  In quantum metrology, nonlinear many-body interactions can enhance the
precision of Hamiltonian parameter estimation to surpass the Heisenberg
scaling. Here, we consider the estimation of the interaction strength in linear
systems with long-range interactions and using the Kitaev chains as a case
study, we establish a transition from the Heisenberg to super-Heisenberg
scaling in the quantum Fisher information by varying the interaction range. We
further show that quantum control can improve the prefactor of the quantum
Fisher information. Our results explore the advantage of optimal quantum
control and long-range interactions in many-body quantum metrology.
