Hutch++ and XTrace to Improve Stochastic Trace Estimation

We present the analysis of two recently proposed noise reduction techniques, Hutch++ and XTrace, both based on inexact deflation. These methods were proven to have a better asymptotic convergence to the solution than the classical Girard-Hutchinson stochastic method. We applied these methods to the computation of the trace of the inverse of the Dirac operator with $O(a)$ improved Wilson fermions on the QCD ensemble generated by the RC${}^{\star }$ collaboration with $m_{\pi }\approx 400$ MeV and $V=64\times {32}^3$. Unfortunately, we see no noise reduction with a moderate number of sources, and we attempt an explanation of why this is the case. This study was part of the effort to evaluate isospin-breaking effects using the RM123 with C${}^{\star }$ boundary conditions in an unquenched set-up.