Frame-Based Filter-Function Formalism for Quantum Characterization and Control

We introduce a theoretical framework for resource-efficient characterization and control of non-Markovian open quantum systems, which naturally allows the integration given, experimentally motivated, capabilities constraints. This is achieved by developing transfer filter-function formalism based on general notion frame appropriately tying choice to available control. While recovering standard frequency-based as special instance, this control-adapted generalization affords intrinsic flexibility and, crucially, it permits an efficient representation relevant matrix elements dynamical integrals if appropriate finite-size condition obeyed. Our frame-based formulation overcomes important limitations existing approaches. In particular, we show how implement noise spectroscopy in presence nonstationary sources, effectively achieve control-driven model reduction noise-optimized prediction gate design.