A first look at quasi-Monte Carlo for lattice field theory problems

TL;DR

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

Contribution

It is the first investigation applying Quasi-Monte Carlo to lattice field theories, showing potential for better error behavior compared to traditional Monte Carlo methods.

Findings

Improved error scaling from 1/√N to 1/N in simple quantum systems.

Successful adaptation of Quasi-Monte Carlo methods to lattice field theory problems.

Verification of enhanced accuracy in quantum harmonic and anharmonic oscillators.

Abstract

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 observable calculated by averaging over random observations generated from an ordinary Monte Carlo simulation behaves like 1/sqrt(N), 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 up to 1/N. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling.