Related papers: High-dimensional discrete Fourier transform gates …
In this paper, an algorithm for Quantum Inverse Fast Fourier Transform (QIFFT) is developed to work for quantum data. Analogous to a classical discrete signal, a quantum signal can be represented in Dirac notation, application of QIFFT is a…
The present chapter [submitted for publication in "Fourier Transforms, Theory and Applications", G. Nikolic (Ed.), InTech (Open Access Publisher), Vienna, 2011] is concerned with the introduction and study of a quadratic discrete Fourier…
A new method of quantum state tomography for quantum information processing is described. The method based on two-dimensional Fourier transform technique involves detection of all the off-diagonal elements of the density matrix in a…
Photons' frequency degree of freedom is promising to realize large-scale quantum information processing. Quantum frequency combs (QFCs) generated in integrated nonlinear microresonators can produce multiple frequency modes with narrow…
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…
Extremely large antenna arrays (ELAAs) operating in high-frequency bands have spurred the development of near-field communication, driving advancements in beam training design. This paper introduces an efficient near-field beam training…
The Phase Estimation Algorithm (PEA) is an important quantum algorithm used independently or as a key subroutine in other quantum algorithms. Currently most implementations of the PEA are based on qubits, where the computational units in…
A Discrete Fourier Transform Method (DFTM) for discrimination between the signal of neutrons and gamma rays in organic scintillation detectors is presented. The method is based on the transformation of signals into the frequency domain…
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…
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…
The one-dimensional (1D) fractional Fourier transform (FRFT) generalizes the Fourier transform, offering significant advantages in the time-frequency analysis of non-stationary signals. While various 2D extensions exist, such as the 2D…
A distributed quantum computing network requires a quantum communication channel between spatially separated processing units. In superconducting circuits, such a channel can be implemented based on propagating microwave photons to encode…
Quantum Key Distribution (QKD) protocols enable two distant parties to communicate with information-theoretically proven secrecy. However, these protocols are generally vulnerable to potential mismatches between the physical modeling and…
Realizing the theoretical promise of quantum computers will require overcoming decoherence. Here we demonstrate numerically that high fidelity quantum gates are possible within a framework of quantum dynamical decoupling. Orders of…
Photonic computing has emerged as a promising platform for accelerating computational tasks with high degrees of parallelism, such as image processing and neural network. We present meta-DFT (discrete Fourier transform), a single layer…
Density Functional Theory (DFT) is widely used for atomistic simulations. However, its reach stays limited due to several limitations such as lack of accurate exchange-correlation functional, requirement of costly O(N 3) diagonalization…
The 3D Discrete Fourier Transform (DFT) is a technique used to solve problems in disparate fields. Nowadays, the commonly adopted implementation of the 3D-DFT is derived from the Fast Fourier Transform (FFT) algorithm. However, evidence…
The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a…
The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…
This summary of the doctoral thesis provides a comprehensive formulation of the Extended Discrete Fourier Transform (EDFT), derived directly from the Fourier integral and its orthogonality properties. The method is obtained by solving…