相关论文: Making the most of data: Quantum Monte Carlo Post-…

This review covers applications of quantum Monte Carlo methods to quantum mechanical problems in the study of electronic and atomic structure, as well as applications to statistical mechanical problems both of static and dynamic nature. The…

This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The…

An algorithm is proposed to optimize quantum Monte Carlo (QMC) wave functions based on New ton's method and analytical computation of the first and second derivatives of the variati onal energy. This direct application of the variational…

We extend the recently introduced phaseless auxiliary-field quantum Monte Carlo (QMC) approach to any single-particle basis, and apply it to molecular systems with Gaussian basis sets. QMC methods in general scale favorably with system…

We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum…

It is known that the estimating equations for quantile regression (QR) can be solved using an EM algorithm in which the M-step is computed via weighted least squares, with weights computed at the E-step as the expectation of independent…

Monte Carlo methods are widely used for approximating complicated, multidimensional integrals for Bayesian inference. Population Monte Carlo (PMC) is an important class of Monte Carlo methods, which utilizes a population of proposals to…

The efficiency of a Markov chain Monte Carlo algorithm might be measured by the cost of generating one independent sample, or equivalently, the total cost divided by the effective sample size, defined in terms of the integrated…

Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the…

A control in feedback form is derived for linear quadratic, time-invariant optimal control problems subject to parabolic partial differential equations with coefficients depending on a countably infinite number of uncertain parameters. It…

We revisit the accuracy of the variational Monte Carlo (VMC) method by taking an example of ground state properties for the one-dimensional Hubbard model. We start from the variational wave functions with the Gutzwiller and long-range…

Quantum Monte Carlo (QMC) is a family of powerful tools for addressing quantum many-body problems. However, its applications are often plagued by the fermionic sign problem. A promising strategy is to simulate an interaction without sign…

We apply the Average Spectrum Method to the problem of getting the excitation spectrum from imaginary-time quantum Monte Carlo simulations. We show that with high quality QMC data this method reproduces the dominant spectral features very…

Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of…

Large particle systems are often described by high-dimensional (linear) kinetic equations that are simulated using Monte Carlo methods for which the asymptotic convergence rate is independent of the dimensionality. Even though the…

Accurately predicting the formation energy of a compound, which describes its thermodynamic stability, is a key challenge in materials physics. Here, we employ many-body quantum Monte Carlo (QMC) with single-reference trial functions to…

Modern quantum Monte Carlo (QMC) methods often capture electron correlation through both explicitly correlating Jastrow factors and small to mid-sized configuration interaction (CI) expansions. Here, we study the additional optimization…

Quantum scattering at zero energy is studied with stochastic methods. A path integral representation for the scattering cross section is developed. It is demonstrated that Monte Carlo simulation can be used to compare effective potentials…

Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…

This paper considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In particular, the application of the multilevel quasi-Monte Carlo…