Related papers: Non-Uniform Quantum Fourier Transform
The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…
Density-functional theory (DFT) has revolutionized computational prediction of atomic-scale properties from first principles in physics, chemistry and materials science. Continuing development of new methods is necessary for accurate…
We discuss the advantages of using the approximate quantum Fourier transform (AQFT) in algorithms which involve periodicity estimations. We analyse quantum networks performing AQFT in the presence of decoherence and show that extensive…
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…
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…
Deep learning has delivered its powerfulness in many application domains, especially in image and speech recognition. As the backbone of deep learning, deep neural networks (DNNs) consist of multiple layers of various types with hundreds to…
We prove that the theorems of TDDFT can be applied to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used…
The standard particle-in-cell algorithm suffers from grid heating. There exists a gridless alternative which bypasses the deposition step and calculates each Fourier mode of the charge density directly from the particle positions. We show…
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…
Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal inherent…
Scalable quantum computing requires architectural solutions beyond monolithic processors. Distributed quantum computing (DQC) addresses this challenge by interconnecting smaller quantum nodes through quantum communication protocols,…
Conventional inversion of the discrete Fourier transform (DFT) requires all DFT coefficients to be known. When the DFT coefficients of a rasterized image (represented as a matrix) are known only within a pass band, the original matrix…
Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal inherent…
Orbital-free density functional theory (OFDFT) is a quantum chemistry formulation that has a lower cost scaling than the prevailing Kohn-Sham DFT, which is increasingly desired for contemporary molecular research. However, its accuracy is…
This paper introduces a novel approach to implementing non-unitary linear transformations of basis on quantum computational platforms, a significant leap beyond the conventional unitary methods. By integrating Singular Value Decomposition…
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…
Conventional mutual information (MI) based feature selection (FS) methods are unable to handle heterogeneous feature subset selection properly because of data format differences or estimation methods of MI between feature subset and class…
We present a novel algorithm, named the 2D-FFAST, to compute a sparse 2D-Discrete Fourier Transform (2D-DFT) featuring both low sample complexity and low computational complexity. The proposed algorithm is based on mixed concepts from…
The explicit analytical expression of the Nonlinear Fourier Transform (NFT) of a finite set of data is provided. Then a simple recursion relation for the NFT is constructed as a function of the spectral parameter. These tools provide a…
Diffuse scattering is a rich source of information about disorder in crystalline materials, which can be modelled using atomistic techniques such as Monte Carlo and molecular dynamics simulations. Modern X-ray and neutron scattering…