  Generative modeling with machine learning has provided a new perspective on
the data-driven task of reconstructing quantum states from a set of qubit
measurements. As increasingly large experimental quantum devices are built in
laboratories, the question of how these machine learning techniques scale with
the number of qubits is becoming crucial. We empirically study the scaling of
restricted Boltzmann machines (RBMs) applied to reconstruct ground-state
wavefunctions of the one-dimensional transverse-field Ising model from
projective measurement data. We define a learning criterion via a threshold on
the relative error in the energy estimator of the machine. With this criterion,
we observe that the number of RBM weight parameters required for accurate
representation of the ground state in the worst case - near criticality -
scales quadratically with the number of qubits. By pruning small parameters of
the trained model, we find that the number of weights can be significantly
reduced while still retaining an accurate reconstruction. This provides
evidence that over-parametrization of the RBM is required to facilitate the
learning process.
