Flexible Representation Of Quantum Images Research Articles

A biological sequence comparison algorithm using quantum computers

Genetic information is encoded as linear sequences of nucleotides, represented by letters ranging from thousands to billions. Differences between sequences are identified through comparative approaches like sequence analysis, where variations can occur at the individual nucleotide level or collectively due to various phenomena such as recombination or deletion. Detecting these sequence differences is vital for understanding biology and medicine, but the complexity and size of genomic data require substantial classical computing power. Inspired by human visual perception and pixel representation on quantum computers, we leverage these techniques to implement pairwise sequence analysis. Our method utilizes the Flexible Representation of Quantum Images (FRQI) framework, enabling comparisons at a fine granularity to single letters or amino acids within gene sequences. This novel approach enhances accuracy and resolution, surpassing traditional methods by capturing subtle genetic variations with precision. In summary, our approach offers algorithmic advantages, including reduced time complexity, improved space efficiency, and accurate sequence comparisons. The novelty lies in applying the FRQI algorithm to compare quantum images in genome sequencing, allowing for examination at the individual letter or amino acid level. This breakthrough holds promise for advancing biological data analysis and enables a more comprehensive understanding of genetic information.

Improved FRQI on superconducting processors and its restrictions in the NISQ era

In image processing, the amount of data to be processed grows rapidly, in particular when dealing with images of more than two dimensions or time series of images. Thus, efficient processing is a challenge, as data sizes may push even supercomputers to their limits. Quantum image processing promises to encode images with logarithmically less qubits than classical pixels in the image. In theory, this is a huge progress, but so far not many experiments have been conducted in practice, in particular on real backends. Often, the precise conversion of classical data to quantum states, the exact implementation, and the interpretation of the measurements in the classical context are challenging. We investigate these practical questions in this paper. In particular, we study the feasibility of the flexible representation of quantum images (FRQI). Furthermore, we check experimentally the limit in the current noisy intermediate-scale quantum era, i.e., up to which image size an image can be encoded, both on simulators and on real backends. Finally, we propose a method for simplifying the circuits needed for the FRQI. With our alteration, the number of gates can be reduced, especially the one of the error-prone controlled-NOT gates. As a consequence, the size of manageable images increases.

Data loss in quantum image representation methods

Quantum Image Representation is a well-studied area in quantum informatics. The first proposed algorithm was the qubit lattice method introduced in 2003. This method was not harnessing the full potential of the quantum system - using as many qubits as there were pixels in the image.The most commonly used methods right now are Flexible Representation of Quantum Images (FRQI) proposed in 2011, and Novel Enhanced Quantum Representation (NEQR) proposed in 2013, which uses superposition to encode a monochrome image on a quantum computer using a reduced number of qubits. In this paper, we want to compare these two methods, alongside Local Phase Image Quantum Encoding (LPIQE) method proposed in 2020, to see which method produces images with minimal data loss. Another comparison will be done with image encoded using the LPIQE method with Phase Distortion Unraveling (PDU) error mitigation method, which is done entirely on a classical computer. LPIQE implementation was intended for using the photonic quantum system since the phase-shift is easy to produce, and it will be implemented on real, photonic quantum computers after further development.

An Overview on Quantum Image Watermarking for Security of COVID-19 Patient Record

The basics of Quantum Information Processing (QIP) is summarized below, in addition to a comprehensive survey of quantum image-based data hiding techniques. QIP is more efficient and provides higher security than classical information processing. A comparative analysis of the Flexible Representation of Quantum Images (FRQI) and Novel Enhanced Quantum Representation (NEQR) model is also presented. QIP is used in various potential applications, hence offering an interesting and demanding area for researchers [1]. Some of the important applications include medicine, military, environmental monitoring, image processing, communications, computations, and cryptography. This article focusses on the processing of information that can be represented using quantum mechanics [2]. Furthermore, coherence, entanglement, and superposition of quantum states makes quantum computing more suitable to its classical counterpart for information storage and processing [1], [3].

Analysis of Five Techniques for the Internal Representation of a Digital Image Inside a Quantum Processor

In this paper, five techniques of representing 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.

