  Finding the exact counterdiabatic potential is, in principle, particularly
demanding. Following recent progresses about variational strategies to
approximate the counterdiabatic operator, in this paper we apply this technique
to the quantum annealing of the $p$-spin model. In particular, for $ p = 3 $ we
find a new form of the counterdiabatic potential originating from a cyclic
ansatz, that allows us to have optimal fidelity even for extremely short
dynamics, independently of the size of the system. We compare our results with
a nested commutator ansatz, recently proposed in P. W. Claeys, M. Pandey, D.
Sels, and A. Polkovnikov, Phys. Rev. Lett. 123, 090602 (2019), for $ p = 1 $
and $ p = 3 $. We also analyze generalized $ p $-spin models to get a further
insight into our ansatz.
