Speaker
Description
We study trace estimation for disconnected quark loop contributions in lattice QCD, focusing on single-time-slice traces such as $ \operatorname{Tr}\left[\Gamma_5(t)D^{-1}(t,t)\right]$. We build on the standard use of hopping-parameter expansions (HPE) in trace estimation, where the truncated term has bounded graph range and can be evaluated exactly using distance-(d) probing.
We first investigate multiplier-based colorings as an alternative to hierarchical probing for the exact truncated HPE contribution. The advantage becomes most relevant at larger expansion orders, where exact evaluation requires higher coloring distances and therefore more probing vectors. Since multiplier-based colorings can achieve the same distance with fewer colors, higher HPE orders can be used at lower cost. This removes more short-distance contributions exactly before estimating the stochastic remainder, whose inverse application is solved with multigrid-preconditioned FGMRES.
We also study replacing the classical Neumann-series HPE polynomial by a GMRES polynomial. While the Neumann expansion is fixed by the chosen splitting, the GMRES polynomial is constructed from the action of the Dirac operator and can adapt more effectively to non-ideal spectral distributions.