Ultrahigh Error Threshold for Surface Codes with Biased Noise

TL;DR

This paper demonstrates that a modified surface code tailored for biased noise with dominant dephasing errors achieves a significantly higher error threshold, approaching theoretical limits, by adjusting stabilizer measurements.

Contribution

It introduces a simple modification to the surface code that greatly enhances error thresholds under biased noise, using only local measurements and a tensor network decoder.

Findings

Achieves a 43.7% threshold under pure dephasing noise.

Maintains high thresholds (28.2%) at realistic noise bias ratios.

Thresholds are near the hashing bound across bias regimes.

Abstract

We show that a simple modification of the surface code can exhibit an enormous gain in the error correction threshold for a noise model in which Pauli Z errors occur more frequently than X or Y errors. Such biased noise, where dephasing dominates, is ubiquitous in many quantum architectures. In the limit of pure dephasing noise we find a threshold of 43.7(1)% using a tensor network decoder proposed by Bravyi, Suchara and Vargo. The threshold remains surprisingly large in the regime of realistic noise bias ratios, for example 28.2(2)% at a bias of 10. The performance is in fact at or near the hashing bound for all values of the bias. The modified surface code still uses only weight-4 stabilizers on a square lattice, but merely requires measuring products of Y instead of Z around the faces, as this doubles the number of useful syndrome bits associated with the dominant Z errors. Our results demonstrate that large efficiency gains can be found by appropriately tailoring codes and decoders to realistic noise models, even under the locality constraints of topological codes.