Fault-tolerant noise guessing decoding of quantum random codes

TL;DR

This paper introduces a fault-tolerant noise-guessing decoding method for quantum random linear codes, effectively handling various physical errors and achieving a significant error threshold in realistic conditions.

Contribution

It presents a novel decoding technique for QRLCs that accounts for preparation, measurement, and gate errors, extending previous work limited to channel errors and perfect gates.

Findings

Achieves an error threshold of approximately 1% in the asymptotic limit.

Demonstrates robustness of QRLCs under realistic noise conditions.

Extends decoding strategies to include preparation, measurement, and gate errors.

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.