Multilevel segmentation of medical images in the framework of quantum and classical techniques

Nowadays, the numerical segmentation is an important step in the processing and interpretation of medical images. The segmentation consists in extracting, from the image, one or more objects forming the regions of interest. Image thresholding is one of the simplest and effective techniques of image segmentation. In this work, we propose and compare multilevel segmentation approaches based on classical and quantum techniques. The Classical Renyi (CR) and the Quantum Renyi (QR) entropies are used to quantify the information contained in the image. Within the quantum framework, the digital image is expressed as a quantum system by means of the Flexible Representation of Quantum Images (FRQI). Generally, the multilevel thresholding formulation leads to a complex optimization problem. The Classical Genetic Algorithm (CGA) and the Quantum Genetic Algorithm (QGA) are employed to efficiently determine the optimal thresholding values by maximizing the entropy-based fitness functions. The segmentation performances of the proposed methods are assessed and compared using some prevailing criteria. The achieved results on a sample of medical images demonstrated that the QGA-QR method outperforms significantly the other combinations for this thresholding exercise.

Quantum image processing: the pros and cons of the techniques for the internal representation of the image. A reply to: A comment on “Quantum image processing?”

This work demonstrates the practical infeasibility in the implementation of the techniques known as flexible representation of quantum images (and its variants) and novel enhanced quantum representation of digital images (and its variants). Besides, the implementation of the technique known as quantum Boolean image processing has proven to be extremely successful on: (a) the four main quantum simulators on the cloud, (b) two physical quantum computers, and (c) three optical tables where it also demonstrated: its resource economy and its great robustness (immunity to noise), among other advantages, in fact, without any exceptions.

Quantum image encryption algorithm based on Arnold scrambling and wavelet transforms

Based on the modified flexible representation of quantum images, a novel quantum image encryption algorithm was proposed in this paper. The encryption process performs Arnold scrambling operation to disturb the quantum image information in spatial domain first. Then, quantum wavelet transforms are employed to decompose the scrambled quantum image into multiscale resolution (i.e., a sequence of subimages) in the frequency domain, which are mainly divided into two parts: the low-frequency component (i.e., the approximation) and high-frequency detail information (i.e., the horizontal details, vertical details and diagonal details in each decomposition level). Following that, Arnold scrambling operations are implemented to encrypt the wavelet coefficients within each subimage in the frequency domain once again. Finally, based on inverse quantum wavelet transforms, the encrypted wavelet coefficients can affect the pixel values of the entire reconstructed quantum images. Due to the fact that all the quantum operations are invertible, the decryption process of the encrypted image is performed in a straightforward manner by reversing all of the quantum operations within quantum image encryption process. The proposed encryption algorithm is simulated on a classical computer with MATLAB environments. Experimental results and numerical analysis indicate that the presented algorithm has a good encrypted effect and high security.

Correlation Property of Multipartite Quantum Image

Inspired on the classical Bayesian method also called mutual information, by generalizing the classical case to quantum approach to study the multipartite correlation in quantum image by using the flexible representation of quantum images (FRQI) method. Some important entanglement measures are calculated including von Neumann entropy, conditional entropy, joint entropy, discord and mutual information. We take two typical images of size 2 × 2 pixels and 8 × 8 pixels and study their entanglement measures from different classical and quantum point of view. The quantum image of size 2 × 2 is studied under the change of color for one pixel, but the quantum image of 8 × 8 is treated under translation transform. We find that the classical joint entropy remains invariant under the change of color for one pixel but the quantum entropy is sensitive to such change. It is shown that the total correlation IT could arrive to the double amount of the classical joint entropy. The discord in the classical case is zero, but it varies much in the quantum case.

An improved flexible representation of quantum images

The flexible representation of quantum images (FRQI) and novel enhanced quantum representation (NEQR) are well-known models used for storing and processing quantum images. In this article, we establish that the complexity of image preparation in FRQI model is $$O(n2^{2n})$$ , which is linear in the size of image. Moreover, by analyzing the FRQI and NEQR models, we propose an improved flexible representation of quantum images (IFRQI) which uses p qubits to store grayscale value of every pixel of a 2p-bit-deep image. The grayscale values are encoded by employing rotation matrices corresponding to chosen values of angles which assist in accurate retrieval of original image information through projective measurements. The quantum image compression algorithm and basic image processing operations are discussed in detail to establish the effectiveness of IFRQI model. The performance analysis in respect of time and space complexity exhibits that the IFRQI model is comparable to FRQI and NEQR models.

