Related papers: Quantum Pseudo-fractional Fourier Transform and it…
We present a new number theoretic definition of discrete fractional Fourier transform (DFrFT) . In this approach the DFrFT is defined as the $N \times N$ dimensional unitary representation of the generator of the arithmetic rotational group…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
We propose a quantum analogue of Bluestein's algorithm (QBA) that implements an exact $N$-point Quantum Fourier Transform (QFT) for arbitrary $N$. Our construction factors the $N$-dimensional QFT unitary into three diagonal quadratic-phase…
A nonparametric method is proposed for estimating the quantile spectra and cross-spectra introduced in Li (2012; 2014) as bivariate functions of frequency and quantile level. The method is based on the quantile discrete Fourier transform…
This paper is concerned with the phase estimation algorithm in quantum computing algorithms, especially the scenarios where (1) the input vector is not an eigenvector; (2) the unitary operator is not exactly implemented; (3) random…
The graph fractional Fourier transform (GFRFT) for unitary graph Fourier transform (GFT) matrices can be interpreted through the scalar function $e^{j\alpha\theta}$ on the unit circle. Under the principal branch, its Fourier-series…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
We present the detailed process of converting the classical Fourier Transform algorithm into the quantum one by using QR decomposition. This provides an example of a technique for building quantum algorithms using classical ones. The…
A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability…
Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…
In this paper, we mainly establish the uncertainty principle (UP) for a function and its quaternion Fractional Fourier transform (QFrFT), as well as the UP for two QFrFTs. Using the polar representation of quaternion-valued signals, we give…
Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, we pay special attention to the description of complex-data FFT. We analyze two common descriptions of…
The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…
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…
Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…
The short-time Fourier transform (STFT) usually computes the same number of frequency components as the frame length while overlapping adjacent time frames by more than half. As a result, the number of components of a spectrogram matrix…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
The Fractional Fourier Transform (FRT) corresponds to an arbitrary-angle rotation in the phase space, e.g. the time-frequency (TF) space, and generalizes the fundamentally important Fourier Transform. FRT applications range from classical…
In this research, we create a scalable version of the quantum Fourier transform-based arithmetic circuit to perform addition and subtraction operations on N n-bit unsigned integers encoded in quantum registers, and it is compatible with…
The Fast Fourier Transform (FFT) is a numerical operation that transforms a function into a form comprised of its constituent frequencies and is an integral part of scientific computation and data analysis. The objective of our work is to…