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arXiv · 2407.01658

Fault-tolerant noise guessing decoding of quantum random codes

Diogo Cruz·Francisco A. Monteiro·André Roque·Bruno C. Coutinho
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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 ($\pth$) of approximately $\pnum$ in the asymptotic limit, while considering realistic noise levels in the mentioned physical procedures.

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Diogo Cruz, Francisco A. Monteiro, André Roque, Bruno C. Coutinho. 2024-07-01. Fault-tolerant noise guessing decoding of quantum random codes. https://arxiv.org/abs/2407.01658

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