Stochastic Estimation with $Z_2$ Noise

TL;DR

This paper introduces a $Z_2$ noise method for stochastic matrix inversion estimation, demonstrating its advantages over Gaussian noise in lattice QCD applications like quark loop calculations.

Contribution

The paper presents a novel $Z_2$ noise technique that improves stochastic estimation accuracy and efficiency in matrix inversion problems, especially in lattice QCD.

Findings

$Z_2$ noise outperforms Gaussian noise in estimation accuracy.

The method effectively computes diagonal and off-diagonal traces.

Limitations depend on the inverse matrix structure.

Abstract

We introduce a $Z_2$ noise for the stochastic estimation of matrix inversion and discuss its superiority over other noises including the Gaussian noise. This algorithm is applied to the calculation of quark loops in lattice quantum chromodynamics that involves diagonal and off-diagonal traces of the inverse matrix. We will point out its usefulness in its applications to estimating determinants, eigenvalues, and eigenvectors, as well as its limitations based on the structure of the inverse matrix.