Identify which outer codes benefit most from erasure-based error correction

Determine which families of quantum error-correcting outer codes stand to gain most significantly when enabling erasure-based error correction by concatenation with dual-rail encoded superconducting erasure qubits, including a precise comparison across candidate codes under realistic erasure-biased noise and decoder models.

Background

Erasure qubits convert dominant amplitude-damping events into heralded erasures whose locations are known, allowing decoders to correct errors more efficiently and raising thresholds for some codes. The paper reviews substantial gains for surface and Floquet codes, while studies of high-rate qLDPC codes show mixed threshold improvements but strong sub-threshold scaling benefits, indicating that performance gains depend on code details.

Because the magnitude of threshold improvement and logical error-rate reduction varies across code families (e.g., surface vs. qLDPC variants), a systematic determination of which codes benefit most from erasure-based correction is needed. This includes evaluating code-specific decoders that incorporate erasure flags, and benchmarking under realistic circuit-level noise with imperfect erasure checks.

References

We have discussed several open questions which could lead to interesting further explorations in the near term. These include the possibility of modifying hardware designs to further optimise the advantage to be gained from engineering erasure noise, discussed in section \ref{subsection:alternative-qubits}, and the unknowns regarding which codes stand to gain most significantly from enabling erasure-based error correction.

— Developments in superconducting erasure qubits for hardware-efficient quantum error correction  (2601.02183 - Violaris et al., 5 Jan 2026) in Section: Open questions and avenues for progress