Variational quantum metrology for multiparameter estimation under noise

We introduce a hybrid quantum-classical variational approach designed to elevate 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. This integrated approach facilitates the maximization of information acquired regarding the measured quantity. We explore its practical applications in the context of 3D magnetic field sensing, accounting for various dephasing noise scenarios. Our results showcase its capacity to simultaneously estimate all relevant parameters, surpassing the constraints of the standard quantum limit. This innovation emerges as a robust and invaluable tool for a wide range of metrological applications.