Local Probabilistic Decoding of a Quantum Code
Local Probabilistic Decoding of a Quantum Code
复制标题
量子码的局部概率解码
作者：
T. Scruby;K. Nemoto
翻转是一个非常简单的，最大限度地局部经典解码器，已用于某些类别的经典码的巨大影响。当应用于量子编码时，存在不可修正的等重误差（例如稳定器的一半），因此先前的研究考虑了flip的修改版本，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，并提出数值证据的存在阈值翻转时，应用于一个三维环码在一个立方晶格上的环样证。这一结果可以归因于这样一个事实，即该解码器的最低权重不可纠正错误比其他不可纠正错误更接近可纠正错误（就汉明距离而言），因此它们很可能在经过额外噪声转换后的未来代码循环中变得可纠正。将随机性引入解码器可以允许它以有限概率纠正这些“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，我们观察到现象学噪声下的阈值为~ 5.5%。这与该代码最著名的阈值（∼7.1%）相当，该阈值是使用信念传播和有序统计解码[Higgott和Breuckmann， 2022]实现的，该策略的运行时为O(n3)，而不是我们本地解码器的O(n)（并行化时为O(1)）运行时。我们希望这种策略可以推广到其他低密度奇偶校验码中，并希望这些结果将促进对其他以前被忽视的解码器的研究。
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 ∼5.5% under phenomenological noise. This is comparable to the best known threshold for this code (∼7.1%) which was achieved using belief propagation and ordered statistics decoding [Higgott and Breuckmann, 2022], a strategy with a runtime of O(n3) 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.
影响因子：
16.6
作者：
Brown BJ;Nickerson NH;Browne DE
通讯作者：
Browne DE
影响因子：
4.2
作者：
Scruby T
通讯作者：
Scruby T