论文标题
保护定律和量子误差校正：朝向广义匹配解码器
Conservation laws and quantum error correction: towards a generalised matching decoder
论文作者
论文摘要
解码算法对于耐故障量子计算架构至关重要。从这个角度来看，我们探索了表面代码的解码算法。典型的量子低密度奇迹检查代码是许多领先的努力，以证明可扩展的量子计算。我们讨论的核心是最小重量匹配的解码器。解码器通过利用由于表面代码稳定元件之间实现的对称性而产生的基础结构来起作用。通过专注于这些对称性，我们开始解决一个问题，即如何将最小重量匹配的解码器推广到其他代码家族。我们首先通过调查其他代码的匹配解码器的示例来解决这个问题。其中包括已专门用于校正噪声模型的解码算法，这些噪声模型证明了有关某些代码的特定结构或偏差。除此之外，我们还提出了一种系统的方法，用于为具有某些特征性能的代码构建最小重量匹配的解码器。我们使用的属性在拓扑代码中很常见。我们讨论了该提案的更广泛的适用性，并提出了一些可以解决的问题，可能会向我们展示如何为任意稳定器代码设计通用的匹配解码器。
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the leading efforts to demonstrate scalable quantum computing. Central to our discussion is the minimum-weight perfect-matching decoder. The decoder works by exploiting underlying structure that arises due to materialised symmetries among surface-code stabilizer elements. By concentrating on these symmetries, we begin to address the question of how a minimum-weight perfect-matching decoder might be generalised for other families of codes. We approach this question first by investigating examples of matching decoders for other codes. These include decoding algorithms that have been specialised to correct for noise models that demonstrate a particular structure or bias with respect to certain codes. In addition to this, we propose a systematic way of constructing a minimum-weight perfect-matching decoder for codes with certain characteristic properties. The properties we make use of are common among topological codes. We discuss the broader applicability of the proposal, and we suggest some questions we can address that may show us how to design a generalised matching decoder for arbitrary stabilizer codes.
