Precise environmental-noise characterization in open quantum systems is a key step toward high-fidelity quantum control and targeted decoherence suppression in computing and sensing applications. Nonparametric quantum noise spectroscopy (QNS) provides a general-purpose, model-agnostic framework for estimating the spectral properties of an environment. The ability to perform such protocols under realistic constraints is key to their practical applicability. Notably, it is important to account for control constraints and understand how they limit the ability to learn about noise correlations as experiment-agnostic objects. We show how adopting a control-centric point of view allows one to recast the noise spectroscopy problem in such a way that (i) the central objects are now the time-ordered polyspectra and (ii) control filter functions are no longer encumbered by time ordering. In particular, we show that this approach enables the generalization of frequency-comb QNS protocols to arbitrary control scenarios without introducing additional control symmetries that remove time ordering from filter functions, improving estimation in typically pathological scenarios. We demonstrate the targeted reconstruction of the time-ordered polyspectra across classical Gaussian and quantum non-Gaussian environments via simulations.

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• Open quantum systems & decoherence
• Quantum control
• Qubits
• Spectroscopy