CMT Seminar Nisarga Paul: Learning quantum matter with neural quantum states

Neural quantum states (NQS), wavefunctions parameterized by classical neural networks, have become a state-of-the-art variational method for quantum many body physics, yet little is known about their fundamental constraints. In this talk, I'll give an introduction to NQS, reviewing empirical results and presenting some new theoretical results. I show that feed-forward neural quantum states acting on n spins with k scalar nonlinearities, under certain analyticity assumptions, obey a bound on entanglement entropy for any subregion: S < c k log n, for a constant c. This establishes an NQS analog of the area law constraint for matrix product states. I'll demonstrate analytically and numerically that the scaling with n is tight for a wide variety of NQS. I'll close with some interesting open questions about how we may best characterize the power of NQS and where they may give an advantage over tensor network methods.