We explain how the following four theories are equivalent:
(1) The equivariant quantum cohomology of Hilb^d(C^2), the Hilbert scheme of degree d points in the plane,
(2) The equivariant orbifold quantum cohomology of Sym^d(C^2), the (orbifold) dth symmetric product of the plane,
(3) The degree d, all genus, equivariant, relative Gromov-Witten theory of P^1xC^2, and
(4) The degree d, equivariant, relative Donaldson-Thomas theory of P^1xC^2.