Efficient decoding schemes for the XYZ² hexagonal stabilizer code

The XYZ² code is a topological stabilizer code on a honeycomb lattice which demonstrates high thresholds and highly suppressed logical failure rates for Z-biased noise using maximum-likelihood decoding, under the assumption of perfect stabilizer measurements. The code is equivalent to a concatenation of a low-level two-qubit error detection code, and a high-level YZZY-type surface code. In this work, we investigate an efficient two-step decoding algorithm that uses the concatenated structure of the code with a minimum-weight perfect matching decoder in order to study its behaviour under biased noise error models. We demonstrate that the matching decoder achieves close to optimal performance for certain noise models.