# Deep Neural Network Probabilistic Decoder for Stabilizer Codes

## TL;DR

This paper introduces a neural network-based probabilistic decoder for stabilizer codes that predicts error distributions conditioned on syndromes, demonstrating improved performance on the toric code by effectively capturing error correlations.

## Contribution

It presents a universal neural network decoder for stabilizer codes that outperforms existing decoders by leveraging probabilistic modeling and correlation awareness.

## Key findings

- Higher threshold than known decoders on the toric code
- Effectively finds the most probable error
- Accounts for error correlations

## Abstract

Neural networks can efficiently encode the probability distribution of errors in an error correcting code. Moreover, these distributions can be conditioned on the syndromes of the corresponding errors. This paves a path forward for a decoder that employs a neural network to calculate the conditional distribution, then sample from the distribution - the sample will be the predicted error for the given syndrome. We present an implementation of such an algorithm that can be applied to any stabilizer code. Testing it on the toric code, it has higher threshold than a number of known decoders thanks to naturally finding the most probable error and accounting for correlations between errors.