Quantum Image Watermarking Algorithm Based on Haar Wavelet Transform

In this paper, a novel frequency domain quantum watermarking scheme is proposed based on the Flexible Representation of Quantum Images, which can embed a 2 n1 × 2 n1 binary watermark image into a 2 n × 2 n grayscale carrier image. The quantum Haar wavelet transform is developed and used to decompose quantum images. The diagonal detail coefficients of the carrier image are obtained from the image decomposition. Then, according to the watermark image information, the diagonal wavelet coefficients are either unchanged or slightly modified. Since all of the used quantum operations are invertible, extraction of the watermark image is performed in a straightforward manner by reversing the watermarking embedding process. Finally, the proposed quantum image watermarking scheme is simulated on a classical computer and evaluated under different carrier and watermark images. The simulation results and performance analyses indicate the high performance of the presented watermarking scheme in terms of the similarity between the watermarked and carrier images.

Quantum multidimensional color image scaling using nearest-neighbor interpolation based on the extension of FRQI

Reviewing past researches on quantum image scaling, only 2D images are studied. And, in a quantum system, the processing speed increases exponentially since parallel computation can be realized with superposition state when compared with classical computer. Consequently, this paper proposes quantum multidimensional color image scaling based on nearest-neighbor interpolation for the first time. Firstly, flexible representation of quantum images (FRQI) is extended to multidimensional color model. Meantime, the nearest-neighbor interpolation is extended to multidimensional color image and cycle translation operation is designed to perform scaling up operation. Then, the circuits are designed for quantum multidimensional color image scaling, including scaling up and scaling down, based on the extension of FRQI. In addition, complexity analysis shows that the circuits in the paper have lower complexity. Examples and simulation experiments are given to elaborate the procedure of quantum multidimensional scaling.

A Strategy of Quantum Image Filtering in Frequency Domain

In the field of quantum image processing, the method for quantum image representation has been a hot issue. However the computational complexity of the whole preparation for the mature model (Flexible Representation of Quantum Images) is too high. In this paper we present a fast image storage method based on the transformation about two quantum image representation models. Then a filtering algorithm is proposed via using quantum Fourier transform. With low time complexity, the good performance of this filtering operation can be presented in the simulation experiments.

Quantum Realization of Arnold Scrambling for IFRQI

This paper is concerned with the feasibility of the Arnold scrambling based on Improved Flexible Representation of Quantum Images (IFRQI). Firstly, the flexible representation of quantum image is updated to the improved flexible representation of quantum image (IFRQI) to represent a quantum image with arbitrary size L × B. Then, by making use of Control-NOT gate and Adder-Modular operation, the concrete quantum circuit of Arnold scrambling for IFRQI is designed. Simulation results show the effectiveness of the proposed circuit.

Quantum realization of the nearest-neighbor interpolation method for FRQI and NEQR

This paper is concerned with the feasibility of the classical nearest-neighbor interpolation based on flexible representation of quantum images (FRQI) and novel enhanced quantum representation (NEQR). Firstly, the feasibility of the classical image nearest-neighbor interpolation for quantum images of FRQI and NEQR is proven. Then, by defining the halving operation and by making use of quantum rotation gates, the concrete quantum circuit of the nearest-neighbor interpolation for FRQI is designed for the first time. Furthermore, quantum circuit of the nearest-neighbor interpolation for NEQR is given. The merit of the proposed NEQR circuit lies in their low complexity, which is achieved by utilizing the halving operation and the quantum oracle operator. Finally, in order to further improve the performance of the former circuits, new interpolation circuits for FRQI and NEQR are presented by using Control-NOT gates instead of a halving operation. Simulation results show the effectiveness of the proposed circuits.

Novel quantum gray-scale image matching

Image matching, also known as correspondence problem, can be defined as the establishment of the correspondence between two or more digital images depicting at least partly the same scene. In this paper, we propose a method for matching gray-scale images consisting of quantum information. Quantum template image is directly mapped with quantum reference image, i.e., the quantum register representing each corresponding pixel of the quantum template image is subtracted from that of the quantum reference image by running a quantum subtracter. According to the quantum measurement results, we can save the gray-scale difference and sum all the differences. Then we compare the sum with Tolerance value. If the sum is smaller than Tolerance value, then quantum image matching succeeds. Experimental simulations show that the proposed approach can distinguish any two quantum gray-scale images successfully. Compared to the schemes based on flexible representation of quantum images (FRQI), our approach based on novel enhanced quantum representation of digital images (NEQR) has the advantages of retrieving the original classical image accurately from the quantum image so that it can be generalized to the case where the dimension of quantum template image is smaller than that of quantum reference image.

