Quasi-Monte Carlo methods for lattice systems: a first look

TL;DR

This paper explores the use of Quasi-Monte Carlo methods to enhance the accuracy of observable calculations in lattice quantum systems, demonstrating improved error scaling in simple models.

Contribution

It introduces the application of Quasi-Monte Carlo techniques to lattice quantum systems and verifies improved error behavior in basic models.

Findings

Error scaling improved from N^{-1/2} to N^{-1} in tested models

Quasi-Monte Carlo methods are effective for simple quantum oscillators

Potential for better accuracy in lattice quantum simulations

Abstract

We investigate the applicability of Quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable calculated by averaging over random observations generated from an ordinary Markov chain Monte Carlo simulation behaves like N^{-1/2}, where N is the number of observations. By means of Quasi-Monte Carlo methods it is possible to improve this behavior for certain problems to N^{-1}, or even further if the problems are regular enough. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling.