  For even dimensional smooth complete intersections, of dimension at least 4,
of two quadric hypersurfaces in a projective space, we study the genus zero
Gromov-Witten invariants by the monodromy group of its whole family. We compute
the invariants of length 4 and show that, besides a special invariant, all
genus zero Gromov-Witten invariants can be reconstructed from the invariants of
length 4. In dimension 4, we compute the special invariant by solving a curve
counting problem. We show that the generating function of genus zero
Gromov-Witten invariants has a positive radius of convergence. We show that,
although the small quantum cohomology is not semisimple, the associated
Frobenius manifold is generically tame semisimple.
