# Fault-tolerant thresholds for the surface code in excess of 5% under biased noise

## TL;DR

This paper presents a high-threshold decoder for the surface code tailored to biased noise, achieving fault-tolerance thresholds over 5%, significantly improving quantum error correction under realistic noise conditions.

## Contribution

Introduction of an efficient, bias-aware surface code decoder that exploits syndrome symmetries and extends to fault-tolerant regimes with measurement errors.

## Key findings

- Fault-tolerance threshold exceeds 6% under biased noise.
- Threshold remains above 5% with realistic noise bias levels.
- Decoder exploits noise symmetries for improved performance.

## Abstract

Noise in quantum computing is countered with quantum error correction. Achieving optimal performance will require tailoring codes and decoding algorithms to account for features of realistic noise, such as the common situation where the noise is biased towards dephasing. Here we introduce an efficient high-threshold decoder for a noise-tailored surface code based on minimum-weight perfect matching. The decoder exploits the symmetries of its syndrome under the action of biased noise and generalises to the fault-tolerant regime where measurements are unreliable. Using this decoder, we obtain fault-tolerant thresholds in excess of $6\%$ for a phenomenological noise model in the limit where dephasing dominates. These gains persist even for modest noise biases: we find a threshold of $\sim 5\%$ in an experimentally relevant regime where dephasing errors occur at a rate one hundred times greater than bit-flip errors.