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Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…
The number of parameters in deep neural networks (DNNs) is rapidly increasing to support complicated tasks and to improve model accuracy. Correspondingly, the amount of computations and required memory footprint increase as well.…
We study scattering by a high aspect ratio particle using boundary integral equation methods. This problem has important applications in nanophotonics problems, including sensing and plasmonic imaging. To illustrate the effect of parity and…
Quantitative phase microscopy (QPM), a technique combining phase imaging and microscopy, enables visualization of the 3D topography in reflective samples, as well as the inner structure or refractive index distribution of transparent and…
Quantum phase estimation (QPE) is the key subroutine of several quantum computing algorithms as well as a central ingredient in quantum computational chemistry and quantum simulation. While QPE strategies have focused on the estimation of a…
Quantum Monte Carlo (QMC) techniques are widely used in a variety of scientific problems and much work has been dedicated to developing optimized algorithms that can accelerate QMC on standard processors (CPU). With the advent of various…
Fault-tolerant Quantum Processing Units (QPUs) promise to deliver exponential speed-ups in select computational tasks, yet their integration into modern deep learning pipelines remains unclear. In this work, we take a step towards bridging…
High-dimensional (HD) entanglement promises both enhanced key rates and overcoming obstacles faced by modern-day quantum communication. However, modern convex optimization-based security arguments are limited by computational constraints;…
We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum…
The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…
We present a simple and effective method for evaluating double-and single-layer potentials for Laplace's equation in three dimensions close to the boundary. The close evaluation of these layer potentials is challenging because they are…
Approximation using Fourier features is a popular technique for scaling kernel methods to large-scale problems, with myriad applications in machine learning and statistics. This method replaces the integral representation of a…
We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…
The theory of fuzzy mathematics has been proven very effective for defining and solving optimization problems. Fuzzy quadratic programming (FQP) is a consequence of this approach. In this paper, an algorithm has been proposed to solve FQP…
Existing fast algorithms for bilateral and nonlocal means filtering mostly work with grayscale images. They cannot easily be extended to high-dimensional data such as color and hyperspectral images, patch-based data, flow-fields, etc. In…
In this work, the fast-convolving reproducing kernel particle method (FC-RKPM) is introduced. This method is hundreds to millions of times faster than the traditional RKPM for 3D meshfree simulations. In this approach, the meshfree…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
Large language models (LLMs) have been widely applied but face challenges in efficient inference. While quantization methods reduce computational demands, ultra-low bit quantization with arbitrary precision is hindered by limited GPU Tensor…
The kernel embedding algorithm is an important component for adapting kernel methods to large datasets. Since the algorithm consumes a major computation cost in the testing phase, we propose a novel teacher-learner framework of learning…
In this paper, we present a fast boundary integral method accelerated by the fast multipole method (FMM) for acoustic wave scattering governed by the scalar Helmholtz equation in multi-layered two-dimensional media. Multiple scatterers are…