Fault-Tolerant Noise Guessing Decoding of Quantum Random Codes
Cruz, D.
;
Monteiro, F. A.
; Roque, A. R.
; Coutinho, B.
IEEE Transactions on Quantum Engineering Vol. 6, Nº , pp. 1 - 26, August, 2025.
ISSN (print):
ISSN (online): 2689-1808
Scimago Journal Ranking: 0,94 (in 2025)
Digital Object Identifier: 10.1109/TQE.2025.3595778
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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 ($p_{threshold}$) of approximately $2 imes 10^{-5}$ in the asymptotic limit, while considering realistic noise levels in the mentioned physical procedures.
