Optimal control for Hamiltonian parameter estimation in non-commuting 
and bipartite quantum dynamics

Abstract

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, 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.