  We propose a general, fully gate-based quantum algorithm for counterdiabatic
driving. The algorithm does not depend on heuristics as in previous variational
methods, and exploits regularisation of the adiabatic gauge potential to
suppress only the transitions from the eigenstate of interest. This allows for
a rigorous quantum gate complexity upper bound in terms of the minimum gap
$\Delta$ around this target eigenstate. We find that the algorithm requires at
most $\tilde O(\Delta^{-(3 + o(1))} \epsilon^{-(1 + o(1))})$ quantum gates to
achieve a target state fidelity of at least $1 - \epsilon^2$, which is nearly
equivalent to the gate complexity of gate-based adiabatic state preparation.
This calls into question the perception of counterdiabatic driving as a general
shortcut to adiabaticity.
