Related papers: A Discrete Fourier Transform on Lattices with Quan…
We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density…
The efficient multiangle centered discrete fractional Fourier transform (MA-CDFRFT) [1] has proven to be a useful tool for time-frequency analysis; in this paper, we generalize the MA-CDFRFT to general M -periodic transforms, which, among…
It is demonstrated is this letter that linear multistep methods for integrating ordinary differential equations can be used to develop a family of fast forward scattering algorithms with higher orders of convergence. Excluding the cost of…
Density functional theory is a successful branch of numerical simulations of quantum systems. While the foundations are rigorously defined, the universal functional must be approximated resulting in a `semi'-ab initio approach. The search…
We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…
Deep-learning density functional theory (DFT) shows great promise to significantly accelerate material discovery and potentially revolutionize materials research. However, current research in this field primarily relies on data-driven…
This paper is devoted to the efficient numerical solution of the Helmholtz equation in a two- or three-dimensional rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and…
Modulated symmetries are internal symmetries that are not invariant under spacetime symmetry actions. We propose a general way to describe the lattice translation modulated symmetries in 1+1D, including the non-invertible ones, via the…
Efficient sampling from un-normalized target distributions is pivotal in scientific computing and machine learning. While neural samplers have demonstrated potential with a special emphasis on sampling efficiency, existing neural implicit…
We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…
The quantum Fourier transform (QFT), a quantum analog of the classical Fourier transform, has been shown to be a powerful tool in developing quantum algorithms. However, in classical computing there is another class of unitary transforms,…
Discrete trigonometric transformations, such as the discrete Fourier and cosine/sine transforms, are important in a variety of applications due to their useful properties. For example, one well-known property is the convolution theorem for…
We present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite group. By extending work which connects Bratteli diagrams to the construction of Fast…
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…
Density functional theory (DFT) stands as a cornerstone method in computational quantum chemistry and materials science due to its remarkable versatility and scalability. Yet, it suffers from limitations in accuracy, particularly when…
The Quaternion Fourier transform (QFT) is one of the key tools in studying color image processing. Indeed, a deep understanding of the QFT has created the color images to be transformed as whole, rather than as color separated component. In…
Discriminating data classes emanating from sensors is an important problem with many applications in science and technology. We describe a new transform for pattern identification that interprets patterns as probability density functions,…
We present an asymptotically improved algorithm for implementing the Quantum Fourier Transform (QFT) in both the exact and approximate settings. Historically, the approximate QFT has been implemented in $\Theta(n \log n)$ gates, and the…
We propose a new class of linear Transformers called FourierLearner-Transformers (FLTs), which incorporate a wide range of relative positional encoding mechanisms (RPEs). These include regular RPE techniques applied for sequential data, as…
The graph Fourier transform (GFT) is an important tool for graph signal processing, with applications ranging from graph-based image processing to spectral clustering. However, unlike the discrete Fourier transform, the GFT typically does…