A Neural Decoder for Topological Codes

TL;DR

This paper introduces a neural network-based decoder for topological quantum error correction, leveraging Boltzmann machines to improve decoding strategies across various stabilizer codes.

Contribution

It develops a general training and decoding method using neural networks, specifically Boltzmann machines, for topological codes, applicable to many stabilizer codes with minimal adjustments.

Findings

Successfully applied to 2D toric code with phase-flip errors

Demonstrates the versatility of neural decoders for different stabilizer codes

Provides a scalable approach for quantum error correction

Abstract

We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep learning. We provide a general prescription for the training of the network and a decoding strategy that is applicable to a wide variety of stabilizer codes with very little specialization. We demonstrate the neural decoder numerically on the well-known two dimensional toric code with phase-flip errors.