@article{discovery1494042,
           title = {Qudit color codes and gauge color codes in all spatial dimensions},
            year = {2015},
            note = {This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions.},
          volume = {92},
           month = {August},
          number = {2},
       publisher = {AMER PHYSICAL SOC},
         journal = {Physical Review A},
        abstract = {The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant
quantum computation. A fault-tolerant decoder is a vital part of the error correction process-it is the algorithm
which computes the operations needed to correct or compensate for the errors according to the measured
syndrome, even when the measurement itself is error prone. Previously decoders based on minimum-weight
perfect matching have been studied. However, these are not immediately generalizable from qubit to qudit codes.
In this work, we develop a fault-tolerant decoder for the surface code, capable of efficient operation for qubits
and qudits of any dimension, generalizing the decoder first introduced by Bravyi and Haah [Phys. Rev. Lett. 111,
200501 (2013)]. We study its performance when both the physical qudits and the syndromes measurements are
subject to generalized uncorrelated bit-flip noise (and the higher-dimensional equivalent). We show that, with
appropriate enhancements to the decoder and a high enough qudit dimension, a threshold at an error rate of more
than 8\% can be achieved.},
             url = {http://doi.org/10.1103/PhysRevA.92.022312},
            issn = {1094-1622},
          author = {Watson, FHE and Campbell, ET and Anwar, H and Browne, DE}
}