Symmetry in Multi-Qubit Correlated Noise Errors Enhances Surface Code Thresholds

TL;DR

This paper analyzes how symmetry in correlated noise errors, especially along straight lines, can improve the error threshold of surface codes, aiding more robust quantum circuit design.

Contribution

It provides an analytical threshold for surface codes under correlated noise and highlights the positive impact of error symmetry on error thresholds.

Findings

Errors correlated along straight lines increase thresholds due to symmetry.

Symmetry in correlated errors enhances surface code robustness.

Analytical thresholds are derived for various correlated error types.

Abstract

Surface codes are promising for practical quantum error correction due to their high threshold and experimental feasibility. However, their performance under realistic noise conditions, particularly those involving correlated errors, requires further investigation. In this study, we investigate the impact of correlated errors on the error threshold. In particular, we focus on several distinct types of correlated errors that could potentially arise from next-nearest-neighbor (NNN) coupling in quantum systems. We present the analytical threshold of the surface code under these types of correlated noise, and find that errors correlated along straight lines possess a type of crucial symmetry, resulting in higher thresholds compared to other types of correlated errors. This deepens our insight into the threshold of surface code and hence facilitates a more robust design of quantum circuits with a higher noise threshold.