Title: Fault-tolerant noise guessing decoding of quantum random codes Show Chinese title

Title: 量子随机码的容错噪声猜测解码

Abstract: This work addresses the open question of implementing fault-tolerant QRLCs with feasible computational overhead. We present a new decoder for quantum random linear codes (QRLCs) capable of dealing with imperfect decoding operations. A first approach, introduced by Cruz et al., only considered channel errors, and perfect gates at the decoder. Here, we analyze the fault-tolerant characteristics of QRLCs with a new noise-guessing decoding technique, when considering preparation, measurement, and gate errors in the syndrome extraction procedure, while also accounting for error degeneracy. Our findings indicate a threshold error rate ($\pth$) of approximately $\pnum$ in the asymptotic limit, while considering realistic noise levels in the mentioned physical procedures. Show Chinese abstract

Abstract: 这项工作解决了实现具有可行计算开销的容错量子随机线性码的开放问题。 我们提出了一种用于量子随机线性码（QRLCs）的新解码器，能够处理不完善的解码操作。 Cruz 等人提出的第一种方法仅考虑了信道错误，并假设解码器中的门操作是完美的。 在此，我们分析了在考虑 syndrome 提取过程中准备、测量和门错误的同时，也考虑到错误退化情况下的 QRLCs 的容错特性，采用了一种新的噪声猜测解码技术。 我们的研究结果表明，在考虑所述物理过程中的现实噪声水平时，在渐近极限下有一个阈值错误率（$\pth$）约为$\pnum$。