  In this work we present a systematic study of AdS$_{d+1}$ loop amplitudes for
gluons and gravitons using momentum space techniques. Inspired by the recent
progress in tree level computation, we construct a differential operator that
can act on a scalar factor in order to generate gluon and graviton loop
integrands: this systematizes the computation for any given loop level Witten
diagram. We then give a general prescription in this formalism, and discuss it
for bubble, triangle, and box diagrams.
