  Local counterdiabatic driving (CD) provides a feasible approach for realizing
approximate reversible/adiabatic processes like quantum state preparation using
only local controls and without demanding excessively long protocol times.
However, in many instances getting high accuracy of such CD protocols requires
engineering very complicated new controls or pulse sequences. In this work, we
describe a systematic method for altering the adiabatic path by adding extra
local controls along which performance of local CD protocols is enhanced, both
close to and far away from the adiabatic limit. We also identify an iterative
procedure to improve the performance of local counterdiabatic driving further
without any knowledge of the quantum wavefunction. We then show that these
methods provides dramatic improvement in the preparation of non-trivial GHZ
ground states of several different spin systems with both short-range and
long-range interactions.
