Optimal Control of Coupled Sensor-Ancilla Qubits for Multiparameter Estimation

Designing optimal control for multiparameter quantum sensing is essential for approaching the ultimate precision limits. However, analytical solutions are generally available only for simple systems, while realistic scenarios often involve coupled qubits and time-dependent Hamiltonians. Here we numerically investigate optimal control of a two-qubit sensor-ancilla system coupled via an Ising term using Gradient Ascent Pulse Engineering (GRAPE) to minimize the objective function. By seeding the optimization recursively with solutions obtained for smaller coupling strengths and selecting a suitable initial guess, we achieve robust convergence and high precision across a wide range of interaction strengths and field configurations. The proposed approach offers a practical route toward high-sensitivity, robust multiparameter magnetometry and it is applicable to solid-state quantum sensors such as nitrogen-vacancy (NV) centers in realistic experimental settings.