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Exact Machine Learning Topological States

January 27, 2017 - 12:10pm
Dong-Ling Deng
Artificial neural networks play a prominent role in the rapidly growing field of machine learning and are recently introduced to quantum many-body systems to tackle complex problems. In this talk, I will show that even topological states with long-range quantum entanglement  can be represented with classical artificial neural networks with short-range connections. This is demonstrated by using three concrete spin systems, namely the one-dimensional (1D) symmetry-protected topological cluster states, the 2D and 3D toric code states with  intrinsic topological orders. For all three cases, I will show rigorously that the topological ground states can be represented by short-range neural networks in an exact and efficient fashion (efficient in the sense that  the number of parameters scales only linearly with the system size) . In addition, for the toric-code models the proposed short-range neural networks can also describe precisely the excited states with abelain anyons and their nontrivial mutual statistics. 
Based on the paper: arXiv:1609.09060.
Lunch served at 12:00pm
PSC 2136