  Quantum metrology makes use of quantum mechanics to improve precision
measurements and measurement sensitivities. It is usually formulated for
time-independent Hamiltonians but time-dependent Hamiltonians may offer
advantages, such as a $T^4$ time dependence of the Fisher information which
cannot be reached with a time-independent Hamiltonian. In Optimal adaptive
control for quantum metrology with time-dependent Hamiltonians (Nature
Communications 8, 2017), Shengshi Pang and Andrew N. Jordan put forward a
Shortcut-to-adiabaticity (STA)-like method, specifically an approach formally
similar to the "counterdiabatic approach", adding a control term to the
original Hamiltonian to reach the upper bound of the Fisher information. We
revisit this work from the point of view of STA to set the relations and
differences between STA-like methods in metrology and ordinary STA. This
analysis paves the way for the application of other STA-like techniques in
parameter estimation. In particular we explore the use of physical unitary
transformations to propose alternative time-dependent Hamiltonians which may be
easier to implement in the laboratory.
