  We provide an inductive algorithm to compute the bulk-deformed potentials for
toric Fano surfaces via wall-crossing techniques and a tropical-holomorphic
correspondence theorem for holomorphic discs. As an application of the
correspondence theorem, we also prove a big quantum period theorem for toric
Fano surfaces which relates the log descendant Gromov-Witten invariants with
the oscillatory integrals of the bulk-deformed potentials.
