Speaker
Description
Trace estimation in lattice QCD benefits from two complementary variance-reduction techniques: probing methods that exploit operator structure, and multigrid multilevel Monte Carlo, an efficient deflation technique. We propose a unified framework that combines these ideas and evaluate it on three representative targets: the trace of the inverse of the Dirac operator, traces entering the connected pseudoscalar correlator, and disconnected fermion loops. Multigrid multilevel Monte Carlo achieves deflation using a projector derived from the multigrid prolongator $P$, which captures low-mode information of the Wilson–Dirac operator. Probing is implemented by applying distance-$d$ graph colorings to the lattice, which exploit locality to suppress off-diagonal noise. Within each lattice site, further restricting the noise vectors to subsets such as spin or color is referred to as dilution. We observe systematic variance reductions across all problems, with the disconnected case in particular profiting from the complementary strengths of deflation and probing.
| Parallel Session (for talks only) | Software development and machines |
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