Neural Network Representation of Tensor Network and Chiral States
Yichen Huang, Joel E. Moore
Abstract
We study the representational power of Boltzmann machines (a type of neural network) in quantum many-body systems. We prove that any (local) tensor network state has a (local) neural network representation. The construction is almost optimal in the sense that the number of parameters in the neural network representation is almost linear in the number of nonzero parameters in the tensor network representation. Despite the difficulty of representing (gapped) chiral topological states with local tensor networks, we construct a quasilocal neural network representation for a chiral p-wave superconductor. These results demonstrate the power of Boltzmann machines.
Topics & Concepts
Boltzmann machineRepresentation (politics)Artificial neural networkTensor (intrinsic definition)Topology (electrical circuits)Computer scienceRestricted Boltzmann machineState (computer science)PhysicsMathematicsStatistical physicsPure mathematicsArtificial intelligenceAlgorithmCombinatoricsPolitical sciencePoliticsLawQuantum many-body systemsModel Reduction and Neural NetworksQuantum Computing Algorithms and Architecture