NEQR: a novel enhanced quantum representation of digital images
TL;DR: Performance comparisons with FRQI reveal that NEQR can achieve a quadratic speedup in quantum image preparation, increase the compression ratio of quantum images by approximately 1.5X, and retrieve digital images from quantum images accurately.
Abstract: Quantum computation is becoming an important and effective tool to overcome the high real-time computational requirements of classical digital image processing. In this paper, based on analysis of existing quantum image representations, a novel enhanced quantum representation (NEQR) for digital images is proposed, which improves the latest flexible representation of quantum images (FRQI). The newly proposed quantum image representation uses the basis state of a qubit sequence to store the gray-scale value of each pixel in the image for the first time, instead of the probability amplitude of a qubit, as in FRQI. Because different basis states of qubit sequence are orthogonal, different gray scales in the NEQR quantum image can be distinguished. Performance comparisons with FRQI reveal that NEQR can achieve a quadratic speedup in quantum image preparation, increase the compression ratio of quantum images by approximately 1.5X, and retrieve digital images from quantum images accurately. Meanwhile, more quantum image operations related to gray-scale information in the image can be performed conveniently based on NEQR, for example partial color operations and statistical color operations. Therefore, the proposed NEQR quantum image model is more flexible and better suited for quantum image representation than other models in the literature.
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TL;DR: This paper gathers the current mainstream quantum image representations (QIRs) and discusses the advances made in the area and believes this compendium will provide the readership an overview of progress witnessed while also simulating further interest to pursue more advanced research in it.
Abstract: Quantum image processing (QIMP) is devoted to utilizing the quantum computing technologies to capture, manipulate, and recover quantum images in different formats and for different purposes. Logically, percolating this requires that representations to encode images based on the quantum mechanical composition of any potential quantum computing hardware be conjured. This paper gathers the current mainstream quantum image representations (QIRs) and discusses the advances made in the area. Some similarities, differences, and likely applications for some of the available QIRs are reviewed. We believe this compendium will provide the readership an overview of progress witnessed in the area of QIMP while also simulating further interest to pursue more advanced research in it.
246 citations
Cites background or methods from "NEQR: a novel enhanced quantum repr..."
...This step is divided into 22n sub-operations to store the grayscale information for every pixel [125]....
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...They include multi-channel representation for quantum images (MCQI) [86], the so-called Caraiman’s QIR approach (presented as CQIR for brevity) [10]; novel enhanced quantum representation of digital image model (NEQR) [125]; quantum image representation for log-polar images (QUALPI) [126]; simple quantum representation of infrared images (SQR) [120]; color image representation utilizing two sets of quantum states for M colors and N coordinates, respectively (QSMC & QSNC) [58]; and multi-dimensional image representation using a normal arbitrary quantum superposition state (NAQSS) [60]....
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...Similar toNEQR that uses a qubit sequence to encode the color information in quantum images [125], Caraiman and Manta proposed an approach, i....
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...Interestingly, the authors, in [125], assert that more image operations can be performed conveniently based on NEQR than on FRQI, especially some complex color operations such as partial color operations and statistical color operations....
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...Therefore, to store the digital image in NEQR using quantum mechanics, two entangled qubit sequences are used to store the whole image, which represent the grayscale and positional information of all the pixels [125]....
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TL;DR: Numerical simulations and theoretical analyses demonstrate that the proposed quantum image encryption algorithm with good feasibility and effectiveness has lower computational complexity than its classical counterpart.
Abstract: A quantum realization of the generalized Arnold transform is designed. A novel quantum image encryption algorithm based on generalized Arnold transform and double random-phase encoding is proposed. The pixels are scrambled by the generalized Arnold transform, and the gray-level information of images is encoded by the double random-phase operations. The keys of the encryption algorithm include the independent parameters of coefficients matrix, iterative times and classical binary sequences, and thus, the key space is extremely large. Numerical simulations and theoretical analyses demonstrate that the proposed algorithm with good feasibility and effectiveness has lower computational complexity than its classical counterpart.
194 citations
TL;DR: It is the first time to give the quantum image processing method that changes the size of an image and the quantum strategies developed in this paper initiate the research about quantum image scaling.
Abstract: Although image scaling algorithms in classical image processing have been extensively studied and widely used as basic image transformation methods, the quantum versions do not exist. Therefore, this paper proposes quantum algorithms and circuits to realize the quantum image scaling based on the improved novel enhanced quantum representation (INEQR) for quantum images. It is necessary to use interpolation in image scaling because there is an increase or a decrease in the number of pixels. The interpolation method used in this paper is nearest neighbor which is simple and easy to realize. First, NEQR is improved into INEQR to represent images sized $$2^{n_{1}} \times 2^{n_{2}}$$2n1×2n2. Based on it, quantum circuits for image scaling using nearest neighbor interpolation from $$2^{n_{1}} \times 2^{n_{2}}$$2n1×2n2 to $$2^{m_{1}} \times 2^{m_{2}}$$2m1×2m2 are proposed. It is the first time to give the quantum image processing method that changes the size of an image. The quantum strategies developed in this paper initiate the research about quantum image scaling.
182 citations
Cites background or methods from "NEQR: a novel enhanced quantum repr..."
...Reference [3] gives methods for color inverse and image binarization....
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...Research in the field of QIP started with proposals on quantum image representations such as qubit lattice [1], FRQI [2], NEQR [3], QSMC & QSNC [4] and etc....
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...NEQR method that our circuits are based on is developed from FRQI [3]....
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TL;DR: Performance comparison with classical brute-force image registration method reveals that the proposed quantum algorithm can achieve a quartic speedup.
