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Quantum information can be protected from decoherence and other errors, butonly if these errors are sufficiently rare. For quantum computation to become ascalable technology, practical schemes for quantum error correction that cantolerate realistically high error rates will be necessary. In some physicalsystems, errors may exhibit a characteristic structure that can be carefullyexploited to improve the efficacy of error correction. Here, we describe ascheme for topological quantum error correction to protect quantum informationfrom a dephasing-biased error model, where we combine a repetition code with atopological cluster state. We find that the scheme tolerates error rates of upto 1.37%-1.83% per gate, requiring only short-range interactions in atwo-dimensional array.

High-threshold topological quantum error correction against biased noise