Entanglement features of random neural network quantum states
Abstract: Neural networks offer a novel approach to represent wave functions for solving quantum many-body problems. But what kinds of quantum states are efficiently represented by neural networks? In this talk, we will discuss both analytic and numerical results on the entanglement properties of an ensemble of neural network states represented by random restricted Boltzmann machines. Phases with distinct entanglement features are identified and characterized which may help inform the initialization of neural network ansatzes for future computational tasks. For certain parameters, we will show that these random neural network quantum states generically have nearly maximal entanglement similar to a typical state. While entanglement is not the limiting factor for representing quantum states with restricted Boltzmann machines, we will show that generic wavefunctions represented by restricted Boltzmann machines are multifractal in the Ising spin basis which may limit the applications of these ansatzes in certain tasks.
