  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.
