Threshold of D"unnweber et al.'s quantum construction

Determine the threshold noise strength of D"unnweber et al.'s quantum extension of Gács' two-dimensional self-simulating construction.

Background

The comparison table surveys local-decoder constructions and reports threshold values where they are known. For D"unnweber et al.'s construction, the threshold has not been established, although the paper states that qualitative features suggest it may be impractically small.

A rigorous or numerical determination of this threshold would clarify whether the construction is viable at physically relevant noise rates and would enable a quantitative comparison with the local-decoder architecture developed in the paper.

References

For D"unnweber et al.'s construction, the threshold is unknown, but its value is expected to be impractically small.

— Local decoders for fault-tolerant quantum computation and translation-invariant stabilizer codes  (2609.11457 - Selub et al., 10 Sep 2026) in Table 1, caption, subsection “Comparison with prior work”