Semisimplicity of the quantum cohomology for smooth Fano toric varieties   associated with facet symmetric polytopes
  The degree zero part of the quantum cohomology algebra of a smooth Fano toric symplectic manifold is determined by the superpotential function, W, of its moment polytope. In particular, this algebra is semisimple, i.e. splits as a product of fields, if and only if all the critical points of W are non-degenerate. In this paper we prove that this non-degeneracy holds for all smooth Fano toric varieties with facet-symmetric duals to moment polytopes. 
Benjamin P. Mirabelli and Maksim Maydanskiy
math.SG