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

A key obstacle to achieve optimal control performance is the interaction between the target system and its unknown environment. Thus, obtaining a quantitative characterization of such environment is instrumental. We introduce a new framework for resource-efficient characterization and control of non-Markovian open quantum systems, which allows for the integration of given, experimentally motivated, control capabilities and constraints. This is achieved by developing a transfer filter-function formalism based on the notion of a frame and by tying the choice of frame to the available control. While recovering the standard frequency-based filter-function formalism as a special instance, this control-adapted generalization affords intrinsic flexibility and allows us to overcome limitations of existing approaches. In particular, we show how to implement quantum noise spectroscopy in the presence of non-stationary noise sources, and how to achieve control-driven model reduction for noise-tailored optimized quantum gate design.