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The first results from the Fermilab E989 experiment have confirmed thelong-standing tension between the experimental determination of the muonanomalous magnetic moment $a_\mu=(g_\mu-2)/2$ and its SM determination usingthe dispersive approach. In order to match the expected final precision fromE989, the current uncertainty on ab initio determinations using lattice QCDmust be decreased by a factor 5-15, a goal which is hampered by thesignal-to-noise ratio problem of the electromagnetic current correlator.Multi-level Monte Carlo integration with fermions is a method which reduces thevariance of correlators exponentially in the distance of the fields. Here wedemonstrate that the variance reduction in a realistic two-level simulationwith a pion mass of 270 MeV, linear size of 3 fm and lattice spacing around0.065 fm is sufficient to compute the tail of the current correlator with thestatistical accuracy required for the hadronic vacuum polarization contributionto $a_\mu$. An efficient estimator is also employed for computing thedisconnected contribution.

Multi-level computation of the hadronic vacuum polarization contribution to $(g_\mu-2)$