Title: Scalable accuracy gains from postselection in quantum error correcting codes Show Chinese title

Title: 量子纠错码中后选择带来的可扩展精度提升

Abstract: Decoding stabilizer codes such as the surface and toric codes involves evaluating free-energy differences in a disordered statistical mechanics model, in which the randomness comes from the observed pattern of error syndromes. We study the statistical distribution of logical failure rates across observed syndromes in the toric code, and show that, within the coding phase, logical failures are predominantly caused by exponentially unlikely syndromes. Therefore, postselecting on not seeing these exponentially unlikely syndrome patterns offers a scalable accuracy gain. In general, the logical error rate can be suppressed from $p_f$ to $p_f^b$, where $b \geq 2$ in general; in the specific case of the toric code with perfect syndrome measurements, we find numerically that $b = 3.1(1)$. Our arguments apply to general topological stabilizer codes, and can be extended to more general settings as long as the decoding failure probability obeys a large deviation principle. Show Chinese abstract

Abstract: 解码如表面码和环面码这样的稳定子码涉及在无序统计力学模型中评估自由能差异，其中随机性来自于观测到的误差伴随式模式。 我们研究了环面码中观测到的伴随式逻辑故障率的统计分布，并表明在编码相内，逻辑故障主要由指数上不可能的伴随式引起。 因此，对未看到这些指数上不可能的伴随式模式进行后选择可以提供可扩展的精度提升。 一般来说，逻辑错误率可以从$p_f$降低到$p_f^b$，其中$b \geq 2$一般成立；在完美伴随式测量的环面码特定情况下，我们数值上发现$b = 3.1(1)$。 我们的论证适用于一般的拓扑稳定子码，并且只要解码失败概率满足大偏差原理，就可以扩展到更一般的设置。