Establish the optimal distance-5 Clifford deformation under HBD noise

Establish whether the XZZX Clifford deformation is globally optimal among the distance-5 surface-code Clifford deformations under the HBD circuit-level noise model with the PyMatching decoder.

Background

For the distance-5 surface code under HBD noise, Evolution-Based Best-arm Identification (EBBI) repeatedly reaches the XZZX deformation, and neither EBBI nor random search finds a better Clifford deformation within the explored candidates.

The paper does not perform an exhaustive search over the exponentially large distance-5 deformation space. Consequently, the claim that XZZX is optimal is based on the search results and remains tentative rather than established.

References

Under HBD noise, the EBBI median reaches the XZZX deformation for all three $p_\mathrm{search}$ settings [Fig.~\ref{fig:Results}b]; we believe it to be optimal, as no CD explored by EBBI or random search beats it.

— Decoder- and Noise-Aware Optimization Framework for Clifford-Deformed Quantum Error-Correcting Codes  (2610.13589 - Bønnelykke et al., 9 Oct 2026) in Section 4.1, “Performance”