  A numerical method is presented for reproducing fermionic quantum gas
microscope experiments in equilibrium. By employing nested componentwise direct
sampling of fermion pseudo-density matrices, as they arise naturally in
determinantal quantum Monte Carlo (QMC) simulations, a stream of
pseudo-snapshots of occupation numbers on large systems can be produced. There
is a sign problem even when the conventional determinantal QMC algorithm can be
made sign-problem free, and every pseudo-snapshot comes with a sign and a
reweighting factor. Nonetheless, this "sampling sign problem" turns out to be
weak and manageable in a large, relevant parameter regime. The method allows to
compute distribution functions of arbitrary quantities defined in occupation
number space and, from a practical point of view, facilitates the computation
of complicated conditional correlation functions. While the projective
measurements in quantum gas microscope experiments achieve direct sampling of
occupation number states from the density matrix, the presented numerical
method requires a Markov chain as an intermediate step and thus achieves only
indirect sampling, but the full distribution of pseudo-snapshots after (signed)
reweighting is identical to the distribution of snapshots from projective
measurements
