期刊
NEW JOURNAL OF PHYSICS
卷 16, 期 -, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1367-2630/16/6/063038
关键词
topological error correcting codes; toric code; qudits; thresholds; renormalization group decoders
资金
- Engineering and Physical Sciences Research Council [EP/K022512/1] Funding Source: researchfish
- EPSRC [EP/K022512/1] Funding Source: UKRI
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.
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