Strong Resilience of Topological Codes to Depolarization

TL;DR

This paper demonstrates that topological quantum codes, specifically the toric code, exhibit high resilience to depolarization noise, with an increased error threshold of approximately 18.9%, by mapping the problem to classical statistical models.

Contribution

It introduces a novel analysis of the toric code's stability under depolarization noise using mappings to classical eight-vertex models, revealing higher error thresholds.

Findings

Error threshold of 18.9% for the toric code under depolarization.

Mapping to classical models provides insights into code stability.

Topological codes show strong resilience to noise.

Abstract

The inevitable presence of decoherence effects in systems suitable for quantum computation necessitates effective error-correction schemes to protect information from noise. We compute the stability of the toric code to depolarization by mapping the quantum problem onto a classical disordered eight-vertex Ising model. By studying the stability of the related ferromagnetic phase both via large-scale Monte Carlo simulations and via the duality method, we are able to demonstrate an increased error threshold of 18.9(3)% when noise correlations are taken into account. Remarkably, this agrees within error bars with the result for a different class of codes-topological color codes-where the mapping yields interesting new types of interacting eight-vertex models.