  In these proceedings we address the computation of quark-line disconnected
diagrams in lattice QCD. The evaluation of these diagrams is required for many
phenomenologically interesting observables, but suffers from large statistical
errors due to the vacuum and random-noise contributions to their variances.
Motivated by a theoretical analysis of the variances, we introduce a new family
of stochastic estimators of single-propagator traces built upon a frequency
splitting combined with a hopping expansion of the quark propagator, and test
their efficiency in two-flavour QCD with pions as light as 190 MeV. The use of
these estimators reduces the cost of the computation by one to two orders of
magnitude over standard estimators depending on the fermion bilinear. As a
concrete application, we show the impact of these findings on the computation
of the hadronic vacuum polarization contribution to the muon anomalous magnetic
moment.
