Cost-Aware Online Switching of Four-Qubit Probe States for Quantum Magnetometry Under Non-Stationary Noise

Quantum magnetometry can be enhanced through the use of entangled probe states, yet the optimal probe selection depends greatly on the noise, readout errors, and costs involved in preparation. An analysis is given of a simulation of a four-qubit magnetic field estimation experiment where the optimal probe state is adaptively chosen via an online controller that changes between product and GHZ probes using delayed and self-consistent feedback without knowing the underlying noise model. The performance of the controller is compared to that of a validation-selected fixed probe state strategy, a hindsight fixed probe strategy, a fixed product probe strategy, a fixed GHZ probe strategy, a fixed graph-state probe strategy, and an oracle-based dynamic probe strategy in eight stationary and non-stationary noise environments. In the actual experiment, 20 random seeds, 1200 timesteps per noise scenario, and 2000 measurement shots per timestep in the case of local dephasing with readout error are used. The sliding-window controller yields an overall RMSE of 0.015542 versus 0.017305 for the validation-selected fixed probe state, 0.017330 for the fixed product, 0.017821 for fixed GHZ, and 0.061184 for the fixed graph state. A paired permutation test on 160 trial cases gives the mean RMSE difference of -0.001763 versus the validation-selected fixed probe state with p=9.99×10-4. The adaptive algorithm improves performance in seven out of eight noise environments but still does not do well enough in the constant high-noise scenario at 5.4% worse than the global fixed baseline in the constant-high-noise scenario.