Impact of thermal excitations on fault-tolerant syndrome extraction

Quantify the impact of thermal excitations in the gain-engineered transmon ancilla on the logical-qubit backaction and ancilla error-detection infidelity during fault-tolerant syndrome extraction.

Background

The simulations of the gain-engineered transmon as an ancilla for binomial, four-legged cat, and GKP bosonic codes omit dephasing noise and thermal excitations in order to isolate the effect of relaxation. The paper argues that dephasing is comparatively manageable because its operator commutes with the ancilla–logical-qubit interaction, whereas thermal excitations do not commute with that interaction. Thermal excitation events may therefore propagate to the logical qubit and increase both the ancilla error-detection infidelity and the logical-qubit measurement backaction. A quantitative treatment of these effects remains unresolved in the presented analysis.

References

Thermal excitations, by contrast, generate errors that do not commute with $V$ and could increase both $E$ and $B$. Quantifying their impact is an important direction for future work.

— The Gain-Engineered Transmon  (2608.26018 - Yang et al., 26 Aug 2026) in Supplementary Information, Section VI, Subsection “Discussion and limitations” (Subsubsection \ref{subsubsec:ancilla_discussion})