Comment on "Can Neural Quantum States Learn Volume-Law Ground States?"

Abstract

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.