  Rydberg atom arrays are programmable quantum simulators capable of preparing
interacting qubit systems in a variety of quantum states. Due to long
experimental preparation times, obtaining projective measurement data can be
relatively slow for large arrays, which poses a challenge for state
reconstruction methods such as tomography. Today, novel groundstate
wavefunction ans\"atze like recurrent neural networks (RNNs) can be efficiently
trained not only from projective measurement data, but also through
Hamiltonian-guided variational Monte Carlo (VMC). In this paper, we demonstrate
how pretraining modern RNNs on even small amounts of data significantly reduces
the convergence time for a subsequent variational optimization of the
wavefunction. This suggests that essentially any amount of measurements
obtained from a state prepared in an experimental quantum simulator could
provide significant value for neural-network-based VMC strategies.
