Fast and precise control for quantum sensing of stochastic signals

Enhancing precision sensors for stochastic signals using quantum techniques is an exciting emerging field. Estimating a weak stochastic waveform is the core task of many fundamental physics experiments including searches for stochastic gravitational waves, quantum gravity, and axionic dark matter. Simultaneously, learning Pauli quantum channels is crucial to understanding the noise processes within and building the next generation of quantum computers. We consider the ultimate limit on the sensitivity of these devices to stochastic signals given any choice of the initial quantum state, the particular control executed over the dynamics of the device, and the measurement scheme. We show that it is optimal to operate in the limit of fast and precise control where we rapidly projectively measure and re-initialise the quantum state. We determine the optimal measurement scheme and discuss the optimal state for applications to stochastic waveform estimation and Pauli channel learning.