Suppression of non-Markovian noise by randomized compiling

Randomized compiling (RC) is a widely used tool to tailor arbitrary quantum noise channels into Pauli errors. While RC is well established, its effect on temporally correlated errors is not fully understood. Here, we make use of a recent cumulant expansion technique [1] to show that for a broad class of correlated Gaussian noise, RC reduces both the strength and temporal range of correlations. For Clifford circuits, we derive a simple analytical expression for the average gate fidelity (AGF) of randomly compiled circuits. Surprisingly, we show that the AGF is always higher than in the corresponding Markovian limit, suggesting that randomized compiling effectively leverages the temporal correlations to mitigate the effects of the noise. To lowest order, we also show that RC removes the quantum component of bath correlations, suggesting that similar mechanisms may extend to generic stationary quantum baths. These results clarify how RC mitigates memory effects and enhances circuit robustness.