Quantum metrology promises measurement precision beyond the classical limit by using suitably tailored quantum states and detection strategies. However, scaling up this advantage is experimentally challenging, due to the difficulty of generating high-quality large-scale probes. Here, we build a photonic setup that achieves enhanced precision scaling by manipulating the probe’s dynamics through operations performed in a coherently controlled order. Our setup applies an unknown rotation and a known orbital angular momentum increase in a coherently controlled order, in a way that reproduces a hybrid quantum switch involving gates generated by both discrete and continuous variables. The unknown rotation angle $\theta$ is measured with precision scaling as $1/4ml$ when a photon undergoes a rotation of $2m\theta$ and an angular momentum shift of $2l\hslash$. With a practical enhancement factor as high as 2317, we achieve a normalized precision of approximately equal to ${10}^{-4}$ rad per photon. The precision enhancement consumes only a linearly increasing number of applications of the gates while achieving a nonlinear scaling of the precision. We further indicate that this nonlinear enhancement roots in an in-depth exploration of the Heisenberg uncertainty principle (HUP). The very quantum noncommutativity that imposes fundamental limitations on measurement precision under the HUP is transformed into a valuable quantum resource that enables the observed nonlinear enhancement.

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• Quantum information theory
• Quantum metrology
• Quantum parameter estimation