  Quantum metrology plays a fundamental role in many scientific areas. However,
the complexity of engineering entangled probes and the external noise raise
technological barriers for realizing the expected precision of the
to-be-estimated parameter with given resources. Here, we address this problem
by introducing adjustable controls into the encoding process and then utilizing
a hybrid quantum-classical approach to automatically optimize the controls
online. Our scheme does not require any complex or intractable off-line design,
and it can inherently correct certain unitary errors during the learning
procedure. We also report the first experimental demonstration of this
promising scheme for the task of finding optimal probes for frequency
estimation on a nuclear magnetic resonance (NMR) processor. The proposed scheme
paves the way to experimentally auto-search optimal protocol for improving the
metrology precision.
