Related papers: On semifast Fourier transform algorithms
Fast multidimensional convolution can be performed naively in quadratic time and can often be performed more efficiently via the Fourier transform; however, when the dimensionality is large, these algorithms become more challenging. A…
Semisort is a fundamental algorithmic primitive widely used in the design and analysis of efficient parallel algorithms. It takes input as an array of records and a function extracting a \emph{key} per record, and reorders them so that…
Quantum computers provide a super-exponential speedup for performing a Fourier transform over the symmetric group, an ability for which practical use cases have remained elusive so far. In this work, we leverage this ability to unlock…
The spectral analysis of the Fourier operator truncated on the positive half-axis is done
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from…
The quantum Fourier transform (QFT) has been implemented on a three bit nuclear magnetic resonance (NMR) quantum computer, providing a first step towards the realization of Shor's factoring and other quantum algorithms. Implementation of…
The spectral analysis of the operator Fourier truncated on the positive half-axis is done.
We present a historiographical review of algorithms and computer codes developed for solving integration-by-parts relations for Feynman integrals. This procedure is one of the key steps in the evaluation of Feynman integrals, since it…
In this paper, we introduce an algorithm that provides approximate solutions to semi-linear ordinary differential equations with highly oscillatory solutions, which, after an appropriate change of variables, can be rewritten as…
We consider the problem of approximating two, possibly unrelated probability distributions from a single complex-valued function $\psi$ and its Fourier transform. We show that this problem always has a solution within a specified degree of…
We give some new characterizations of almost weak Dunford-Pettis operators and we investigate their relationship with weak Dunford-Pettis operators.
This paper proposes a class of power-of-two FFT (Fast Fourier Transform) algorithms, called AM-QFT algorithms, that contains the improved QFT (Quick Fourier Transform), an algorithm recently published, as a special case. The main idea is to…
Pseudo-spectral method is one of the most accurate techniques for simulating turbulent flows. Fast Fourier transform (FFT) is an integral part of this method. In this paper, we present a new procedure to compute FFT in which we save…
The plane wave method is most widely used for solving the Kohn-Sham equations in first-principles materials science computations. In this procedure, the three-dimensional (3-dim) trial wave functions' fast Fourier transform (FFT) is a…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
We consider a hybrid quantum system consisting of a qubit system continuously evolving according to its fixed own Hamiltonian and a quantum computer. The qubit system couples to a quantum computer through a fixed interaction Hamiltonian,…
We present an algorithm to find invariant poynomial transformations of integer sequences, using the classical invariant theory approach.
Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a…
We construct connections on $S^1$-equivariant Hamiltonian Floer cohomology, which differentiate with respect to certain formal parameters.
We introduce an algebra $\mathcal H$ consisting of difference-reflection operators and multiplication operators that can be considered as a $q=1$ analogue of Sahi's double affine Hecke algebra related to the affine root system of type…