  A quantum advantage can be achieved in the unitary charging of quantum
batteries if their cells are interacting. Here, we try to clarify with some
analytical calculations whether and how this quantum advantage is achieved for
sparse Sachdev-Ye-Kitaev (SYK) interactions and in general for fermionic
interactions with disorder. To do this we perform a simple modelization of the
interactions. In particular, we find that for $q$-point rescaled sparse SYK
interactions the quantum advantage goes as $\Gamma\sim
N^{\frac{\alpha-q}{2}+1}$ for $\alpha\geq q/2$ and $\Gamma\sim
N^{1-\frac{\alpha}{2}}$ for $q/2>\alpha\geq 0$, where $\alpha$ is related to
the connectivity and $N$ is the number of cells.
