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Deep learning (DL) has recently changed the development of intelligent systems and is widely adopted in many real-life applications. Despite their various benefits and potentials, there is a high demand for DL processing in different computationally limited and energy-constrained devices. It is natural to study game-changing technologies such as Binary Neural Networks (BNN) to increase DL capabilities. Recently remarkable progress has been made in BNN since they can be implemented and embedded on tiny restricted devices and save a significant amount of storage, computation cost, and energy consumption. However, nearly all BNN acts trade with extra memory, computation cost, and higher performance. This article provides a complete overview of recent developments in BNN. This article focuses exclusively on 1-bit activations and weights 1-bit convolution networks, contrary to previous surveys in which low-bit works are mixed in. It conducted a complete investigation of BNN's development—from their predecessors to the latest BNN algorithms/techniques, presenting a broad design pipeline and discussing each module's variants. Along the way, it examines BNN (a) purpose: their early successes and challenges; (b) BNN optimization: selected representative works that contain essential optimization techniques; (c) deployment: open-source frameworks for BNN modeling and development; (d) terminal: efficient computing architectures and devices for BNN and (e) applications: diverse applications with BNN. Moreover, this paper discusses potential directions and future research opportunities in each section. [ABSTRACT FROM AUTHOR]

Quantum computing algorithms offer the potential to revolutionize computational efficiency across a wide range of applications. However, one significant challenge that has impeded progress in color image processing is the difficulty of representing color relationships in quantum computers. In addition to this challenge, another major hurdle is efficiently representing data in quantum computers and performing quantum operations or arithmetic. To overcome these challenges, researchers have proposed various novel approaches, including using qubit lattices and flexible representations of quantum images. Despite these advancements, the quantum color image processing field is still in its early stages. This paper proposes a new arithmetic for processing quantum color images using novel operations for 2-qubits and the concept of quantum quaternion Fourier transform. We first study arithmetic operations in the 2-qubit setting, such as multiplication, inverse, and division on 2-qubits in quantum computation. The space of 2-qubits with real amplitudes is considered, and prototypes of power and exponent operations are also defined. The presented operations are applied to quantum superpositions of 2-qubits, to enable processing of quaternion images, which are 4-dimensional vectors and can be represented by 2-qubits at each pixel. The proposed methods and tools are designed to be embedded in a quantum device, which allows them to be used in various applications in the 2-qubits domain. To facilitate practical applications, the paper also introduces a tool for processing color images that can be used for color image filtering. Furthermore, this work provides a foundation to explore theoretical and practical aspects of color image processing on quantum computers. [ABSTRACT FROM AUTHOR]

This paper defines an operation of multiplication of qubits and describes a subspace of multi-qubit superpositions on which this operation can be applied. In this subspace of superpositions, we describe the operation of quantum convolution using the Fourier transform. The multiplicative group of qubits is described with inverse operations and division of qubits. Since the quantum superpositions require the normalization of amplitudes of the basis states, all these operations are operations composed of Givens rotations. Examples of the ideal low-pass and high-pass filters over the quantum signals described by such superpositions are given. Also, we describe qubit quadratic equations and solutions with an example. [ABSTRACT FROM AUTHOR]

Various methods of representation of signals exist in quantum computation, but it is essential to select the representations which allow to perform the operations, transforms, and methods which are widely used in classical signal processing. In this work, we analyse the quantum representation of one-dimensional signals, which is called the Fourier transform quantum representation (FTQR). This representation describes the signal as the superposition of states with amplitudes lying on the unit circle. The same is for two-dimensional signals or images in grays and colors. The tensor product of FTQRs is described, and examples are given for simple operations on discrete-time signals, such as the sum of signals, parallel addition of a few constants to the signal, and time-scaling. All these operations are performed in the phases of qubits in the Fourier transform quantum representation. [ABSTRACT FROM AUTHOR]

Image representation plays an essential role in quantum image processing and quantum computer vision in numerous, computationally expensive applications. Quantum image processing is a new discipline with tremendous potential. However, there is a critical problem in applying quantum computing to process data: how to represent data (signal, image, and video data) using quantum states without losing information. In this paper, we describe briefly a few known models for image representation and propose a new approach for representing discrete signals and images in quantum computing, by mapping the input data into the unit circle, or only part of the circle. Such a representation allows for introducing the concept of the Fourier transform qubit representation. For grayscale images, we consider the similar concept of the Fourier representation of images and, for color images, we introduce models with the concept of the 3-point DFT of color qubits. The circuits for proposed signal and image representations are described. [ABSTRACT FROM AUTHOR]

The quantum Fourier transform (QFT) is perhaps the furthermost central building block in creation quantum algorithms. In this work, we present a new approach to compute the standard quantum Fourier transform of the length N = 2 r , r > 1 , which also is called the r-qubit discrete Fourier transform. The presented algorithm is based on the paired transform developed by authors. It is shown that the signal-flow graphs of the paired algorithms could be used for calculating the quantum Fourier and Hadamard transform with the minimum number of stages. The calculation of all components of the transforms is performed by the Hadamard gates and matrices of rotations and all simple NOT gates. The new presentation allows for implementing the QFT (a) by using only the r Hadamard gates and (b) organizing parallel computation in r stages. Also, the circuits for the length-2r fast Hadamard transform are described. Several mathematical illustrative examples of the order the N = 4 , 8 , and 16 cases are illustrated. Finally, the QFT for inputs being two, three and four qubits is described in detail. [ABSTRACT FROM AUTHOR]