Related papers: An integral transform for quantum amplitudes
The integrals of motion of the classical two dimensional superintegrable systems with quadratic integrals of motion close in a restrained quadratic Poisson algebra, whose the general form is investigated. Each classical superintegrable…
We present a general methodology to obtain the basis of qudits which are admissible to Quantum Fourier Transform (QFT). We first study this method for qubits to characterize the ensemble that works for the Hadamard transformation (QFT for…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
Amplitude amplification is one of primary tools in building algorithms for quantum computers. This technique generalizes key ideas of the Grover search algorithm. Potentially useful modifications are connected with changing phases in the…
We analyse the Gaussian wave packet transform. Based on the Fourier inversion formula and a partition of unity, which is formed by a collection of Gaussian basis functions, a new representation of square-integrable functions is presented.…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
We present a branch-consistent framework for integrals involving quadratic radicals by expressing exponentials of principal inverse trigonometric functions in algebraic form. Two identities for $e^{\pm i\cos^{-1}(y)}$ and $e^{\pm…
A discrete path integral formalism is used to obtain the transition amplitude between 'sources' (slits and detector) in the twin-slit experiment of quantum mechanics. This method explicates the normally tacit construct of dynamic entities…
We present a quasi-analytic perturbation expansion for multivariate N-dimensional Gaussian integrals. The perturbation expansion is an infinite series of lower-dimensional integrals (one-dimensional in the simplest approximation). This…
We continue the study of the Hrushovski-Kazhdan integration theory and consider exponential integrals. The Grothendieck ring is enlarged via a tautological additive character and hence can receive such integrals. We then define the Fourier…
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…
We built up a explicit realization of (0+1)-dimensional q-deformed superspace coordinates as operators on standard superspace. A q-generalization of supersymmetric transformations is obtained, enabling us to introduce scalar superfields and…
We introduce a class of algorithms for constructing Fourier representations of Gaussian processes in $1$ dimension that are valid over ranges of hyperparameter values. The scaling and frequencies of the Fourier basis functions are evaluated…
Recently, it was found that a new set of simple techniques allow one to conveniently express ordinary integrals through differentiation. These techniques add to the general toolbox for integration and integral transforms such as the Fourier…
A q-version of the Fourier transformation and some of its properties are discussed.
It has been found empirically that quasi-Monte Carlo methods are often efficient for very high-dimensional problems, that is, with dimension in the hundreds or even thousands. The common explanation for this surprising fact is that those…
The notion of Fourier transform is among the more important tools in analysis, which has been generalized in abstract harmonic analysis to the level of abelian locally compact groups. The aim of this paper is to further generalize the…
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…
We improve on Fourier transforms (FT) between imaginary time $\tau$ and imaginary frequency $\omega_n$ used in certain quantum cluster approaches using the Hirsch-Fye method. The asymptotic behavior of the electron Green's function can be…
Wavelet transforms are widely used in various fields of science and engineering as a mathematical tool with features that reveal information ignored by the Fourier transform. Unlike the Fourier transform, which is unique, a wavelet…