A two-stage optimization method for wide-range single-electron quantum magnetic sensing

Quantum magnetic sensing is a new paradigm for detecting ultra-weak magnetic fields. Its protocol design concerns the devise of optimal sensing parameters to estimate the underlying signals of interest (SoI). Existing studies mainly rely on adaptive algorithms based on black-box AI models or formula-driven principled searches. However, when the SoI spans a wide range and the quantum sensor has physical constraints, these methods may fail to converge efficiently or optimally, causing prolonged interrogation times and reduced accuracy. This work presents a new protocol using a two-stage optimization method, consisting of a Bayesian neural network to first narrow the SoI range and a federated reinforcement learning agent to subsequently calibrate the SoI. The protocol is developed and evaluated in the challenging context of an NV-center spin system with single-shot readout and limited sensing time; and yet it achieves significant improvements in both accuracy and resource efficiency compared to the state-of-the-art.