Resource-efficient adaptive Bayesian tracking of magnetic fields with a quantum sensor

By addressing single electron spins through Ramsey experiments, nitrogen-vacancy centres can act as high-resolution sensors of magnetic field. In applications where the magnetic field may be changing rapidly, total sensing time is crucial and must be minimised. Bayesian estimation and adaptive experiment optimisation protocols work by computing the probability distribution of the magnetic field based on measurement outcomes and, by computing aquisition settings for the next measurement. These protocols can speed up the sensing process by reducing the number of measurements required. However, the computations feeding into the next iteration measurement settings must be performed quickly enough to allow real-time updates. This paper addresses the issue of computational speed by implementing an approximated Bayesian estimation technique, where probability distributions are approximated by a superposition of Gaussian functions. Given that only three parameters are required to fully describe a Gaussian, we find that the magnetic field probability distribution can typically be described by fewer than ten numbers, achieving a reduction in the number of operations by factor 20 compared to existing approaches, allowing for faster processing.