Related papers: Diffusion Monte Carlo: Exponential scaling of comp…
A self-contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of the method is derived and then a…
We present a systematic and comprehensive study of finite-size effects in diffusion quantum Monte Carlo calculations of metals. Several previously introduced schemes for correcting finite-size errors are compared for accuracy and efficiency…
Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a wide range of challenging applications. However, diffusion…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
Computational codes based on the Diffusion Monte Carlo method can be used to determine the quantum state of two-electron systems confined by external potentials of various nature and geometry. In this work, we show how the application of…
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…
Distortion risk measures play a critical role in quantifying risks associated with uncertain outcomes. Accurately estimating these risk measures in the context of computationally expensive simulation models that lack analytical tractability…
We perform a comprehensive analysis of the quantum-enhanced Monte Carlo method [Nature, 619, 282-287 (2023)], aimed at identifying the optimal working point of the algorithm. We observe an optimal mixing Hamiltonian strength and analyze the…
The quantum Monte Carlo methods represent a powerful and broadly applicable computational tool for finding very accurate solutions of the stationary Schroedinger equation for atoms, molecules, solids and a variety of model systems. The…
We briefly review the principles, mathematical bases, numerical shortcuts and applications of fast random walk (FRW) algorithms. This Monte Carlo technique allows one to simulate individual trajectories of diffusing particles in order to…
Monte Carlo simulation is one of the most important tools in the study of diffusion processes. For constant diffusion coefficients, an appropriate Gaussian distribution of particle's steplengths can generate exact results, when compared…
Modern training and inference pipelines in statistical learning and deep learning repeatedly invoke linear-system solves as inner loops, yet high-accuracy deterministic solvers can be prohibitively expensive when solves must be repeated…
The size of the population of random walkers required to obtain converged estimates in DMC increases dramatically with system size. We illustrate this by comparing ground state energies of small clusters of parahydrogen (up to 48 molecules)…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
We discuss suitable classes of diffusion processes, for which functionals relevant to finance can be computed via Monte Carlo methods. In particular, we construct exact simulation schemes for processes from this class. However, should the…
In this note we study the numerical stability problem that may take place when calculating the cumulative distribution function of the {\it Hypoexponential} random variable. This computation is extensively used during the execution of Monte…
Employing a classical density-functional description of liquid environments, we introduce a rigorous method for the diffusion quantum Monte Carlo calculation of free energies and thermodynamic averages of solvated systems that requires…
This paper develops and analyzes an efficient numerical method for solving elliptic partial differential equations, where the diffusion coefficients are random perturbations of deterministic diffusion coefficients. The method is based upon…