Adaptive measurement protocols for Ramsey sequence quantum sensing

The Ramsey sequence is a canonical example quantum interferometry and a mainstay of quantum sensing.  When readout fidelity is high, the phase can be determined with Heisenberg scaling where precision Δφ is proportional to 1/N after N measurements.  Here, we address Ramsey measurements with low-fidelity readout in a comparison of protocols for choosing the phase accumulation time setting, τ. In simulations of Ramsey measurements using NV^- center spin qbits for magnetic field sensing, we compare a new optimal Bayesian experiment design protocol to an adaptive heuristic protocol, a quantum phase estimation algorithm, and random setting choices. When precession frequency is the lone parameter to estimate, the Bayesian design is faster by factors of roughly 2, 4, and 5 relative to the adaptive heuristic, random τ choices, and the quantum phase estimation algorithm, respectively. When four parameters are to be determined, Bayesian experiment design and random τ choices can converge to roughly equivalent sensitivity, but the Bayesian method converges four times faster.