The ability to characterise a Hamiltonian with high precision is crucial for
the implementation of quantum technologies. In addition to the well-developed
approaches utilising optimal probe states and optimal measurements, the method
of optimal control can be used to identify time-dependent pulses applied to the
system to achieve higher precision in the estimation of Hamiltonian parameters,
especially in the presence of noise. Here, we extend optimally controlled
estimation schemes for single qubits to non-commuting dynamics as well as two
interacting qubits, demonstrating improvements in terms of maximal precision,
time-stability, as well as robustness over uncontrolled protocols.Comment: Submission to SciPost Physics; 18 pages, 13 figure
