# Neural network representation of tensor network and chiral states

## TL;DR

This paper demonstrates that Boltzmann machines can efficiently represent complex quantum many-body states, including tensor network states and certain chiral topological states, highlighting their expressive power.

## Contribution

It proves that local tensor network states can be represented by neural networks with near-linear parameter count and constructs a neural network for chiral p-wave superconductors.

## Key findings

- Neural networks can represent any local tensor network state.
- Constructed a neural network for chiral p-wave superconductor.
- Representation is nearly optimal in parameter efficiency.

## 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 quasi-local neural network representation for a chiral $p$-wave superconductor. These results demonstrate the power of Boltzmann machines.