  Neural quantum states (NQS) attract a lot of attention due to their potential
to serve as a very expressive variational ansatz for quantum many-body systems.
Here we study the main factors governing the applicability of NQS to frustrated
magnets by training neural networks to approximate ground states of several
moderately-sized Hamiltonians using the corresponding wavefunction structure on
a small subset of the Hilbert space basis as training dataset. We notice that
generalization quality, i.e. the ability to learn from a limited number of
samples and correctly approximate the target state on the rest of the space,
drops abruptly when frustration is increased. We also show that learning the
sign structure is considerably more difficult than learning amplitudes.
Finally, we conclude that the main issue to be addressed at this stage, in
order to use the method of NQS for simulating realistic models, is that of
generalization rather than expressibility.
