  We study four-dimensional quantum gravity with negative cosmological constant
in the minisuperspace approximation and compute the partition function for the
$S^3$ boundary geometry. In this approximation scheme the path integrals become
dominated by a class of asymptotically AdS "microstate geometries." Despite the
fact that the theory is pure Einstein gravity without supersymmetry, the result
precisely reproduces, up to higher curvature corrections, the Airy function in
the $S^3$ partition function of the maximally supersymmetric
Chern-Simons-matter (CSM) theory which sums up all perturbative $1/N$
corrections. We also show that this can be interpreted as a concrete
realization of the idea that the CFT partition function is a solution to the
Wheeler-DeWitt equation as advocated in the holographic renormalization group.
Furthermore, the agreement persists upon the inclusion of a string probe and it
reproduces the Airy function in the vev of half-BPS Wilson loops in the CSM
theory. These results may suggest that the supergravity path integrals localize
to the minisuperspace in certain cases and the use of the minisuperspace
approximation in AdS/CFT may be a viable approach to study $1/N$ corrections to
large $N$ CFTs.
