Photonic quantum metrology with variational quantum optical non-linearities

Photonic quantum metrology harnesses quantum states of light to measure unknown parameters beyond classical precision limits. Current protocols suffer from two severe limitations that preclude their scalability: the exponential decrease in fidelities when generating states with large photon numbers due to gate errors, and the increased sensitivity of such states to noise. Here, we develop a deterministic protocol combining quantum optical non-linearities and variational quantum algorithms that provides a substantial improvement on both fronts. The key idea of such hybrid algorithm is to use a classical optimizer to find the set of parameters of a parametrized quantum circuit implemented on the hardware such that it generates states maximizing the quantum Fisher information. Our main result is the generation of metrologically-relevant states with a small number of operations which does not depend on photon-number, resulting in exponential improvements in fidelities when gate errors are considered. On top of that, we show that such states offer a better robustness to noise compared to other states considered noise-resilient.