  The quantum cohomology algebra of a projective manifold X is the cohomology
H(X,Q) endowed with a different algebra structure, which takes into account the
geometry of rational curves in X. We show that this algebra takes a remarkably
simple form for complete intersections when the dimension is large enough
w.r.t. the degree. As a reward we get a number of surprising enumerative
formulas relating lines, conics and twisted cubics on X.
