  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. One twisted quantum double model
state considered here harbors non-abelian anyon excitations. Our result shows
that it is possible to study a variety of quantum models with exotic
topological orders and rich physics using the RBM computational toolbox.
