies, this work aims to inspire further research and innovation in the realm of quantum-enhanced image processing.
Quantum computing is increasingly being viewed as a promising direction for the future of image processing. Conventional approaches to image classification, enhancement, compression, and restoration, although highly developed, often struggle with scalability, computational complexity, and data security—especially when processing high-dimensional or sensitive visual information. This survey explores how quantum computing can help address these limitations through quantum image representation models such as FRQI and NEQR, variational quantum circuits, and hybrid quantum–classical architectures. The primary objective of this review is to present a clear and structured overview of the current state of quantum image processing (QIP). It discusses foundational representation models, emerging hybrid learning techniques, available software frameworks and simulators, benchmarking practices, and practical applications in areas such as medical imaging, remote sensing, and biometric security. Particular attention is given to solutions that are feasible on today’s NISQ-era hardware, including hybrid architectures and quantum-secured image processing schemes. The survey concludes by identifying existing challenges and outlining realistic future research directions. Overall, it emphasizes the practical importance of hybrid models, the need for standardized quantum-oriented benchmarks, and the growing potential of quantum-based security mechanisms for safeguarding visual data.