Abstract: The power of quantum mechanics has been extensively exploited to meet the high computational requirement of classical image processing. However, existing quantum image models can only represent the images sampled in Cartesian coordinates. In this paper, quantum log-polar image (QUALPI), a novel quantum image representation is proposed for the storage and processing of images sampled in log-polar coordinates. In QUALPI, all the pixels of a QUALPI are stored in a normalized superposition and can be operated on simultaneously. A QUALPI can be constructed from a classical image via a preparation whose complexity is approximately linear in the image size. Some common geometric transformations, such as symmetry transformation, rotation, etc., can be performed conveniently with QUALPI. Based on these geometric transformations, a fast rotation-invariant quantum image registration algorithm is designed for log-polar images. Performance comparison with classical brute-force image registration method reveals that our quantum algorithm can achieve a quartic speedup.
177 citations
Cites background from "NEQR: a novel enhanced quantum repr..."
...[14] improved FRQI and more complex color transformations could be performed based on the enhanced model....
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TL;DR: Two blind LSB steganography algorithms in the form of quantum circuits are proposed based on the novel enhanced quantum representation (NEQR) for quantum images which demonstrate that the invisibility is good, and the balance between the capacity and the robustness can be adjusted according to the needs of applications.
Abstract: Quantum steganography is the technique which hides a secret message into quantum covers such as quantum images. In this paper, two blind LSB steganography algorithms in the form of quantum circuits are proposed based on the novel enhanced quantum representation (NEQR) for quantum images. One algorithm is plain LSB which uses the message bits to substitute for the pixels’ LSB directly. The other is block LSB which embeds a message bit into a number of pixels that belong to one image block. The extracting circuits can regain the secret message only according to the stego cover. Analysis and simulation-based experimental results demonstrate that the invisibility is good, and the balance between the capacity and the robustness can be adjusted according to the needs of applications.
173 citations
References
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Book•
01 Jan 2000
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
Abstract: Part I Fundamental Concepts: 1 Introduction and overview 2 Introduction to quantum mechanics 3 Introduction to computer science Part II Quantum Computation: 4 Quantum circuits 5 The quantum Fourier transform and its application 6 Quantum search algorithms 7 Quantum computers: physical realization Part III Quantum Information: 8 Quantum noise and quantum operations 9 Distance measures for quantum information 10 Quantum error-correction 11 Entropy and information 12 Quantum information theory Appendices References Index
25,929 citations
TL;DR: This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing, with a focus on entanglement.
Abstract: This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing.
The first two papers deal with entanglement. The paper by R. Mosseri and P. Ribeiro presents a detailed description of the two-and three-qubit geometry in Hilbert space, dealing with the geometry of fibrations and discrete geometry. The paper by J.-G.Luque et al. is more algebraic and considers invariants of pure k-qubit states and their application to entanglement measurement.
14,205 citations
Additional excerpts
...As a novel computing model, quantum computation can store, process and transport information using the peculiar properties of quantum mechanics [1] such as the superposition and the entangled state....
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TL;DR: In this paper, the authors describe the possibility of simulating physics in the classical approximation, a thing which is usually described by local differential equations, and the possibility that there is to be an exact simulation, that the computer will do exactly the same as nature.
Abstract: This chapter describes the possibility of simulating physics in the classical approximation, a thing which is usually described by local differential equations. But the physical world is quantum mechanical, and therefore the proper problem is the simulation of quantum physics. A computer which will give the same probabilities as the quantum system does. The present theory of physics allows space to go down into infinitesimal distances, wavelengths to get infinitely great, terms to be summed in infinite order, and so forth; and therefore, if this proposition is right, physical law is wrong. Quantum theory and quantizing is a very specific type of theory. The chapter talks about the possibility that there is to be an exact simulation, that the computer will do exactly the same as nature. There are interesting philosophical questions about reasoning, and relationship, observation, and measurement and so on, which computers have stimulated people to think about anew, with new types of thinking.
7,202 citations
"NEQR: a novel enhanced quantum repr..." refers background in this paper
...Starting with Feynman who first proposed this concept in 1982 [2], quantum computation has become a hot topic....
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20 Nov 1994
TL;DR: Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored are given.
Abstract: A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a cost in computation time of at most a polynomial factor: It is not clear whether this is still true when quantum mechanics is taken into consideration. Several researchers, starting with David Deutsch, have developed models for quantum mechanical computers and have investigated their computational properties. This paper gives Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored. These two problems are generally considered hard on a classical computer and have been used as the basis of several proposed cryptosystems. We thus give the first examples of quantum cryptanalysis. >
6,961 citations
"NEQR: a novel enhanced quantum repr..." refers methods in this paper
...In particular, in 1994, Shor designed a quantum integer factoring algorithm [3] to find secret key encryption of the RSA algorithm (Rivest, Shamiv, and Adleman) in polynomial time....
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01 Jul 1996
TL;DR: In this paper, it was shown that a quantum mechanical computer can solve integer factorization problem in a finite power of O(log n) time, where n is the number of elements in a given integer.
Abstract: were proposed in the early 1980’s [Benioff80] and shown to be at least as powerful as classical computers an important but not surprising result, since classical computers, at the deepest level, ultimately follow the laws of quantum mechanics. The description of quantum mechanical computers was formalized in the late 80’s and early 90’s [Deutsch85][BB92] [BV93] [Yao93] and they were shown to be more powerful than classical computers on various specialized problems. In early 1994, [Shor94] demonstrated that a quantum mechanical computer could efficiently solve a well-known problem for which there was no known efficient algorithm using classical computers. This is the problem of integer factorization, i.e. testing whether or not a given integer, N, is prime, in a time which is a finite power of o (logN) . ----------------------------------------------
6,335 citations