  We give a natural filtration F on quantum cohomology QH(G/B) of G/B, which
respects the quantum product structure. Its associated graded algebra is
isomorphic to the tensor product of QH(G/P) and a corresponding graded algebra
of QH(P/B) after localization. When the quantum parameter goes to zero, this
specializes to the filtration on the classical cohomology H(G/B) from the Leray
spectral sequence associated to the fibration P/B --> G/B --> G/P.
