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Passetti et al. [Physical Review Letters 131, 036502 (2023)] recentlyassessed the potential of neural quantum states (NQS) in learning ground-statewave functions with volume-law entanglement scaling. They focused on NQS usingfeedforward neural networks, specifically applied to the complex SYKHamiltonian for fermions. Their numerical results hint at an exponentialincrease in the required variational parameters as the system size grows,apparently tied to the entanglement growth within the SYK ground state. Thischallenges the general utility of NQS for highly entangled wavefunctions,contrasting with established analytical and numerical findings. Based on ourexperiments, we show that suitably chosen NQS can learn ground states withvolume-law entanglement both for spin and fermionic problems. We argue that thesetup utilized in the aforementioned letter reveals the inefficiency ofnon-fermionic NQS to learn fermionic states, rather than a general connectionbetween entanglement content and learnability hardness.

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