  We compute the quantum cohomology of symplectic flag manifolds. Symplectic
flag manifolds can be described by non-abelian GLSMs with superpotential.
Although the ring relations cannot be directly read off from the equations of
motion on the Coulomb branch due to complication introduced by the non-abelian
gauge symmetry, it can be shown that they can be extracted from the
localization formula in a gauge-invariant form. Our result is general for all
symplectic flag manifolds, which reduces to previously established results on
symplectic Grassmannians and complete symplectic flag manifolds derived by
other means. We also explain why a (0,2) deformation of the GLSM does not give
rise to a deformation of the quantum cohomology.
