A note on improved stochastic trace estimation for fermionic string fluctuations

TL;DR

This paper introduces an improved stochastic trace estimation method using mutually unbiased bases for lattice superstring simulations, demonstrating reduced variance compared to traditional Gaussian estimators.

Contribution

The paper presents a novel stochastic trace estimator based on mutually unbiased bases, enhancing accuracy in lattice superstring computations.

Findings

Reduced variance in trace estimates compared to Gaussian methods

Effective for discretized superstring worldsheet operators

Potentially applicable to other lattice simulation contexts

Abstract

We report on the use of a stochastic trace estimator algorithm, based on mutually unbiased bases, for evaluating the trace of a matrix differential operator appearing in the context of lattice simulations for the discretized superstring worldsheet. A study of the variance, in a setup which is slightly modified with respect to the original one, confirms advantages with respect to more traditional methods like the Gaussian estimator.