Quantum Image Processing: the truth, the whole truth, and nothing but the truth about its problems on internal image representation and outcomes recovering
In this paper, three techniques of internal image-representation in a quantum computer are compared: Flexible Representation of Quantum Images (FRQI), Novel Enhanced Quantum Representation of digital images (NEQR), and Quantum Boolean Image Processing (QBIP). All conspicuous technical items are considered in this comparison for complete analysis: i) performance as Classical-to-Quantum (Cl2Qu) interface, ii) characteristics of the employed qubits, iii) sparsity of the used internal registers, iv) number and size of the required registers, v) quality in the outcomes recovering, vi) number of required gates and its consequent accumulated noise, vi) decoherence, and vii) fidelity. These analyses and demonstrations are automatically extended to all variants of FRQI and NEQR. This study demonstrated the practical infeasibility in the implementation of FRQI and NEQR on a physical quantum computer (QPU), while QBIP has proven to be extremely successful on a) the four main quantum simulators on the cloud, b) two QPUs, and c) optical circuits from three labs. Moreover, QBIP also demonstrated its economy regarding the required resources needed for its proper function and its great robustness (immunity to noise), among other advantages, in fact, without any exceptions.
In this paper, three techniques of internal image-representation in a quantum computer are compared: Flexible Representation of Quantum Images (FRQI), Novel Enhanced Quantum Representation of digital images (NEQR), and Quantum Boolean Image Processing (QBIP). All conspicuous technical items are considered in this comparison for complete analysis: i) performance as Classical-to-Quantum (Cl2Qu) interface, ii) characteristics of the employed qubits, iii) sparsity of the used internal registers, iv) number and size of the required registers, v) quality in the outcomes recovering, vi) number of required gates and its consequent accumulated noise, vi) decoherence, and vii) fidelity. These analyses and demonstrations are automatically extended to all variants of FRQI and NEQR. This study demonstrated the practical infeasibility in the implementation of FRQI and NEQR on a physical quantum computer (QPU), while QBIP has proven to be extremely successful on a) the four main quantum simulators on the cloud, b) two QPUs, and c) optical circuits from three labs. Moreover, QBIP also demonstrated its economy regarding the required resources needed for its proper function and its great robustness (immunity to noise), among other advantages, in fact, without any exceptions.
In this paper, five techniques, for the representation of a digital image inside a quantum processor, are compared. The techniques are: flexible representation of quantum images (FRQI), novel enhanced quantum representation (NEQR), generalized quantum image representation (GQIR), multi-channel representation for quantum images (MCQI), and quantum Boolean image processing (QBIP). The comparison will be based on implementations on the Quirk simulator, and on the IBM Q Experience processors, from the point of view of performance, robustness (noise immunity), deterioration of the outcomes due to decoherence, and technical viability.
Quantum image processing represents a transformative approach to visual data analysis, leveraging the principles of quantum computing to overcome classical limitations. This work explores two prominent quantum image encoding methods: FRQI (Flexible Representation of Quantum Images) and NEQR (Novel Enhanced Quantum Representation). FRQI excels in qubit efficiency, making it suitable for hardware implementation, while NEQR offers superior precision in pixel intensity representation, ideal for complex image processing tasks. We detail the implementation of these algorithms, including preprocessing, quantum circuit design, and simulation, using platforms like Qiskit. The study highlights the potential of quantum image processing in fields such as medicine, industry, and environmental monitoring, while addressing challenges like qubit limitations and noise sensitivity. This research contributes to advancing quantum computing applications, paving the way for innovative and sustainable technological solutions.
This study presents a comparative evaluation of three quantum image representation techniques: FRQI, QPIE, and NEQR. The Baboon image is used as a benchmark, and performance is assessed through PSNR, MSE, SSIM, and execution time. Simulations were conducted using a noiseless quantum simulator to ensure fair comparison across methods. Results indicate that QPIE achieves the best reconstruction quality, with PSNR = 117.97, MSE = 1.037, and SSIM = 0.975 for the 8 x 8 image, while maintaining strong performance for larger sizes. In contrast, FRQI shows lower quality and high execution time. NEQR is computationally faster (4.85 s) but delivers moderate quality (PSNR = 79.38, SSIM = 0.859). Additionally, QPIE requires fewer qubits, making it more resource-efficient. Overall, QPIE emerges as the most effective representation, striking a balance between image quality, computational cost, and qubit utilization. These findings highlight QPIE as a promising candidate for future quantum image processing tasks such as compression, edge detection, and negative transformation.
With the advancement of quantum computing, quantum image representations (QIRs) have been widely studied as platforms for quantum image processing. While previous studies have focused on theoretical qubit counts and circuit complexities, there has been limited quantitative evaluation of image reconstruction performance from quantum states. In this study, we clarify the theoretical upper bounds of restoration performance for three representative QIRs: qubit lattice (QL), flexible representation of quantum images (FRQI), and novel enhanced quantum representation (NEQR). Also, we validate them through large-scale GPU-based simulations using cuQuantum. Specifically, we (1) derive a prediction formula for PSNR in probabilistic schemes like QL and FRQI, independent of image content and size; (2) show that deterministic schemes like NEQR require a number of samples following a harmonic number for complete restoration; and (3) perform large-scale simulations to verify these findings. These results provide fundamental insights for designing QIRs and their applications on NISQ devices.
Quantum Image Representation (QIR) is a key element in Quantum Image Processing (QIP) and is essential for the effective management of quantum information. To process quantum images, it is necessary to convert classical digital image data into formats suitable for quantum computers. This conversion involves managing, manipulating, and storing the data efficiently in quantum states. The importance of QIR has spurred numerous studies based on the principles of quantum mechanics, aiming to develop effective methods for representing quantum images. These methods are vital for advancing quantum computing applications related to image processing. In this paper, we will discuss and compare two prominent techniques for encoding images into quantum states: the Flexible Representation of Quantum Images (FRQI) and the Novel Enhanced Quantum Representation (NEQR). These methods showcase different approaches to quantum image handing, highlighting the evolving nature of quantum image processing technology.
In the era of big data and artificial intelligence, the increasing volume of data and the demand to solve more and more complex computational challenges are two driving forces for improving the efficiency of data storage, processing, and analysis. Quantum image processing is an interdisciplinary field between quantum information science and image processing, which has the potential to alleviate some of these challenges by leveraging the power of quantum computing. In this work, we compare and examine the compression properties of four different quantum image representations (QImRs): namely, tensor network representation (TNR), flexible representation of quantum image (FRQI), novel enhanced quantum representation (NEQR), and quantum probability image encoding (QPIE). Our simulations show that FRQI and QPIE perform a higher compression of image information than TNR and NEQR. Furthermore, we investigate the trade-off between accuracy and memory in binary classification problems, evaluating the performance of quantum kernels based on QImRs compared to the classical linear kernel. Our results indicate that quantum kernels provide comparable classification average accuracy but require exponentially fewer resources for image storage.