Quantum Computation-Based Image Representation, Processing Operations and Their Applications

A flexible representation of quantum images (FRQI) was proposed to facilitate the extension of classical (non-quantum)-like image processing applications to the quantum computing domain. The representation encodes a quantum image in the form of a normalized state, which captures information about colors and their corresponding positions in the images. Since its conception, a handful of processing transformations have been formulated, among which are the geometric transformations on quantum images (GTQI) and the CTQI that are focused on the color information of the images. In addition, extensions and applications of FRQI representation, such as multi-channel representation for quantum images (MCQI), quantum image data searching, watermarking strategies for quantum images, a framework to produce movies on quantum computers and a blueprint for quantum video encryption and decryption have also been suggested. These proposals extend classical-like image and video processing applications to the quantum computing domain and offer a significant speed-up with low computational resources in comparison to performing the same tasks on traditional computing devices. Each of the algorithms and the mathematical foundations for their execution were simulated using classical computing resources, and their results were analyzed alongside other classical computing equivalents. The work presented in this review is intended to serve as the epitome of advances made in FRQI quantum image processing over the past five years and to simulate further interest geared towards the realization of some secure and efficient image and video processing applications on quantum computers.

Quantum Hilbert Image Scrambling

Analogies between quantum image processing (QIP) and classical one indicate that quantum image scrambling (QIS), as important as quantum Fourier transform (QFT), quantum wavelet transform (QWT) and etc., should be proposed to promote QIP. Image scrambling technology is commonly used to transform a meaningful image into a disordered image by permutating the pixels into new positions. Although image scrambling on classical computers has been widely studied, we know much less about QIS. In this paper, the Hilbert image scrambling algorithm, which is commonly used in classical image processing, is carried out in quantum computer by giving the scrambling quantum circuits. First, a modified recursive generation algorithm of Hilbert scanning matrix is given. Then based on the flexible representation of quantum images, the Hilbert scrambling quantum circuits, which are recursive and progressively layered, is proposed. Theoretical analysis indicates that the network complexity scales squarely with the size of the circuit’s input n.

SQR: a simple quantum representation of infrared images

A simple quantum representation (SQR) of infrared images is proposed based on the characteristic that infrared images reflect infrared radiation energy of objects. The proposed SQR model is inspired from the Qubit Lattice representation for color images. Instead of the angle parameter of a qubit to store a color as in Qubit Lattice representation, probability of projection measurement is used to store the radiation energy value of each pixel for the first time in this model. Since the relationship between radiation energy values and probability values can be quantified for the limited radiation energy values, it makes the proposed model more clear. In the process of image preparation, only simple quantum gates are used, and the performance comparison with the latest flexible representation of quantum images reveals that SQR can achieve a quadratic speedup in quantum image preparation. Meanwhile, quantum infrared image operations can be performed conveniently based on SQR, including both the global operations and local operations. This paper provides a basic way to express infrared images in quantum computer.

Towards Realising Secure and Efficient Image and Video Processing Applications on Quantum Computers

Exploiting the promise of security and efficiency that quantum computing offers, the basic foundations leading to commercial applications for quantum image processing are proposed. Two mathematical frameworks and algorithms to accomplish the watermarking of quantum images, authentication of ownership of already watermarked images and recovery of their unmarked versions on quantum computers are proposed. Encoding the images as 2n-sized normalised Flexible Representation of Quantum Images (FRQI) states, with n-qubits and 1-qubit dedicated to capturing the respective information about the colour and position of every pixel in the image respectively, the proposed algorithms utilise the flexibility inherent to the FRQI representation, in order to confine the transformations on an image to any predetermined chromatic or spatial (or a combination of both) content of the image as dictated by the watermark embedding, authentication or recovery circuits. Furthermore, by adopting an apt generalisation of the criteria required to realise physical quantum computing hardware, three standalone components that make up the framework to prepare, manipulate and recover the various contents required to represent and produce movies on quantum computers are also proposed. Each of the algorithms and the mathematical foundations for their execution were simulated using classical (i.e., conventional or non-quantum) computing resources, and their results were analysed alongside other longstanding classical computing equivalents. The work presented here, combined together with the extensions suggested, provide the basic foundations towards effectuating secure and efficient classical-like image and video processing applications on the quantum-computing framework.