Simulated Annealing-Assisted GRAPE for Superior Quantum Fisher Information in Quantum Parameter Estimation

Quantum metrology leverages quantum superposition and entanglement to surpass the Standard Quantum Limit (SQL). This work enhances parameter estimation precision by integrating control fields into quantum systems subject to dephasing and spontaneous emission noise. We provide dynamical equations for controlled systems and construct quantum control landscapes (QCL) for quantum Fisher information (QFI), revealing prevalent local extrema that limit gradient-based optimization. To overcome this, we propose a simulated annealing-guided algorithm (SAGRAPE) that escapes local traps, significantly increasing QFI. The numerical results demonstrate precision enhancement beyond conventional methods under realistic noise conditions.