TY - JOUR AV - public TI - Fast decoders for qudit topological codes SN - 1367-2630 Y1 - 2014/06/17/ ID - discovery1417667 UR - http://dx.doi.org/10.1088/1367-2630/16/6/063038 EP - 37 N2 - Qudit toric codes are a natural higher-dimensional generalization of the well-studied qubit toric code. However, standard methods for error correction of the qubit toric code are not applicable to them. Novel decoders are needed. In this paper we introduce two renormalization group decoders for qudit codes and analyse their error correction thresholds and efficiency. The first decoder is a generalization of a 'hard-decisions' decoder due to Bravyi and Haah (arXiv:1112.3252). We modify this decoder to overcome a percolation effect which limits its threshold performance for many-level quantum systems. The second decoder is a generalization of a 'soft-decisions' decoder due to Poulin and Duclos-Cianci (2010 Phys. Rev. Lett. 104 050504), with a small cell size to optimize the efficiency of implementation in the high dimensional case. In each case, we estimate thresholds for the uncorrelated bit-flip error model and provide a comparative analysis of the performance of both these approaches to error correction of qudit toric codes. N1 - © 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. http://creativecommons.org/licenses/by/3.0/ VL - 16 KW - Topological error correcting codes KW - toric code KW - qudits KW - thresholds KW - renormalization group decoders KW - Tolerant Quantum Computation KW - Error-correction KW - Gauge-theory KW - Memory JF - New Journal of Physics PB - IOP PUBLISHING LTD A1 - Anwar, H A1 - Brown, BJ A1 - Campbell, ET A1 - Browne, DE ER -