Stochastic automatic differentiation and the Signal to Noise problem

TL;DR

This paper proposes a novel stochastic automatic differentiation method to completely eliminate the exponential signal-to-noise problem in lattice field theory simulations, improving the extraction of particle properties.

Contribution

Introducing stochastic automatic differentiation to compute correlators as derivatives, effectively solving the signal-to-noise problem in Monte Carlo estimations.

Findings

Successful application to scalar field theories

Potential for extension to gauge theories and QCD

Significant improvement in signal-to-noise ratio

Abstract

Lattice Field theory allows to extract properties of particles in strongly coupled quantum field theories by studying Euclidean vacuum expectation values. When estimated from numerical Monte Carlo simulations these are typically affected by the so called Signal to Noise problem: both the signal and the variance decay exponentially with the Euclidean time, but the variance decays slower, making the signal to noise ratio to degrade exponentially fast. In this work we show that writing correlators as derivatives with respect to sources and evaluating these derivatives using techniques of stochastic automatic differentiation can eliminate completely the signal to noise problem. We show some results in scalar field theories, and comment on the prospects for applicability in Gauge theories and QCD.