Related papers: Mollified Monte Carlo
A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo J. Chem.…
For a long time, people have been focusing on how to extract more information, such as off-diagonal observables, from the quantum Monte Carlo (QMC) simulation of the partition function, but there have been numerous difficulties, and many of…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. In some cases, like in the…
This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…
We introduce and discuss Monte Carlo methods in quantum field theories. Methods of independent Monte Carlo, such as random sampling and importance sampling, and methods of dependent Monte Carlo, such as Metropolis sampling and Hamiltonian…
The Markov chain Monte Carlo (MCMC) method is used to evaluate the imaginary-time path integral of a quantum oscillator with a potential that includes both a quadratic term and a quartic term whose coupling is varied by several orders of…
Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies.…
This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth survey of a similar title by the same authors, with an…
Minkowski functionals provide a novel tool to characterize the large-scale galaxy distribution in the Universe. Here we give a brief tutorial on the basic features of these morphological measures and indicate their practical application for…
In this paper we will give a Monte Carlo algorithm by which the moments of a functions of Dirichlet probability distributions can be estimated. This algorithm is called Inner Nested Sampling and is an implementation of Skilling's general…
This article provides an overview of some interfaces between the theory of quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC theoretical settings: first order QMC methods in the unit cube $[0,1]^s$ and in…
In this article, we propose several quantization-based stratified sampling methods to reduce the variance of a Monte Carlo simulation. Theoretical aspects of stratification lead to a strong link between optimal quadratic quantization and…
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…
The Monte Carlo method is a thriving and mathematically beautiful numerical technique used extensively, nowadays, to deal with many demanding problems in diverse fields. Here, we present an iterative Monte Carlo algorithm to work out very…
Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…
We discuss an alternative accurate Monte Carlo method to calculate the ground-state energy and related quantities for Laughlin states of the fractional quantum Hall effect in a disk geometry. This alternative approach allows us to obtain…
We propose quantum algorithms that provide provable speedups for Markov Chain Monte Carlo (MCMC) methods commonly used for sampling from probability distributions of the form $\pi \propto e^{-f}$, where $f$ is a potential function. Our…
For qubits, Monte Carlo estimation of the average fidelity of Clifford unitaries is efficient -- it requires a number of experiments that is independent of the number $n$ of qubits and classical computational resources that scale only…
We study cluster perturbation theory [Phys. Rev. Lett. \textbf{84}, 522 (2000)] when auxiliary field quantum Monte Carlo method is used for solving the cluster hamiltonian. As a case study, we calculate the spectral functions of the Hubbard…