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Media type:
E-Article
Title:
Efficient color code decoders in d≥2 dimensions from toric code decoders
Contributor:
Kubica, Aleksander;
Delfosse, Nicolas
Published:
Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, 2023
Published in:
Quantum, 7 (2023), Seite 929
Language:
English
DOI:
10.22331/q-2023-02-21-929
ISSN:
2521-327X
Origination:
Footnote:
Description:
We introduce an efficient decoder of the color code in d≥2 dimensions, the Restriction Decoder, which uses any d-dimensional toric code decoder combined with a local lifting procedure to find a recovery operation. We prove that the Restriction Decoder successfully corrects errors in the color code if and only if the corresponding toric code decoding succeeds. We also numerically estimate the Restriction Decoder threshold for the color code in two and three dimensions against the bit-flip and phase-flip noise with perfect syndrome extraction. We report that the 2D color code threshold p2D≈10.2% on the square-octagon lattice is on a par with the toric code threshold on the square lattice.