Fast decoders for qudit topological codes
Fast decoders for qudit topological codes
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DOI：
10.1088/1367-2630/16/6/063038
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发表时间：
2014-06-17
影响因子：
3.3
通讯作者：
Browne, Dan E.
中科院分区：
文献类型：
--
作者：
Anwar, Hussain;Brown, Benjamin J.;Browne, Dan E.
量子位环码是对已得到充分研究的量子位环码的自然高维推广。但是，量子比特环码的标准纠错方法并不适用于它们。需要新颖的解码器。本文介绍了两种quit码的重整化群解码器，并分析了它们的纠错阈值和效率。第一个解码器是基于Bravyi和Haah （arXiv: 1112.3252）的“硬决策”解码器的泛化。我们修改了该解码器以克服限制其阈值性能的渗透效应。第二个解码器是由Poulin和Duclos-Cianci（2010物理学）提出的“软决策”解码器的推广。Rev. Lett. 104 050504)，具有较小的单元尺寸，以优化高维情况下的实现效率。在每种情况下，我们估计了不相关的比特翻转错误模型的阈值，并提供了两种方法的性能比较分析，以纠错quit环码。
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.