Label and Recover Coherent Errors: Randomized Compiling Does Not Destroy Coherent-Error Information
arXiv:2607.26756
The paper shows that the random gate choices (labels) used in randomized compiling retain full information about coherent gate errors, and by correlating these labels with measurement outcomes one can recover coherent‑error parameters at the quantum Fisher‑information limit without extra circuit overhead.
Abstract
Randomized compiling (RC) is the standard technique for converting coherent (systematic) gate errors into stochastic noise. The prevailing view is that the twirl destroys coherent-error information. An exact Fisher-information conservation law shows the opposite: the coherent-error information RC removes from the averaged output is preserved in full in the twirl labels -- the per-shot random gate choices that standard RC discards. Retaining the labels and forming a label-outcome correlation recovers the coherent error parameters at the quantum Fisher-information limit, unbiased under all standard incoherent channels, at zero additional circuit cost. Two theorems are proved, the conservation law is verified to machine precision across 12 circuit families, and recovery is confirmed on a 127-qubit IBM Quantum processor (ibm_marrakesh). The labeled estimator recovers injected coherent phases to within 0.0063 rad of the true value across all depths tested, while the standard marginal estimator returns near-zero signal at every depth.
3 pages, 1 figure, 1 table