Efficient Representation of Topologically Ordered States with Restricted Boltzmann Machines

TL;DR

This paper demonstrates that restricted Boltzmann machines can efficiently represent a broad spectrum of topologically ordered quantum states, enabling new computational approaches for complex quantum many-body systems.

Contribution

It shows that RBMs can efficiently encode diverse topologically ordered states, including non-abelian anyon models, expanding their applicability in quantum physics.

Findings

RBMs can represent ground states of topologically ordered models.

RBMs successfully encode symmetry protected and fracton topological states.

The approach enables studying complex quantum models with rich physics.

Abstract

Representation by neural networks, in particular by restricted Boltzmann machines (RBM), 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 the RBM. Here, we show that the RBM 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 2D CZX model with symmetry protected topological order; (3) states of Haah code model with fracton topological order; (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.