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

## TL;DR

This paper introduces a scalable, control-enhanced sequential scheme for quantum parameter estimation that achieves Heisenberg-limited precision under general noncommuting dynamics, demonstrated experimentally with optical controls.

## Contribution

It develops a novel controlled sequential scheme for quantum metrology that surpasses previous limitations under noncommuting dynamics and simplifies experimental implementation.

## Key findings

- Achieves near-Heisenberg limit precision in experiments.
- Demonstrates the scheme with up to eight controls.
- Provides a geometrical framework for optimal control timing.

## Abstract

The advantage of quantum metrology has been experimentally demonstrated for phase estimations where the dynamics are commuting. General noncommuting dynamics, however, can have distinct features. For example, the direct sequential scheme, which can achieve the Heisenberg scaling for the phase estimation under commuting dynamics, can have even worse performances than the classical scheme under noncommuting dynamics. Here we realize a scalable optimally controlled sequential scheme, which can achieve the Heisenberg precision under general noncommuting dynamics. We also present an intuitive geometrical framework for the controlled scheme and identify sweet spots in time at which the optimal controls used in the scheme can be pre-fixed without adaptation, which simplifies the experimental protocols significantly. We successfully implement the scheme up to eight controls in an optical platform, demonstrate a precision near the Heisenberg limit. Our work opens the avenue for harvesting the power of quantum control in quantum metrology, and provides a control-enhanced recipe to achieve the Heisenberg precision under general noncommuting dynamics.