Fault-Tolerant Noise Guessing Decoding of Quantum Random Codes

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 (pthreshold) of approximately 2×10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> in the asymptotic limit, while considering realistic noise levels in the mentioned physical procedures.