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Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds for normwise absolute and relative errors apply to Monte…
The hybrid Monte Carlo (HMC) algorithm is arguably the most efficient sampling method for general probability distributions of continuous variables. Together with exact Fourier acceleration (EFA) the HMC becomes equivalent to direct…
Estimating the density of a continuous random variable X has been studied extensively in statistics, in the setting where n independent observations of X are given a priori and one wishes to estimate the density from that. Popular methods…
While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for \textit{ab initio} electronic structure calculations, in practice the fermionic sign problem necessitates the use of the fixed-node approximation and trial…
In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential…
Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates…
We explore the application of an extrapolative method that yields very accurate total and relative energies from variational and diffusion quantum Monte Carlo (VMC and DMC) results. For a trial wave function consisting of a small…
Direct sampling of multi-dimensional systems with quantum Monte Carlo methods allows exact account of many-body effects or particle correlations. The most straightforward approach to solve the Schr\"odinger equation, Diffusion Monte Carlo,…
Nuclear physics seeks to describe both bound and unbound states within a unified predictive framework. While coordinate-space Quantum Monte Carlo (QMC) methods have successfully computed bound states for systems with $A \leq 12$, their…
Quantum Monte Carlo methods are used to calculate various ground state properties of charged bosons in two dimensions, throughout the whole density range where the fluid phase is stable. Wigner crystallization is predicted at $r_s\simeq…
We study beryllium dihydride (BeH$_2$) and acetylene (C$_2$H$_2$) molecules using real-space diffusion Monte Carlo (DMC) method. The molecules serve as perhaps the simplest prototypes that illustrate the difficulties with biases in the…
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…
Path integral Monte Carlo (PIMC) simulations are used to calculate the momentum distribution of the homogeneous electron gas at finite temperature. This is done by calculating the off-diagonal elements of the real-space density matrix,…
We present a cross-language C++/Python program for simulations of quantum mechanical systems with the use of Quantum Monte Carlo (QMC) methods. We describe a system for which to apply QMC, the algorithms of variational Monte Carlo and…
Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…
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…
Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number, uniformly distributed between 0 and 1. Here we consider the…
In quantum Monte Carlo (QMC) methods, energy estimators are calculated as the statistical average of the Markov chain sampling of energy estimator along with an associated statistical error. This error estimation is not straightforward and…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…