  In a standard Quantum Sensing (QS) task one aims at estimating an unknown
parameter $\theta$, 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 system response $\mathcal{R}(\theta)$ (i.e.,
changes in the measurement outcomes). For simple cases the form of
$\mathcal{R}(\theta)$ is known, but the same cannot be said for realistic
scenarios, as no general closed-form expression exists. In this work we present
an inference-based scheme for QS. We show that, for a general class of unitary
families of encoding, $\mathcal{R}(\theta)$ can be fully characterized by only
measuring the system response at $2n+1$ parameters. This allows us to infer the
value of an unknown parameter given the measured response, as well as to
determine the sensitivity of the scheme, which characterizes its overall
performance. We show that inference error is, with high probability, smaller
than $\delta$, if one measures the system response with a number of shots that
scales only as $\Omega(\log^3(n)/\delta^2)$. Furthermore, the framework
presented can be broadly applied as it remains valid for arbitrary probe states
and measurement schemes, and, even holds in the presence of quantum noise. We
also discuss how to extend our results beyond unitary families. Finally, to
showcase our method we implement it for a QS task on real quantum hardware, and
in numerical simulations.
