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.
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.
Quantum Image Representation (QIR) has become a key component of Quantum Image Processing (QIP), enabling the encoding and manipulation of visual data within quantum computing environments.Its integration with Quantum Artificial Intelligence (QAI) and Quantum Machine Learning (QML) has attracted significant research interest due to the potential advantages of quantum parallelism and compact data representation.This survey reviews major QIR techniques, analyzes their encoding strategies and computational characteristics, and examines their opportunities, challenges, and future relevance in quantum AI and machine learning applications.A systematic review of 70 peer-reviewed journal and conference publications published between 1992 and 2025 was conducted.The selected studies were evaluated based on encoding mechanisms, qubit requirements, circuit complexity, retrieval capability, scalability, and suitability for quantum image processing and learning tasks.The review covers prominent QIR models, including FRQI, NEQR, MCQI, QPIE, GQIR, QRMW, and tensor-network-based representations.Comparative analysis reveals important trade-offs between qubit efficiency, encoding complexity, retrieval accuracy, and scalability.Amplitude-based approaches provide compact image encoding but suffer from probabilistic retrieval, whereas basis-state representations offer deterministic recovery at the expense of increased circuit complexity.QIR demonstrates significant potential in image classification, feature extraction, image compression, and hybrid quantum-classical learning frameworks.QIR provides a promising foundation for next-generation quantum-enhanced visual intelligence systems.However, practical implementation remains constrained by state preparation overhead, noise, decoherence, limited qubit availability, and the lack of standardized evaluation frameworks.Future research should focus on scalable encoding methods, fault-tolerant quantum architectures, benchmarking standards, and deeper integration with advanced QML models to accelerate the development of practical quantum image analytics.
Image classification is an important task in many practical applications. Recently, there have been various works on classification problems using quantum neural network (QNN). Different data encoders have been investigated, but efficient quantum encoding schemes for high-dimensional data such as images are still an open question. In this study, we investigate popular representation formats of quantum images, namely FRQI and NEQR, as data encoders for quantum neural networks. It is found that the FRQI format not only provides the best classification accuracy compared to NEQR and other popular encoding methods but also is consistent across different circuit depths of QNN. It should be noted that FRQI is notorious for its probabilistic representation in quantum image processing. The finding of this study is interesting because FRQI can play an important role in the field of quantum machine learning.
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.
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 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.