Let $A$ be an abelian variety over $\mathbb{F_q}$ with dimension $n$. Let $q$ be a constant. Is there polynomial algorithm of finding discrete logarithm in $A$?

Let $A$ be an abelian variety over $\mathbb{F_q}$ with dimension $n$. Let $q$ be a constant. Is there polynomial algorithm of finding discrete logarithm in $A$?

UPD: really I don't undestend: can we polynomial fast calculate $P+Q$ if $P, Q \in A$ (as it is in case of elliptic curve)?