Resource-efficient digital characterization and control of classical non-Gaussian noise

We show the usefulness of frame-based characterization and control [PRX Quantum 2, 030315 (2021)] for non-Markovian open quantum systems subject to classical non-Gaussian dephasing. By focusing on the paradigmatic case of random telegraph noise and working in a digital window frame, we demonstrate how to achieve higher-order control-adapted spectral estimation for noise-optimized dynamical decoupling design. We find that, depending on the operating parameter regime, control that is optimized based on non-Gaussian noise spectroscopy can substantially outperform standard Walsh decoupling sequences as well as sequences that are optimized based solely on Gaussian noise spectroscopy. This approach is also intrinsically more resource-efficient than frequency-domain comb-based methods.