二维彩色编码的图形算法和阈值误差率
Graphical algorithms and threshold error rates for the 2d colour code
摘要：
利用拓扑纠错的容错量子计算的最近工作显示出巨大的潜力，其中2d表面码具有接近1%的阈值错误率（NJoP 9：199，2007），（arXiv：0905.0531）。然而，二维表面码需要使用复杂的状态蒸馏过程来实现通用量子计算。（PRL 97：180501，2006）的颜色代码是部分解决该问题的相关方案，提供了横向执行所有Clifford群门的手段。我们回顾了色码及其纠错方法，讨论了一种基于图匹配的近似技术。我们推导出一个分析下限的阈值错误率为6.25%的无错误的伴随式提取，而数值模拟表明，它可能高达13.3%。包含故障综合征提取电路将阈值降低到约0.1%。
英文摘要：
Recent work on fault-tolerant quantum computation making use of topological error correction shows great potential, with the 2d surface code possessing a threshold error rate approaching 1% (NJoP 9:199, 2007), (arXiv:0905.0531). However, the 2d surface code requires the use of a complex state distillation procedure to achieve universal quantum computation. The colour code of (PRL 97:180501, 2006) is a related scheme partially solving the problem, providing a means to perform all Clifford group gates transversally. We review the colour code and its error correcting methodology, discussing one approximate technique based on graph matching. We derive an analytic lower bound to the threshold error rate of 6.25% under error-free syndrome extraction, while numerical simulations indicate it may be as high as 13.3%. Inclusion of faulty syndrome extraction circuits drops the threshold to approximately 0.1%.
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