Clifford-Deformed Compass Codes

We can make more efficient quantum error-correcting codes by tailoring them to the noise models of quantum computing architectures. In this work, we create codes that can correct biased dephasing errors commonly observed in experiments by combining Clifford deformations and appropriate gauge fixing of compass codes. Clifford deformations and gauge fixing are tools we can use to modify codes while preserving the desirable qualities of the original code. For example, Clifford deformed codes such as the XZZX and XY surface codes achieve high thresholds under noise models biased toward dephasing errors. Compass code stabilizers are obtained through gauge fixing of the two body interaction terms of the compass model Hamiltonian, and they can be chosen to get more information on high-rate errors. The resulting codes have thresholds that increase with bias and can exhibit lower logical error rates, particularly at low physical error rates.