Quantum image processing (QIMP) is using quantum computing or quantum information processing to create and work with quantum images. [1] [2]
Due to some of the properties inherent to quantum computation, notably entanglement and parallelism, it is hoped that QIMP technologies will offer capabilities and performances that surpass their traditional equivalents, in terms of computing speed, security, and minimum storage requirements. [2] [3]
A. Y. Vlasov's work [4] in 1997 focused on using a quantum system to recognize orthogonal images. This was followed by efforts using quantum algorithms to search specific patterns in binary images [5] and detect the posture of certain targets. [6] Notably, more optics-based interpretations for quantum imaging were initially experimentally demonstrated in [7] and formalized in [8] after seven years.
In 2003, Salvador Venegas-Andraca and S. Bose presented Qubit Lattice, the first published general model for storing, processing and retrieving images using quantum systems. [9] [10] Later on, in 2005, Latorre proposed another kind of representation, called the Real Ket, [11] whose purpose was to encode quantum images as a basis for further applications in QIMP. Furthermore, in 2010 Venegas-Andraca and Ball presented a method for storing and retrieving binary geometrical shapes in quantum mechanical systems in which it is shown that maximally entangled qubits can be used to reconstruct images without using any additional information. [12]
Technically, these pioneering efforts with the subsequent studies related to them can be classified into three main groups: [3]
A survey of quantum image representation has been published in. [14] Furthermore, the recently published book Quantum Image Processing [15] provides a comprehensive introduction to quantum image processing, which focuses on extending conventional image processing tasks to the quantum computing frameworks. It summarizes the available quantum image representations and their operations, reviews the possible quantum image applications and their implementation, and discusses the open questions and future development trends.
A lot of the effort in QIMP has been focused on designing algorithms to manipulate the position and color information encoded using flexible representation of quantum images (FRQI) and its many variants. For instance, FRQI-based fast geometric transformations including (two-point) swapping, flip, (orthogonal) rotations [16] and restricted geometric transformations to constrain these operations to a specified area of an image [17] were initially proposed. Recently, NEQR-based quantum image translation to map the position of each picture element in an input image into a new position in an output image [18] and quantum image scaling to resize a quantum image [19] were discussed. While FRQI-based general form of color transformations were first proposed by means of the single qubit gates such as X, Z, and H gates. [20] Later, Multi-Channel Quantum Image-based channel of interest (CoI) operator to entail shifting the grayscale value of the preselected color channel and the channel swapping (CS) operator to swap the grayscale values between two channels have been fully discussed. [21]
To illustrate the feasibility and capability of QIMP algorithms and application, researchers always prefer to simulate the digital image processing tasks on the basis of the QIRs that we already have. By using the basic quantum gates and the aforementioned operations, so far, researchers have contributed to quantum image feature extraction, [22] quantum image segmentation, [23] quantum image morphology, [24] quantum image comparison, [25] quantum image filtering, [26] quantum image classification, [27] quantum image stabilization, [28] among others. In particular, QIMP-based security technologies have attracted extensive interest of researchers as presented in the ensuing discussions. Similarly, these advancements have led to many applications in the areas of watermarking, [29] [30] [31] encryption, [32] and steganography [33] etc., which form the core security technologies highlighted in this area.
In general, the work pursued by the researchers in this area are focused on expanding the applicability of QIMP to realize more classical-like digital image processing algorithms; propose technologies to physically realize the QIMP hardware; or simply to note the likely challenges that could impede the realization of some QIMP protocols.
By encoding and processing the image information in quantum-mechanical systems, a framework of quantum image processing is presented, where a pure quantum state encodes the image information: to encode the pixel values in the probability amplitudes and the pixel positions in the computational basis states.
Given an image , where represents the pixel value at position with and , a vector with elements can be formed by letting the first elements of be the first column of , the next elements the second column, etc.
A large class of image operations is linear, e.g., unitary transformations, convolutions, and linear filtering. In the quantum computing, the linear transformation can be represented as with the input image state and the output image state . A unitary transformation can be implemented as a unitary evolution. Some basic and commonly used image transforms (e.g., the Fourier, Hadamard, and Haar wavelet transforms) can be expressed in the form , with the resulting image and a row (column) transform matrix .
The corresponding unitary operator can then be written as . Several commonly used two-dimensional image transforms, such as the Haar wavelet, Fourier, and Hadamard transforms, are experimentally demonstrated on a quantum computer, [34] with exponential speedup over their classical counterparts. In addition, a novel highly efficient quantum algorithm is proposed and experimentally implemented for detecting the boundary between different regions of a picture: It requires only one single-qubit gate in the processing stage, independent of the size of the picture.
A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior using specialized hardware. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer. In particular, a large-scale quantum computer could break widely used encryption schemes and aid physicists in performing physical simulations; however, the current state of the art is largely experimental and impractical, with several obstacles to useful applications.
Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of Von Neumann entropy and the general computational term.
Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. It is one of the few known quantum algorithms with compelling potential applications and strong evidence of superpolynomial speedup compared to best known classical (non-quantum) algorithms. On the other hand, factoring numbers of practical significance requires far more qubits than available in the near future. Another concern is that noise in quantum circuits may undermine results, requiring additional qubits for quantum error correction.
