Related papers: Multiplication with Fourier Optics Simulating 16-b…
A new method for computing sums on a quantum computer is introduced. This technique uses the quantum Fourier transform and reduces the number of qubits necessary for addition by removing the need for temporary carry bits. This approach also…
This study introduces a short-time Fourier transform-based method for reconstructing signals encoded using modulo analog-to-digital converters with 1-bit folding information. In contrast to existing Fourier-based reconstruction approaches…
Truncated Fourier, Gauss, Kummer and exponential sums can be used to factorize numbers: for a factor these sums equal unity in absolute value, whereas they nearly vanish for any other number. We show how this factorization algorithm can…
The development of large-scale, programmable photonic circuits capable of performing generic matrix-vector multiplication is essential for both classical and quantum information processing. However, this goal is hindered by high losses,…
Based on diffraction theory and the propagation of the light, Fourier optics is a powerful tool allowing the estimation of a visible-range imaging system to transfer the spatial frequency components of an object. The analyses of the imaging…
We present a method to efficiently multiply or divide the orbital angular momentum (OAM) of light beams using a sequence of two optical elements. The key-element is represented by an optical transformation mapping the azimuthal phase…
A general principle says that the matrix of a Fourier integral operator with respect to wave packets is concentrated near the curve of propagation. We prove a precise version of this principle for Fourier integral operators with a smooth…
One of the major promises of quantum computing is the realization of SIMD (single instruction - multiple data) operations using the phenomenon of superposition. Since the dimension of the state space grows exponentially with the number of…
The modular multiplication operator, a central subroutine in Shor's factoring algorithm, is shown to be a coherent superposition of two quantum bakers maps when the multiplier is 2. The classical limit of the maps being completely chaotic,…
Multiplier circuits play an important role in reversible computation, which is helpful in diverse areas such as low power CMOS design, optical computing, DNA computing and bioinformatics. Here we propose a new reversible multiplier circuit…
One of the main advantages of an optical approach to quantum computing is the fact that optical fibers can be used to connect the logic and memory devices to form useful circuits, in analogy with the wires of a conventional computer. Here…
Diffractive optical elements that divide an input beam into a set of replicas are used in many optical applications ranging from image processing to communications. Their design requires time-consuming optimization processes, which, for a…
The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more…
This paper introduces quantum circuit methodologies for pointwise multiplication and convolution of complex functions, conceptualized as "processing through encoding". Leveraging known techniques, we describe an approach where multiple…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
The Fourier transform operation is an important conceptual as well as computational tool in the arsenal of every practitioner of physical and mathematical sciences. We discuss some of its applications in optical science and engineering,…
Floating point multiplication is one of the crucial operations in many application domains such as image processing, signal processing etc. But every application requires different working features. Some need high precision, some need low…
The derivation of a function is a fundamental tool for solving problems in calculus. Consequently, the motivations for investigating physical systems capable of performing this task are numerous. Furthermore, the potential to develop an…
Let (G, V) be a prehomogeneous vector space, let O be any G(F_q)-invariant subset of V(F_q), and let f be the characteristic function of O. In this paper we develop a method for explicitly and efficiently evaluating the Fourier transform of…