  Harnessing quantum correlations can enable sensing beyond the classical
limits of precision, with the realization of such sensors poised for
transformative impacts across science and engineering. Real devices, however,
face the accumulated impacts of noise effects, architecture constraints, and
finite sampling rates, making the design and success of practical quantum
sensors challenging. Numerical and theoretical frameworks that support the
optimization and analysis of imperfections from one end of a sensing protocol
through to the other (i.e., from probe state preparation through to parameter
estimation) are thus crucial for translating quantum advantage into widespread
practice. Here, we present an end-to-end variational framework for quantum
sensing protocols, where parameterized quantum circuits and neural networks
form trainable, adaptive models for quantum sensor dynamics and estimation,
respectively. The framework is general and can be adapted towards arbitrary
qubit architectures, as we demonstrate with experimentally-relevant ans\"atze
for trapped-ion and photonic systems, and enables to directly quantify the
impacts that noisy state preparation/measurement and finite data sampling have
on parameter estimation. End-to-end variational frameworks can thus underpin
powerful design and analysis tools for realizing quantum advantage in
practical, robust sensors.
