Determine whether the B-XZZX advantage persists at larger code distances

Determine whether the relative logical-error-rate advantage of the bordered XZZX (B-XZZX) code over the XZZX surface code continues to increase, remains constant, or decreases beyond code distance 11 under the HBD-SI1000 circuit-level noise model.

Background

The authors report that B-XZZX outperforms XZZX increasingly from distance 3 through distance 11 under the HBD-SI1000 noise model. However, the improvement flattens between distances 9 and 11, and the logical error rate becomes increasingly expensive to estimate at still larger distances.

Because a similar flattening occurred between distances 3 and 5, the observed data do not establish the asymptotic behavior. The authors explicitly leave unresolved whether the advantage will continue increasing or eventually decline.

References

We note that the improvement over XZZX flattens out between $d=9$ and $d=11$ and could potentially decrease after this point; however, the same thing was observed between $d=3$ and $d=5$ making it hard to conclude anything definitively.

— Decoder- and Noise-Aware Optimization Framework for Clifford-Deformed Quantum Error-Correcting Codes  (2610.13589 - Bønnelykke et al., 9 Oct 2026) in Section 4.2, “Generalization to larger codes”