Detecting topological order using recurrent neural network wave functions

In recent years, neural networks were shown to be powerful ansatz to model the state of quantum many-body systems. In particular, recurrent neural networks (RNNs) - borrowed from the field of natural language processing - were shown to be capable of modeling ground state wave functions of quantum many-body Hamiltonians. In this talk, we show that RNNs are also capable of encoding topological properties in quantum systems. We demonstrate that our RNN wave function ansatz can extract the correct value of the topological entanglement entropy for the 2D toric code using entanglement entropy scaling and Kitaev-Preskill construction. We also show the promise of this approach at investigating the existence of spin liquids in Rydberg quantum simulators.