  We present a hybrid quantum-classical variational scheme to enhance precision
in quantum metrology. In the scheme, both the initial state and the measurement
basis in the quantum part are parameterized and optimized via the classical
part. It enables the maximization of information gained about the measured
quantity. We discuss specific applications to 3D magnetic field sensing under
several dephasing noise modes. Indeed, we demonstrate its ability to
simultaneously estimate all parameters and surpass the standard quantum limit,
making it a powerful tool for metrological applications.
