  In our previous article we have proposed that the Virasoro algebra controls
the quantum cohomology of Fano varieties at all genera. In this paper we
construct a free field description of Virasoro operators and quantum
cohomology. We shall show that to each even (odd) homology class of a
K\"{a}hler manifold we have a free bosonic (fermionic) field and Virasoro
operators are given by a simple bilinear form of these fields. We shall show
that the Virasoro condition correctly reproduces the Gromov-Witten invariants
also in the case of manifolds with non-vanishing non-analytic classes
($h^{p,q}\not=0,p\not=q$) and suggest that the Virasoro condition holds
universally for all compact smooth K\"{a}hler manifolds.
