  For a $\mathbb P^1$-orbifold $\mathscr C$, we prove that its big quantum
cohomology is generically semisimple. As a corollary, we verify a conjecture of
Dubrovin for orbi-curves. We also show that the small quantum cohomology of
$\mathscr C$ is generically semisimple iff $\mathscr C$ is Fano, i.e. it has
positive orbifold Euler characteristic.
