Single-shot error correction on toric codes with high-weight stabilizers

TL;DR

This paper demonstrates that single-shot error correction with high-weight stabilizers can achieve a sustainable threshold in toric codes under noisy measurements, outperforming conventional methods in certain error models.

Contribution

The authors implement single-shot check operators for toric codes using Gaussian elimination, achieving a threshold of 5.62% and analyzing their performance under different error models.

Findings

Single-shot checks yield a threshold of 5.62% with noisy measurements.

High-weight stabilizers can be constructed via Gaussian elimination.

Single-shot methods outperform traditional repeated measurements in specific noise models.

Abstract

For quantum error correction codes the required number of measurement rounds typically increases with the code distance when measurements are faulty. Single-shot error correction allows for an error threshold with only one round of noisy syndrome measurements regardless of the code size. Here we implement single-shot check operators for toric codes. The single-shot checks are constructed by Gaussian elimination following Campbell [Campbell, 2019]. The single-shot check operators result in a sustainable threshold at 5.62% for an error model with noisy measurements, outperforming the conventional toric code check operators with multiple rounds of noisy measurement. The cost of the transformation is non-local high-weight stabilizer generators. We then consider a gate-based error model that leads to increased measurement error with stabilizer weight. Here we find no single-shot threshold behavior and instead find the code family will have an optimal code size for a fixed error rate. For this error model, the conventional check operators with multiple measurements yields a lower logical error rate.