论文标题
量子代码的局部概率解码
Local Probabilistic Decoding of a Quantum Code
论文作者
论文摘要
FLIP是一种非常简单且最大的本地古典解码器,在某些类别的经典代码中已使用极大的影响。当应用于量子代码时,对于该解码器而言是不可纠正的恒定重量误差(例如一半的稳定器),因此以前的研究考虑了修改版本的翻转版本,有时与其他解码器结合使用。我们认为,这可能并不总是必要的,并且在将三维曲折代码的环状综合症应用于立方晶格上的环状综合症时,提供了数值证据。该结果可以归因于以下事实:该解码器的最低重量不可纠正的错误(就锤距距离而言)比可更正的错误要比其他不可纠正的错误更接近(在锤距离距离方面),因此在转换后通过其他噪声转换后的代码周期,它们可能会在未来的代码周期中更正。将随机性引入解码器可以使其能够以有限的概率纠正这些“不可纠正的”错误,并且对于使用信念传播和概率翻转组合的解码策略,我们观察到$ \ sim5.5 \%$在现象学噪声下的阈值。 This is comparable to the best known threshold for this code ($\sim7.1\%$) which was achieved using belief propagation and ordered statistics decoding [Higgott and Breuckmann, 2022], a strategy with a runtime of $O(n^3)$ as opposed to the $O(n)$ ($O(1)$ when parallelised) runtime of our local decoder.我们预计该策略可以推广到其他低密度奇偶校验检查代码中,并希望这些结果能促使对其他以前被忽视的解码器进行调查。
flip is an extremely simple and maximally local classical decoder which has been used to great effect in certain classes of classical codes. When applied to quantum codes there exist constant-weight errors (such as half of a stabiliser) which are uncorrectable for this decoder, so previous studies have considered modified versions of flip, sometimes in conjunction with other decoders. We argue that this may not always be necessary, and present numerical evidence for the existence of a threshold for flip when applied to the looplike syndromes of a three-dimensional toric code on a cubic lattice. This result can be attributed to the fact that the lowest-weight uncorrectable errors for this decoder are closer (in terms of Hamming distance) to correctable errors than to other uncorrectable errors, and so they are likely to become correctable in future code cycles after transformation by additional noise. Introducing randomness into the decoder can allow it to correct these "uncorrectable" errors with finite probability, and for a decoding strategy that uses a combination of belief propagation and probabilistic flip we observe a threshold of $\sim5.5\%$ under phenomenological noise. This is comparable to the best known threshold for this code ($\sim7.1\%$) which was achieved using belief propagation and ordered statistics decoding [Higgott and Breuckmann, 2022], a strategy with a runtime of $O(n^3)$ as opposed to the $O(n)$ ($O(1)$ when parallelised) runtime of our local decoder. We expect that this strategy could be generalised to work well in other low-density parity check codes, and hope that these results will prompt investigation of other previously overlooked decoders.