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Implementing general functions of operators is a powerful tool in quantum computation. It can be used as the basis for a variety of quantum algorithms including matrix inversion, real and imaginary-time evolution, and matrix powers. Quantum…
The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions…
In this paper, an algorithm for Quantum Inverse Fast Fourier Transform (QIFFT) is developed to work for quantum data. Analogous to a classical discrete signal, a quantum signal can be represented in Dirac notation, application of QIFFT is a…
A practical and simple stable method for calculating Fourier integrals is proposed, effective both at low and at high frequencies. An approach based on the fruitful idea of Levin, to use of the collocation method to approximate the slowly…
The paper deals with a fractional derivative introduced by means of the Fourier transform. The explicit form of the kernel of general derivative operator acting on the functions analytic on a curve in complex plane is deduced and the…
An efficient numerical algorithm is presented for massively parallel simulations of dispersion-managed wavelength-division-multiplexed optical fiber systems. The algorithm is based on a weak nonlinearity approximation and independent…
Fourier representations play a central role in operator learning methods for partial differential equations and are increasingly being explored in quantum machine learning architectures. The classical fast Fourier transform (FFT),…
The fast algorithms in Fourier optics have invigorated multifunctional device design and advanced imaging technologies. However, the necessity for fast computations has led to limitations in the widely used conventional Fourier methods,…
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 need for wireless communication has driven the communication systems to high performance. However, the main bottleneck that affects the communication capability is the Fast Fourier Transform (FFT), which is the core of most modulators.…
The graph Fourier transform (GFT) is an important tool for graph signal processing, with applications ranging from graph-based image processing to spectral clustering. However, unlike the discrete Fourier transform, the GFT typically does…
An integrated photonic circuit architecture to perform a modified-convolution operation based on the Discrete Fractional Fourier Transform (DFrFT) is introduced. This is accomplished by utilizing two nonuniformly-coupled waveguide lattices…
This paper is concerned with developing an efficient numerical algorithm for fast implementation of the sparse grid method for computing the $d$-dimensional integral of a given function. The new algorithm, called the MDI-SG ({\em multilevel…
This study introduces a Fractional Order Fuzzy PID (FOFPID) controller that uses the Whale Optimization Algorithm (WOA) to manage the Bispectral Index (BIS), keeping it within the ideal range of forty to sixty. The FOFPID controller…
In this work, we extend Wigner's original framework to analyze linear operators by examining the relationship between their Wigner and Schwartz kernels. Our approach includes the introduction of (quasi-)algebras of Fourier integral…
The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier…
In this paper, we develop a Monte Carlo method for solving PDEs involving an integral fractional Laplacian (IFL) in multiple dimensions. We first construct a new Feynman-Kac representation based on the Green function for the fractional…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
This paper introduces a hierarchical interpolative decomposition butterfly-LU factorization (H-IDBF-LU) preconditioner for solving two-dimensional electric-field integral equations (EFIEs) in electromagnetic scattering problems of perfect…
The fuzzy integral is a powerful parametric nonlin-ear function with utility in a wide range of applications, from information fusion to classification, regression, decision making,interpolation, metrics, morphology, and beyond. While the…