  Restricted Boltzmann machines (RBMs) have proven to be a powerful tool for
learning quantum wavefunction representations from qubit projective measurement
data. Since the number of classical parameters needed to encode a quantum
wavefunction scales rapidly with the number of qubits, the ability to learn
efficient representations is of critical importance. In this paper we study
magnitude-based pruning as a way to compress the wavefunction representation in
an RBM, focusing on RBMs trained on data from the transverse-field Ising model
in one dimension. We find that pruning can reduce the total number of RBM
weights, but the threshold at which the reconstruction accuracy starts to
degrade varies significantly depending on the phase of the model. In a gapped
region of the phase diagram, the RBM admits pruning over half of the weights
while still accurately reproducing relevant physical observables. At the
quantum critical point however, even a small amount of pruning can lead to
significant loss of accuracy in the physical properties of the reconstructed
quantum state. Our results highlight the importance of tracking all relevant
observables as their sensitivity varies strongly with pruning. Finally, we find
that sparse RBMs are trainable and discuss how a successful sparsity pattern
can be created without pruning.
