  We demonstrate quantum many-body state reconstruction from experimental data
generated by a programmable quantum simulator, by means of a neural network
model incorporating known experimental errors. Specifically, we extract
restricted Boltzmann machine (RBM) wavefunctions from data produced by a
Rydberg quantum simulator with eight and nine atoms in a single measurement
basis, and apply a novel regularization technique to mitigate the effects of
measurement errors in the training data. Reconstructions of modest complexity
are able to capture one- and two-body observables not accessible to
experimentalists, as well as more sophisticated observables such as the R\'enyi
mutual information. Our results open the door to integration of machine
learning architectures with intermediate-scale quantum hardware.
