Quantum Codes from Neural Networks

TL;DR

This paper explores the use of neural network states as a versatile variational approach for representing complex quantum codes and entangled states, demonstrating superior performance in quantum error correction and information transmission tasks.

Contribution

It introduces neural network states as an effective method for designing quantum codes and entangled states, outperforming existing codes for certain quantum channels.

Findings

Neural network states produce high-coherent-information codes for amplitude damping and dephrasure channels.

They outperform all known codes for these channels and cannot be found by direct parametrization.

They reliably find the best known codes for the depolarizing channel and can represent maximally entangled states.

Abstract

We examine the usefulness of applying neural networks as a variational state ansatz for many-body quantum systems in the context of quantum information-processing tasks. In the neural network state ansatz, the complex amplitude function of a quantum state is computed by a neural network. The resulting multipartite entanglement structure captured by this ansatz has proven rich enough to describe the ground states and unitary dynamics of various physical systems of interest. In the present paper, we initiate the study of neural network states in quantum information-processing tasks. We demonstrate that neural network states are capable of efficiently representing quantum codes for quantum information transmission and quantum error correction, supplying further evidence for the usefulness of neural network states to describe multipartite entanglement. In particular, we show the following main results: a) Neural network states yield quantum codes with a high coherent information for two important quantum channels, the generalized amplitude damping channel and the dephrasure channel. These codes outperform all other known codes for these channels, and cannot be found using a direct parametrization of the quantum state. b) For the depolarizing channel, the neural network state ansatz reliably finds the best known codes given by repetition codes. c) Neural network states can be used to represent absolutely maximally entangled states, a special type of quantum error-correcting codes. In all three cases, the neural network state ansatz provides an efficient and versatile means as a variational parametrization of these highly entangled states.