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

Neural Quantum States of frustrated magnets: generalization and sign structure