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.
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 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.
Abstract Quantum Image Representation (QIR) is a fundamental concept in quantum image processing. It describes how classical images are converted into quantum states for processing on quantum computers. Researchers proposed several QIR models, with FRQI and NEQR being the most popular ones. These models show the possibilities of the quantum image encoding. Nevertheless, they are also limited in some way. Mostly, pixel intensity accuracy, the required number of qubits, and circuit complexity have trade-offs. Their application to Noisy Intermediate-Scale Quantum (NISQ) devices becomes challenging, the quantum resources being small in such devices, due to this. In the following paper, we introduce our own approach, which is the Intensity-Preserving Quantum image Representation (IP-QIR). The key aim of IP-QIR is to maintain the information about the grayscale intensities and decrease the amount of quantum resources. IP-QIR quantifies pixel intensities by a controlled rotation scheme. The measurement statistics of a single qubit hold the intensity information and the position qubits represent the spatial information. The strategy uses small patches of images rather than complete images to make it easy to implement. This will decrease the depth of circuit design and makes the approach less advanced to the near-term quantum hardware. IBM Qiskit simulations are used in assessing the performance of IP-QIR. The three types of grayscale images of which experiments are run are the synthetic image patches, SAR images and medical TB chest X-ray images. It is revealed that IP-QIR maintains the intensity information compared to the FRQI and NEQR. SAR and medical data can reach values of fidelity of 84.12\%. The other notable point is that the size of a 4 x 4 image patch only needs five qubits which are much lower than in NEQR. Meanwhile, good reconstruction accuracy is achieved. These findings demonstrate the fact that IP-QIR is an effective and realistic approach to quantum image representation on the NISQ-era quantum devices.
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.
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.
This paper examines Quantum Image Representation Algorithms (QIRA), which have significantly advanced the encoding and manipulation of visual data using quantum computing. It explores key developments in image representation techniques, focusing on Flexible Representation of Quantum Images (FRQI), Novel Enhanced Quantum Representation (NEQR), Generalized Quantum Image Representation (GQIR), Bit Plane Representation of Quantum Images (BRQI), and Order Encoding Quantum Image Model (OQIM). Using the Qiskit framework, these methods are implemented to encode classical images into quantum states and perform various quantum operations. The paper provides a comprehensive understanding of QIRA by outlining the background of these representation techniques and rigorously evaluating their performance in image reconstruction. The evaluation is based on metrics such as Mean Squared Error (MSE), Cosine Similarity, Normalized Cross-Correlation (NCC), Structural Similarity Index (SSIM), and Peak Signal-to-Noise Ratio (PSNR).
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.