Adaptive Quantum Parameter Estimation Through Feedback-Based Optimal Control

Quantum control is commonly used to address quantum parameter estimation problems. However, when dealing with multi-qubit systems, the usual optimal control methods tend to converge to the local optimum prematurely, leading to poor performance. To solve this problem, we propose a feedback-based automatic differential gradient ascent control algorithm, where feedback is utilized to extract parameter information in the optimal control algorithm, and meanwhile the control resources for each qubit are compressed to two dimensions. This enables the proposed algorithm to surpass the accuracy level of traditional algorithms while being physically easier to implement. To verify the feasibility of the algorithm, some numerical simulations with a designed adaptive estimation scheme are performed. The results show that the proposed algorithm can rapidly converge to a high-precision level even in the scenarios with limited prior knowledge.