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The advantage of quantum metrology has been experimentally demonstrated forphase estimations where the dynamics are commuting. General noncommutingdynamics, however, can have distinct features. For example, the directsequential scheme, which can achieve the Heisenberg scaling for the phaseestimation under commuting dynamics, can have even worse performances than theclassical scheme under noncommuting dynamics. Here we realize a scalableoptimally controlled sequential scheme, which can achieve the Heisenbergprecision under general noncommuting dynamics. We also present an intuitivegeometrical framework for the controlled scheme and identify sweet spots intime at which the optimal controls used in the scheme can be pre-fixed withoutadaptation, which simplifies the experimental protocols significantly. Wesuccessfully implement the scheme up to eight controls in an optical platform,demonstrate a precision near the Heisenberg limit. Our work opens the avenuefor harvesting the power of quantum control in quantum metrology, and providesa control-enhanced recipe to achieve the Heisenberg precision under generalnoncommuting dynamics.

Control-enhanced sequential scheme for general quantum parameter estimation at the Heisenberg limit