Related papers: Fast Algorithm for Quasi-2D Coulomb Systems
Quantum computation offers significant potential for accelerating the simulation of molecules and materials through algorithms such as quantum phase estimation (QPE). However, the expected speedup in ground-state energy estimation depends…
Machine learning algorithms perform well on identifying patterns in many different datasets due to their versatility. However, as one increases the size of the dataset, the computation time for training and using these statistical models…
We give a quantum approximation scheme (i.e., $(1 + \varepsilon)$-approximation for every $\varepsilon > 0$) for the classical $k$-means clustering problem in the QRAM model with a running time that has only polylogarithmic dependence on…
Quantum simulation holds the promise of improving the atomic simulations used at EDF to anticipate the ageing of materials of interest. One simulator in particular seems well suited to modeling interacting electrons: the Rydberg atoms…
Clustering plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…
This paper compares the Wolf method to the shifted forces (SF) method for efficient computer simulation of isotropic systems interacting via Coulomb forces, taking results from the Ewald summation method as representing the true behavior.…
In this article, we present an $O(N \log N)$ rapidly convergent algorithm for the numerical approximation of the convolution integral with radially symmetric weakly singular kernels and compactly supported densities. To achieve the reduced…
Computational fluid dynamics (CFD) is a cornerstone of classical scientific computing, and there is growing interest in whether quantum computers can accelerate such simulations. To date, the existing proposals for fault-tolerant quantum…
A cardinal obstacle to performing quantum-mechanical simulations of strongly-correlated matter is that, with the theoretical tools presently available, sufficiently-accurate computations are often too expensive to be ever feasible. Here we…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
We present a classical algorithm that, for any 3D geometrically-local, polylogarithmic-depth quantum circuit $C$ acting on $n$ qubits, and any bit string $x\in\{0,1\}^n$, can compute the quantity $|< x |C|0^{\otimes n}>|^2$ to within any…
We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…
Learning system dynamics directly from observations is a promising direction in machine learning due to its potential to significantly enhance our ability to understand physical systems. However, the dynamics of many real-world systems are…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
We consider the classic Facility Location, $k$-Median, and $k$-Means problems in metric spaces of doubling dimension $d$. We give nearly linear-time approximation schemes for each problem. The complexity of our algorithms is…
A model based on the sudden approximation has been developed to describe high energy single nucleon removal reactions. Within this approach, which takes as its starting point the formalism of Hansen \cite{Anne2}, the nucleon-removal cross…
Based on the recently developed resummation-based quantum Monte Carlo method for the SU($N$) spin and loop-gas models, we develop a new algorithm, dubbed ResumEE, to compute the entanglement entropy (EE) with greatly enhanced efficiency.…
We propose a fast and general predecision scheme for Metropolis Monte Carlo simulation of $d$-dimensional long-range interacting lattice models. For potentials of the form $V(r)=r^{-d-\sigma}$, this reduces the computational complexity from…