  Recently, Digitized-Counterdiabatic (CD) Quantum Approximate Optimization
Algorithm (QAOA) has been proposed to make QAOA converge to the solution of an
optimization problem in fewer steps, inspired by Trotterized counterdiabatic
driving in continuous-time quantum annealing. In this paper, we critically
revisit this approach by focusing on the paradigmatic weighted and unweighted
one-dimensional MaxCut problem. We study two variants of QAOA with first and
second-order CD corrections. Our results show that, indeed, higher order CD
corrections allow for a quicker convergence to the exact solution of the
problem at hand by increasing the complexity of the variational cost function.
Remarkably, however, the total number of free parameters needed to achieve this
result is independent of the particular QAOA variant analyzed.
