Explain the increasing performance advantage of the B-XZZX code

Explain why the bordered XZZX (B-XZZX) surface code’s performance advantage over the XZZX surface code increases with code distance under the HBD-SI1000 circuit-level noise model, despite both logical-X and logical-Z errors remaining constructible with a single non-Z error and (d) Z-errors.

Background

The paper introduces the bordered XZZX (B-XZZX) code as a boundary-modified version of the XZZX surface code. Under the HBD-SI1000 circuit-level noise model, B-XZZX exhibits an increasing relative performance advantage over XZZX as the code distance grows, although the modification affects only a diminishing fraction of qubits.

The authors compare this behavior with known boundary modifications of the XY code. They argue that the mechanism identified for the XY code does not explain B-XZZX, because both a logical-X error and a logical-Z error remain constructible using one non-Z error together with d-1 Z-errors. The distance-dependent performance improvement therefore remains unresolved.

References

Thus, the increasing performance of the B-XZZX code over XZZX as the code distance $d$ increases remains unexplained.

— 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, “Discussion and outlook,” immediately following the discussion of boundary modifications to the XY code