Efficient Representation of Topologically Ordered States with Restricted Boltzmann Machines

Understand

Representation by neural networks, in particular by restricted Boltzmann machines (RBM), has provided a powerful computational tool to solve quantum many-body problems.

• An important open question is how to characterize which class of quantum states can be efficiently represented with the RBM.
• Here, we show that the RBM can efficiently represent a wide class of many-body entangled states with rich exotic topological orders.
• This includes: (1) ground states of double semion and twisted quantum double models with intrinsic topological orders; (2) states of the AKLT model and 2D CZX model with symmetry protected topological order; (3) states of Haah code model with fracton topological order; (4) generalized stabilizer states and hypergraph states that are important for quantum information protocols.