Related papers: Quasi-Monte Carlo methods for lattice systems: a f…
This project investigates the applicability of quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error scaling of observables for such theories. The error of an observable calculated by averaging over…
In this project we initiate an investigation of the applicability of Quasi-Monte Carlo methods to lattice field theories in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an…
We apply the Quasi Monte Carlo (QMC) and recursive numerical integration methods to evaluate the Euclidean, discretized time path-integral for the quantum mechanical anharmonic oscillator and a topological quantum mechanical rotor model.…
We present an algorithmic framework for a variant of the quantum Monte Carlo operator-loop algorithm, where non-local cluster updates are constructed in a way that makes each individual loop smaller. The algorithm is designed to increase…
Quantiles and expected shortfalls are usually used to measure risks of stochastic systems, which are often estimated by Monte Carlo methods. This paper focuses on the use of quasi-Monte Carlo (QMC) method, whose convergence rate is…
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…
While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error.…
We provide an extension to lattice systems of the reptation quantum Monte Carlo algorithm, originally devised for continuous Hamiltonians. For systems affected by the sign problem, a method to systematically improve upon the so-called…
Many machine learning problems optimize an objective that must be measured with noise. The primary method is a first order stochastic gradient descent using one or more Monte Carlo (MC) samples at each step. There are settings where…
An efficient Quantum Monte Carlo algorithm for the simulation of bosonic systems on a lattice in a grand canonical ensemble is proposed. It is based on the mapping of bosonic models to the spin models in the limit of the infinite total spin…
We propose an efficient method for Monte Carlo simulation of quantum lattice models. Unlike most other quantum Monte Carlo methods, a single run of the proposed method yields the free energy and the entropy with high precision for the whole…
We demonstrate the quantum mean estimation algorithm on Euclidean lattice field theories. This shows a quadratic advantage over Monte Carlo methods which persists even in presence of a sign problem, and is insensitive to critical slowing…
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…
Importance Sampling (IS), an effective variance reduction strategy in Monte Carlo (MC) simulation, is frequently utilized for Bayesian inference and other statistical challenges. Quasi-Monte Carlo (QMC) replaces the random samples in MC…
Quasi-Monte Carlo algorithms are studied for designing discrete approximations of two-stage linear stochastic programs. Their integrands are piecewise linear, but neither smooth nor lie in the function spaces considered for QMC error…
Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…
We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated…
We present a universal parameter-free quantum Monte Carlo (QMC) algorithm designed to simulate arbitrary spin-$1/2$ Hamiltonians. To ensure the convergence of the Markov chain to equilibrium for every conceivable case, we devise a clear and…
In this paper we present a rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems. These problems are motivated by uncertainty…
Quantum Monte Carlo (QMC) methods are the gold standard for studying equilibrium properties of quantum many-body systems -- their phase transitions, ground and thermal state properties. However, in many interesting situations QMC methods…