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Efficient representation of topologically ordered states with restricted Boltzmann machines - 2019

Efficient Representation Of Topologically Ordered States With Restricted Boltzmann Machines

Research Area:  Machine Learning

Abstract:

Representation by neural networks, in particular by restricted Boltzmann machines (RBMs), 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 RBMs. Here, we show that RBMs 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 two-dimensional CZX model with symmetry protected topological orders, (3) states of stabilizer Fracton models with fracton topological order, and (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.

Keywords:  

Author(s) Name:  Sirui Lu, Xun Gao, and L.-M. Duan

Journal name:  Covering condensed matter and materials physics

Conferrence name:  

Publisher name:  American Physical Society

DOI:  https://doi.org/10.1103/PhysRevB.99.155136

Volume Information:  Vol. 99, Iss. 15 — 15