Fault-Tolerant Noise Guessing Decoding of Quantum Random Codes

This work addresses the open question of implementing fault-tolerant quantum random linear codes (QRLCs) with feasible computational overhead. We present a new decoder for QRLCs capable of dealing with imperfect decoding operations. A first approach, introduced by Cruz et al. (2023), 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 (${p_{\text{threshold}}}$) of approximately ${2\times 10^{-5}}$ in the asymptotic limit, while considering realistic noise levels in the mentioned physical procedures.