A Two-stage Optimization Method for Wide-range Single-electron Quantum Magnetic Sensing

Quantum magnetic sensing based on spin systems has emerged as a new paradigm for detecting ultra-weak magnetic fields with unprecedented sensitivity, revitalizing applications in navigation, geo-localization, biology, and beyond. At the heart of quantum magnetic sensing, from the protocol perspective, lies the design of optimal sensing parameters to manifest and then estimate the underlying signals of interest (SoI). Existing studies on this front 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, resulting in prolonged interrogation times and reduced sensing accuracy. In this work, we report the design of a new protocol using a two-stage optimization method. In the 1st Stage, a Bayesian neural network with a fixed set of sensing parameters is used to narrow the range of SoI. In the 2nd Stage, a federated reinforcement learning agent is designed to fine-tune the sensing parameters within a reduced search space. The proposed protocol is developed and evaluated in a challenging context of single-shot readout of an NV-center electron spin under a constrained total sensing time budget; and yet it achieves significant improvements in both accuracy and resource efficiency for wide-range D.C. magnetic field estimation compared to the state of the art.