Related papers: Quantum Fourier Transform Revisited
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 will present a few new generalizations of the multi-controlled X (MCX) gate that uses the quantum Fourier transform (QFT). Firstly, we will optimize QFT-MCX and prove that it is equivalent to a stair MCX gates array. This stair-wise…
The convolution potential arises in a wide variety of application areas, and its efficient and accurate evaluation encounters three challenges: singularity, nonlocality and anisotropy. We introduce a fast algorithm based on a far-field…
In this paper, we reduce the computational complexities of partial and dual partial cyclotomic FFTs (CFFTs), which are discrete Fourier transforms where spectral and temporal components are constrained, based on their properties as well as…
In the field of digital signal processing, the fast Fourier transform (FFT) is a fundamental algorithm, with its processors being implemented using either the pipelined architecture, well-known for high-throughput applications but weak in…
Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…
Applying quantum computing in the computer-aided engineering (CAE) problems are highly expected since quantum computers yield potential exponential speedups for the operations between extremely large matrices and vectors. Although efficient…
Although Fourier series approximation is ubiquitous in computational physics owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for the fast evaluation of a three-dimensional truncated Fourier series at a set of…
Algorithms for processing data in short-time batches are critical for both online and offline processing of streamed and large data respectively due to the quadratic relation between signal length and computational cost of convolution-based…
This paper develops fast graph Fourier transform (GFT) algorithms with O(n log n) runtime complexity for rank-one updates of the path graph. We first show that several commonly-used audio and video coding transforms belong to this class of…
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…
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…
Rapid development in quantum computing leads to the appearance of several quantum applications. Quantum Fourier Transformation (QFT) sits at the heart of many of these applications. Existing work leverages SAT solver or heuristics to…
Due to recent technological advances, actual quantum devices are being constructed and used to perform computations. As a result, many classical problems are being restated so as to be solved on quantum computers. Some examples include…
Truncated Fourier Transforms (TFTs), first introduced by Van der Hoeven, refer to a family of algorithms that attempt to smooth "jumps" in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in…
Finite-element (FE) discretisations have emerged as a powerful real-space alternative to large-scale Kohn-Sham density functional theory (DFT) calculations, offering systematic convergence, excellent parallel scalability, while…
The quantum Fourier transform (QFT) is sometimes said to be the source of various exponential quantum speed-ups. In this paper we introduce a class of quantum circuits which cannot outperform classical computers even though the QFT…
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…
The linear canonical transform (LCT) serves as a powerful generalization of the Fourier transform (FT), encapsulating various integral transforms within a unified framework. This versatility has made it a cornerstone in fields such as…
Quantum computers are known to be qualitatively more powerful than classical computers, but so far only a small number of different algorithms have been discovered that actually use this potential. It would therefore be highly desirable to…