Decoding color codes by projection onto surface codes

Nicolas Delfosse (1, 2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 GRACE - Geometry, arithmetic, algorithms, codes and encryption

We propose a new strategy to decode color codes, which is based on the projection of the error onto three surface codes. This provides a method to transform every decoding algorithm of surface codes into a decoding algorithm of color codes. Applying this idea to a family of hexagonal color codes, with the perfect matching decoding algorithm for the three corresponding surface codes, we find a phase error threshold of approximately 8.7%. Finally, our approach enables us to establish a general lower bound on the error threshold of a family of color codes depending on the threshold of the three corresponding surface codes. These results are based on a chain complex interpretation of surface codes and color codes.

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Physique Quantique [quant-ph]

Nicolas Delfosse. Decoding color codes by projection onto surface codes. Physical Review A : Atomic, molecular, and optical physics [1990-2015], 2014, 89, pp.012317. ⟨10.1103/PhysRevA.89.012317⟩. ⟨hal-00855003⟩