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 wave function 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.

Assuming that the AdS/CFT prescription is valid in the case of noncausal backgrounds, we apply it to the simplest possible eternal time machine solution in AdS 3 based on two conical defects moving around their center of mass along a circular orbit. Closed timelike curves in this space-time extend all the way to the boundary of AdS 3 , violating causality of the boundary field theory. By use of the geodesic approximation we address the issue of self-consistent dynamics of the dual 1 þ 1 dimensional field theory when causality is violated, and calculate the two-point retarded Green function. It has a nontrivial analytical structure both at negative and positive times, providing us with an intuition on how an interacting quantum field could behave once causality is broken.