Optimal Decoder for the Error Correcting Parity Code
Abstract
We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings. For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes while yielding near-optimal decoding for intermediate code sizes and achieving optimality in the limit of large codes. In the regime of unreliable measurements, the decoder demonstrates fault-tolerant thresholds above 5% at the cost of decoding a series of independent repetition codes in (1 + 1) dimensions. Such high thresholds, in conjunction with a practical decoder, efficient long-range logical gates, and suitability for planar implementation, position the parity architecture as a promising candidate for demonstrating quantum advantage on qubit platforms with strong noise bias.
Cite
@article{arxiv.2505.05210,
title = {Optimal Decoder for the Error Correcting Parity Code},
author = {Konstantin Tiurev and Christophe Goeller and Leo Stenzel and Paul Schnabl and Anette Messinger and Michael Fellner and Wolfgang Lechner},
journal= {arXiv preprint arXiv:2505.05210},
year = {2025}
}