  In this proceedings, I will consider quantum aspects of a non-local,
infinite-derivative scalar field theory - a ${\it toy \, model}$ depiction of a
covariant infinite-derivative, non-local extension of Einstein's general
relativity which has previously been shown to be free from ghosts around the
Minkowski background. The graviton propagator in this theory gets an
exponential suppression making it ${\it asymptotically \, free}$, thus
providing strong prospects of resolving various classical and quantum
divergences. In particular, I will find that at $1$-loop, the $2$-point
function is still divergent, but once this amplitude is renormalized by adding
appropriate counter terms, the ultraviolet (UV) behavior of all other $1$-loop
diagrams as well as the $2$-loop, $2$-point function remains well under
control. I will go on to discuss how one may be able to generalize our
computations and arguments to arbitrary loops.
