Exact Machine Learning Topological States. (arXiv:1609.09060v1 [cond-mat.dis-nn])

Artificial neural networks play a prominent role in the rapidly growing fieldof machine learning and are recently introduced to quantum many-body systems totackle complex problems. Here, we find that even topological states withlong-range quantum entanglement can be represented with classical artificialneural networks. This is demonstrated by using two concrete spin systems, theone-dimensional (1D) symmetry-protected topological cluster state and the 2Dtoric code state with an intrinsic topological order. For both cases we showrigorously that the topological ground states can be represented by short-rangeneural networks in an {it exact} fashion. This neural network representation,in addition to being exact, is surprisingly {it efficient} as the requirednumber of hidden neurons is as small as the number of physical spins. Our exactconstruction of topological-order neuron-representation demonstrates explicitlythe exceptional power of neural networks in describing exotic…


Link to Full Article: Exact Machine Learning Topological States. (arXiv:1609.09060v1 [cond-mat.dis-nn])