  We study the main options for a unitary and renormalizable, local quantum
field theory of the gravitational interactions. The first model is a Lee-Wick
superrenormalizable higher-derivative gravity, formulated as a nonanalytically
Wick rotated Euclidean theory. We show that, under certain conditions, the $S$
matrix is unitary when the cosmological constant vanishes. The model is the
simplest of its class. However, infinitely many similar options are allowed,
which raises the issue of uniqueness. To deal with this problem, we propose a
new quantization prescription, by doubling the unphysical poles of the
higher-derivative propagators and turning them into Lee-Wick poles. The
Lagrangian of the simplest theory of quantum gravity based on this idea is the
linear combination of $R$, $R_{\mu \nu }R^{\mu \nu }$, $R^{2}$ and the
cosmological term. Only the graviton propagates in the cutting equations and,
when the cosmological constant vanishes, the $S$ matrix is unitary. The theory
satisfies the locality of counterterms and is renormalizable by power counting.
It is unique in the sense that it is the only one with a dimensionless gauge
coupling.
