  We introduce a counter-diabatic approach for deriving Hamiltonians modeling
superchargable quantum batteries (QBs). A necessary requirement for the
supercharging process is the existence of multipartite interactions among the
cells of the battery. Remarkably, this condition may be insufficient no matter
the number of multipartite terms in the Hamiltonian. We analytically illustrate
this kind of insufficiency through a model of QB based on the adiabatic version
for the Grover search problem. On the other hand, we provide QB supercharging
with just a mild number of global connections in the system. To this aim, we
consider a spin-$1/2$ chain with $n$ sites in the presence of Ising
multipartite interactions. We then show that, by considering the validity of
the adiabatic approximation and by adding $n$ terms of $(n-1)$-site
interactions, we can achieve a Hamiltonian exhibiting maximum QB power, with
respect to a normalized evolution time, growing quadratically with $n$.
Therefore, supercharging can be achieved by $O(n)$ terms of multipartite
connections. The time constraint required by the adiabatic approximation can be
surpassed by considering a counter-diabatic expansion in terms of the gauge
potential for the original Hamiltonian, with a limited $O(n)$ many-body
interaction terms assured via a Floquet approach for the counter-diabatic
implementation.
