Recovering Coherent Errors from Randomized-Compiling Labels

Abstract

Randomized compiling converts a coherent gate error into a stochastic one by dressing each gate with a randomly chosen Pauli operator, and the standard view is that the coherent information is lost once outcomes are averaged over these random choices. This is incorrect: an exact Fisher-information identity shows that the averaged data and the correlation between the outcome and the random choice, the twirl label, together conserve the full information, and only the label is normally discarded. Retaining it turns an unmodified randomized-compiling run into an unbiased estimator for the coherent error, at no added circuit cost, valid under realistic decoherence and at any circuit depth. The same construction extends to coupling between qubits through two further mechanisms: a neighboring qubit prepared in a known, randomized state probes static coupling, and randomizing the pulse count used to prepare that state isolates a second, physically distinct leakage effect found unexpectedly on real hardware during this work. All three results are derived exactly, checked against closed-form oracles, and tested on a 127-qubit IBM processor. The single-qubit case is confirmed cleanly: an injected phase is recovered to 0.006~rad while the same data without labels shows no signal. The two-qubit extensions are validated at the level of the recovery circuit, with clean positive controls on hardware, though the coupling strengths themselves remain below the resolution of the shot budgets used here.