Error correction for encoded quantum annealing

TL;DR

This paper analyzes a quantum annealing architecture that encodes a fully connected spin glass into a local interaction model, interpreting it as an error-correcting code and evaluating its robustness against noise using belief-propagation decoding.

Contribution

It introduces a novel interpretation of the quantum annealing architecture as an error-correcting code and assesses its performance under noise with belief-propagation decoding.

Findings

The architecture is highly robust against weakly correlated bit-flip noise.

The error correction scheme can be analyzed using belief-propagation algorithms.

Potential applicability to other encoding schemes and noise models.

Abstract

Recently, Lechner, Hauke and Zoller [Science Advances, 1(9)e1500838, (2015)] have proposed a quantum annealing architecture, in which a classical spin glass with all-to-all connectivity is simulated by a spin glass with geometrically local interactions. We interpret this architecture as a classical error-correcting code, which is highly robust against weakly correlated bit-flip noise, and we analyze the code's performance using a belief-propagation decoding algorithm. Our observations may also apply to more general encoding schemes and noise models.