相关论文: Quantum Discrete Fourier Transform with Classical …

We examine the performance profile of Convolutional Neural Network training on the current generation of NVIDIA Graphics Processing Units. We introduce two new Fast Fourier Transform convolution implementations: one based on NVIDIA's cuFFT…

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…

Quantum key distribution (QKD) and quantum message encryption protocols promise a secure way to distribute information while detecting eavesdropping. However, current protocols may suffer from significantly reduced eavesdropping protection…

We explore a new form of DFT, which we call the Polynomial Transform. It functions over finite fields, and a size $n$ transform takes $O(n)$ operations. In the multitape Turing machine model, it allows us to multiply two $n$ bit numbers in…

Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. In deep-space optical communications, current receivers for the…

2D Convolutional neural network (CNN) has arguably become the de facto standard for computer vision tasks. Recent findings, however, suggest that CNN may not be the best option for 1D pattern recognition, especially for datasets with over 1…

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…

The notion of fractional Fourier transform (FrFT) has been used and investigated for many years by various research communities, which finds widespread applications in many diverse fields of research study. The potential applications…

Graph signal processing (GSP) facilitates the analysis of high-dimensional data on non-Euclidean domains by utilizing graph signals defined on graph vertices. In addition to static data, each vertex can provide continuous time-series…

We give an new arithmetic algorithm to compute the generalized Discrete Fourier Transform (DFT) over finite groups $G$. The new algorithm uses $O(|G|^{\omega/2 + o(1)})$ operations to compute the generalized DFT over finite groups of Lie…

This work introduces a relative diffusion transformation (RDT) - a simple unitary transformation which acts in a subspace, localized by an oracle. Such a transformation can not be fulfilled on quantum Turing machines with this oracle in…

The fast Fourier transform (FFT) is a primitive kernel in numerous fields of science and engineering. OpenFFT is an open-source parallel package for 3-D FFTs, built on a communication-optimal domain decomposition method for achieving…

The nonuniform fast Fourier transform (NUFFT) generalizes the FFT to off-grid data. Its many applications include image reconstruction, data analysis, and the numerical solution of differential equations. We present FINUFFT, an efficient…

Recently, video classification attracts intensive research efforts. However, most existing works are based on framelevel visual features, which might fail to model the temporal information, e.g. characteristics accumulated along time. In…

The (inverse) discrete Fourier transform (DFT/IDFT) is often perceived as essential to orthogonal frequency-division multiplexing (OFDM) systems. In this paper, a deep complex-valued convolutional network (DCCN) is developed to recover bits…

Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a…

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…

Quantum information processing and its subfield, quantum image processing, are rapidly growing fields as a result of advancements in the practicality of quantum mechanics. In this paper, we propose a quantum algorithm for processing…

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) are powerful techniques for the development of quantum procedures. They allow to derive circuits preparing desired polynomial transformations. Recent research…

Density functional theory (DFT) has emerged as one of the most versatile and lucrative approaches in electronic structure calculations of many-electron systems in past four decades. Here we give an account of the development of a…