Fault-Tolerant Noise Guessing Decoding of Quantum Random Codes
Diogo Cruz, Francisco A. Monteiro, André Roque, Bruno Coelho Coutinho · IEEE Transactions on Quantum Engineering · 2025
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 2×10-5in the asymptotic limit, while considering realistic noise levels in the mentioned physical procedures.