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.

翻译：本研究解决了在可行计算开销下实现容错量子随机线性码（QRLC）这一开放性问题。我们提出了一种能够处理非完美解码操作的新型量子随机线性码解码器。Cruz等人提出的初始方法仅考虑了信道误差，并假设解码器具有完美门操作。本文通过引入新的噪声猜测解码技术，在综合考虑综合征提取过程中制备误差、测量误差与门操作误差，并计及误差简并性的条件下，分析了量子随机线性码的容错特性。研究结果表明，在渐近极限下，当考虑上述物理过程中的实际噪声水平时，阈值错误率（$\pth$）约为$\pnum$。