  Passetti et al. [Physical Review Letters 131, 036502 (2023)] recently
assessed the potential of neural quantum states (NQS) in learning ground-state
wave functions with volume-law entanglement scaling. They focused on NQS using
feedforward neural networks, specifically applied to the complex SYK
Hamiltonian for fermions. Their numerical results hint at an exponential
increase in the required variational parameters as the system size grows,
apparently tied to the entanglement growth within the SYK ground state. This
challenges the general utility of NQS for highly entangled wavefunctions,
contrasting with established analytical and numerical findings. Based on our
experiments, we show that suitably chosen NQS can learn ground states with
volume-law entanglement both for spin and fermionic problems. We argue that the
setup utilized in the aforementioned letter reveals the inefficiency of
non-fermionic NQS to learn fermionic states, rather than a general connection
between entanglement content and learnability hardness.
