Related papers: Quantum Inverse Fast Fourier Transform
In this work, we present the \emph{twiddless fast Fourier transform (TFFT)}, a novel algorithm for computing the $N$-point discrete Fourier transform (DFT). The TFFT's divide strategy builds on recent results that decimate an $N$-point…
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…
Simulating quantum dynamics is expected to be performed more easily on a quantum computer than on a classical computer. However, the currently available quantum devices lack the capability to implement fault-tolerant quantum algorithms for…
The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper…
It is an open question how fast information processing can be performed and whether quantum effects can speed up the best existing solutions. Signal extraction, analysis and compression in diagnostics, astronomy, chemistry and broadcasting…
Quantum walks (QWs) are of interest as examples of uniquely quantum behavior and are applicable in a variety of quantum search and simulation models. Implementing QWs on quantum devices is useful from both points of view. We describe a…
Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…
We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with $P$ the Markov chain transition…
The quantum Fourier transform (QFT) is a key primitive for quantum computing that is typically used as a subroutine within a larger computation, for instance for phase estimation. As such, we may have little control over the state that is…
The quantum Fourier transform (QFT) has emerged as the primary tool in quantum algorithms which achieve exponential advantage over classical computation and lies at the heart of the solution to the abelian hidden subgroup problem, of which…
The nonlinear Fourier transform (NLFT) extends the classical Fourier transform by replacing addition with matrix multiplication. While the NLFT on $\mathrm{SU}(1,1)$ has been widely studied, its $\mathrm{SU}(2)$ variant has only recently…
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…
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),…
In this note we describe a simple and intriguing observation: the quantum Fourier transform (QFT) over $Z_q$, which is considered the most ``quantum'' part of Shor's algorithm, can in fact be simulated efficiently by classical computers.…
Digital Transforms have important applications on subjects such as channel coding, cryptography and digital signal processing. In this paper, two Fourier Transforms are considered, the discrete time Fourier transform (DTFT) and the finite…
Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the…
The Hilbert transform has been one of the foundational transforms in signal processing, finding it's way into multiple disciplines from cryptography to biomedical sciences. However, there does not exist any quantum analogue for the Hilbert…
To overcome the difficulty of realizing large-scale quantum Fourier transform (QFT) within existing technology, this paper presents a resource-saving method, namely t-bit semiclassical QFT over (Z_(2^n)), which could realize large-scale QFT…
Molecular spin qudits based on lanthanide complexes offer a promising platform for quantum technologies, combining chemical tunability with multi-level encoding. However, experimental demonstrations of their envisaged capabilities remain…
We present a quantum Viterbi algorithm (QVA) with better than classical performance under certain conditions. In this paper the proposed algorithm is applied to decoding classical convolutional codes, for instance; large constraint length…