Learning response functions: a data-driven framework for quantum sensing.

Quantum Sensing (QS) is a blossoming field of research and a key use case for practical quantum technologies. In standard QS tasks one aims at estimating an unknown parameter encoded into an n-qubit probe state, via measurements of the system.

The success of this task hinges on the ability to correlate changes in the parameter to changes in the measurement outcomes. For simple cases, such as an idealized magnetometry experiment, the functional form of the system response is well-known. However, the same cannot be said for realistic scenarios as the explicit functional form may not be accessible and would require full device characterization. In this work, we present a novel data-driven inference approach to recover the true response of the system in an efficient and scalable manner. We provide rigorous theoretical guarantees for the performance of our framework, which we verify with numerical simulations and experiments on IBM quantum computers.