In logic circuits, the Toffoli gate, also known as the CCNOT gate (“controlled-controlled-not”), invented by Tommaso Toffoli, is a CNOT gate with two control qubits and one target qubit. That is, the target qubit will be inverted if the first and second qubits are both 1. It is a universal reversible logic gate, which means that any classical reversible circuit can be constructed from Toffoli gates. Formally, we describe the Toffoli gate with the following truth table and matrix:
The Hadamard transform is an example of a generalized class of Fourier transforms. It performs an orthogonal, symmetric, involutive, linear operation on 2m real numbers.
A trapped-ion quantum computer is one proposed approach to a large-scale quantum computer. Ions, or charged atomic particles, can be confined and suspended in free space using electromagnetic fields. Qubits are stored in stable electronic states of each ion, and quantum information can be transferred through the collective quantized motion of the ions in a shared trap. Lasers are applied to induce coupling between the qubit states or coupling between the internal qubit states and the external motional states.
Quantum neural networks are computational neural network models which are based on the principles of quantum mechanics. The first ideas on quantum neural computation were published independently in 1995 by Subhash Kak and Ron Chrisley, engaging with the theory of quantum mind, which posits that quantum effects play a role in cognitive function. However, typical research in quantum neural networks involves combining classical artificial neural network models with the advantages of quantum information in order to develop more efficient algorithms. One important motivation for these investigations is the difficulty to train classical neural networks, especially in big data applications. The hope is that features of quantum computing such as quantum parallelism or the effects of interference and entanglement can be used as resources. Since the technological implementation of a quantum computer is still in a premature stage, such quantum neural network models are mostly theoretical proposals that await their full implementation in physical experiments.
Quantum annealing (QA) is an optimization process for finding the global minimum of a given objective function over a given set of candidate solutions, by a process using quantum fluctuations. Quantum annealing is used mainly for problems where the search space is discrete with many local minima; such as finding the ground state of a spin glass or the traveling salesman problem. The term "quantum annealing" was first proposed in 1988 by B. Apolloni, N. Cesa Bianchi and D. De Falco as a quantum-inspired classical algorithm. It was formulated in its present form by T. Kadowaki and H. Nishimori in 1998 though an imaginary-time variant without quantum coherence had been discussed by A. B. Finnila, M. A. Gomez, C. Sebenik and J. D. Doll in 1994.
Quantum walks are quantum analogs of classical random walks. In contrast to the classical random walk, where the walker occupies definite states and the randomness arises due to stochastic transitions between states, in quantum walks randomness arises through (1) quantum superposition of states, (2) non-random, reversible unitary evolution and (3) collapse of the wave function due to state measurements.
Adiabatic quantum computation (AQC) is a form of quantum computing which relies on the adiabatic theorem to perform calculations and is closely related to quantum annealing.
Quantum block codes are useful in quantum computing and in quantum communications. The encoding circuit for a large block code typically has a high complexity although those for modern codes do have lower complexity.
Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks. The best known example of quantum cryptography is quantum key distribution, which offers an information-theoretically secure solution to the key exchange problem. The advantage of quantum cryptography lies in the fact that it allows the completion of various cryptographic tasks that are proven or conjectured to be impossible using only classical communication. For example, it is impossible to copy data encoded in a quantum state. If one attempts to read the encoded data, the quantum state will be changed due to wave function collapse. This could be used to detect eavesdropping in quantum key distribution (QKD).
In quantum computing, the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. The quantum Fourier transform is a part of many quantum algorithms, notably Shor's algorithm for factoring and computing the discrete logarithm, the quantum phase estimation algorithm for estimating the eigenvalues of a unitary operator, and algorithms for the hidden subgroup problem. The quantum Fourier transform was discovered by Don Coppersmith. With small modifications to the QFT, it can also be used for performing fast integer arithmetic operations such as addition and multiplication.
Quantum machine learning is the integration of quantum algorithms within machine learning programs.
Andrew MacGregor Childs is an American computer scientist and physicist known for his work on quantum computing. He is currently a professor in the department of computer science and Institute for Advanced Computer Studies at the University of Maryland. He also co-directs the Joint Center for Quantum Information and Computer Science, a partnership between the University of Maryland and the National Institute of Standards and Technology.
IBM Quantum Platform is an online platform allowing public and premium access to cloud-based quantum computing services provided by IBM. This includes access to a set of IBM's prototype quantum processors, a set of tutorials on quantum computation, and access to an interactive textbook. As of February 2021, there are over 20 devices on the service, six of which are freely available for the public. This service can be used to run algorithms and experiments, and explore tutorials and simulations around what might be possible with quantum computing.
Continuous-variable (CV) quantum information is the area of quantum information science that makes use of physical observables, like the strength of an electromagnetic field, whose numerical values belong to continuous intervals. One primary application is quantum computing. In a sense, continuous-variable quantum computation is "analog", while quantum computation using qubits is "digital." In more technical terms, the former makes use of Hilbert spaces that are infinite-dimensional, while the Hilbert spaces for systems comprising collections of qubits are finite-dimensional. One motivation for studying continuous-variable quantum computation is to understand what resources are necessary to make quantum computers more powerful than classical ones.
This glossary of quantum computing is a list of definitions of terms and concepts used in quantum computing, its sub-disciplines, and related fields.
Jingbo Wang is an Australian quantum physicist working in the area of quantum simulation, quantum algorithms, and quantum information science.
In the context of quantum computing, the quantum walk search is a quantum algorithm for finding a marked node in a graph.
{{cite journal}}
: Cite journal requires |journal=
(help){{cite book}}
: |journal=
ignored (help){{cite journal}}
: Cite journal requires |journal=
(help)