Efficient learning and optimizing non-Gaussian correlated noise in digitally controlled qubit systems

Precise qubit control in the presence of spatio-temporally correlated noise is pivotal for transitioning to fault-tolerant quantum computing. Generically, such noise can also have non-Gaussian statistics, which hampers existing non-Markovian noise spectroscopy protocols. By utilizing frame-based characterization and a novel symmetry analysis, we show how to achieve higher-order spectral estimation for noise-optimized circuit design. Remarkably, we find that the digitally driven qubit dynamics can be solely determined by the complexity of the applied control, rather than the non-perturbative nature of the non-Gaussian environment. This enables us to address certain non-perturbative qubit dynamics more simply. We delineate several complexity bounds for learning such high-complexity noise and demonstrate our single and two-qubit digital characterization and control using a series of numerical simulations. Our results not only provide insights into the exact solvability of (small-sized) open quantum dynamics but also highlight a resource-efficient approach for optimal control and possible error reduction techniques for current qubit devices.