  The leading quantum correction to Einstein-Hilbert Hamiltonian coming from
large volume vacuum isotropic loop quantum cosmology, is independent of
quantization ambiguity parameters. It is shown here that this correction can be
viewed as finite volume gravitational Casimir energy due to one-loop `graviton'
contributions. In vacuum case sub-leading quantum corrections and in non-vacuum
case even leading quantum correction depend on ambiguity parameters. It may be
recalled that these are in fact analogous features of perturbative quantum
gravity where it is well-known that pure gravity (on-shell) is one-loop finite
whereas higher-loops contributions are not even renormalizable. These features
of the quantum corrections coming from non-perturbative quantization, sheds a
new light on a major open issue; how to communicate between non-perturbative
and perturbative approaches of quantum gravity.
