# Ultrahigh Error Threshold for Surface Codes with Biased Noise. (arXiv:1708.08474v3 [quant-ph] UPDATED)

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.