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Fast decoders for qudit topological codes

Anwar, H; Brown, BJ; Campbell, ET; Browne, DE; (2014) Fast decoders for qudit topological codes. New Journal of Physics , 16 , Article 063038. 10.1088/1367-2630/16/6/063038. Green open access

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Abstract

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.

Type: Article
Title: Fast decoders for qudit topological codes
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/1367-2630/16/6/063038
Publisher version: http://dx.doi.org/10.1088/1367-2630/16/6/063038
Language: English
Additional information: © 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/
Keywords: Topological error correcting codes, toric code, qudits, thresholds, renormalization group decoders, Tolerant Quantum Computation, Error-correction, Gauge-theory, Memory
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy
URI: https://discovery.ucl.ac.uk/id/eprint/1417667
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