Caltech

报告摘要：

Variational wavefunctions offer a practical route around the exponential complexity of many-body Hilbert spaces, but their expressive power is often sharply constrained. Matrix product states, for instance, are efficient but limited to area law entangled states. Neural quantum states (NQS), a variational class based on neural networks, have recently become a state-of-the-art variational method for quantum many body physics, yet little is known about their fundamental constraints. Here we prove 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 and rules out volume law entanglement for NQS with O(1) nonlinearities. We demonstrate analytically and numerically that the scaling with n is tight for a wide variety of NQS. Our work establishes a fundamental constraint on NQS that applies broadly across different network designs, while reinforcing their substantial expressive power.

报告人简介：

Nisarga Paul is a Burke postdoctoral fellow at California Institute of Technology whose interests lie in quantum many-body physics, topological materials, and computational methods. He completed his PhD at MIT where he worked on moiré materials and fractional quantum Hall physics.

报告形式：线上；  Zoom链接：https://mit.zoom.us/j/97042856020