Experimental Phase Estimation Enhanced by Machine Learning

Phase estimation protocols provide a fundamental benchmark for the field of\nquantum metrology. The latter represents one of the most relevant applications\nof quantum theory, potentially enabling the capability of measuring unknown\nphysical parameters with improved precision over classical strategies. Within\nthis context, most theoretical and experimental studies have focused on\ndetermining the fundamental bounds and how to achieve them in the asymptotic\nregime where a large number of resources is employed. However, in most\napplications it is necessary to achieve optimal precisions by performing only a\nlimited number of measurements. To this end, machine learning techniques can be\napplied as a powerful optimization tool. Here, we implement experimentally\nsingle-photon adaptive phase estimation protocols enhanced by machine learning,\nshowing the capability of reaching optimal precision after a small number of\ntrials. In particular, we introduce a new approach for Bayesian estimation that\nexhibit best performances for very low number of photons N. Furthermore, we\nstudy the resilience to noise of the tested methods, showing that the optimized\nBayesian approach is very robust in the presence of imperfections. Application\nof this methodology can be envisaged in the more general multiparameter case,\nthat represents a paradigmatic scenario for several tasks including imaging or\nHamiltonian learning.\n