Publication
Passetti et al. [1] recently assessed the potential of neural quantum states (NQS) [2] 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 [3]. 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 wave functions, contrasting with established analytical [4-9] and numerical findings [4,9]. Based on our experiments, we show that suitably chosen NQS can learn ground states with volumelaw entanglement both for spin and fermionic problems. We argue that the setup utilized in [1] reveals the inefficiency of nonfermionic NQS to learn the sign structure of fermionic states, rather than a general connection between entanglement content and learnability hardness. In Fig. 1(a), we show the average infidelity obtained by performing fidelity optimization on the ground-state wave function of ten instances of the quantum Sherrington-Kirkpatrick model (QSK) [10]. We show results for a two-layer perceptron NQS with real parameters, tanh activation, and varying hidden-unit density α. Although the ground state of the QSK model exhibits volume-law entanglement [10] [see also Fig. 1(d1)], quadratically increasing the number of parameters with system size L proves sufficient to achieve infidelity below a threshold of PHYSICAL REVIEW LETTERS 134, 079701 (2025) 0031-9007=25=134(7)=079701(2) 079701-1
Nicola Marzari, Francesco Libbi