Recently, machine learning has attracted tremendous interest across different communities. In this talk, I will briefly introduce a new neural-network representation of quantum many-body states. I will show that this representation can describe some topological states, either symmetry protected or with intrinsic topological order, in an exact and efficient fashion. I will talk about the entanglement properties, such as entanglement entropy and spectrum, of those quantum states that can be represented efficiently by neural networks. I will also show that neural networks can be used, through reinforcement learning, to solve a challenging problem of calculating the power-law entangled ground state for a model Hamiltonian with long-range interactions.
 D.-L. Deng, X. P. Li, and S. Das Sarma, arXiv: 1609.09060
 D.-L. Deng, X. P. Li, and S. Das Sarma, Phys. Rev. X, 7, 021021 (2017).