  In a previous paper we observed that (classical) tree-level gauge theory
amplitudes can be rearranged to display a duality between color and kinematics.
Once this is imposed, gravity amplitudes are obtained using two copies of
gauge-theory diagram numerators. Here we conjecture that this duality persists
to all quantum loop orders and can thus be used to obtain multiloop gravity
amplitudes easily from gauge-theory ones. As a nontrivial test, we show that
the three-loop four-point amplitude of N = 4 super-Yang-Mills theory can be
arranged into a form satisfying the duality, and by taking double copies of the
diagram numerators we obtain the corresponding amplitude of N = 8 supergravity.
We also remark on a non-supersymmetric two-loop test based on pure Yang-Mills
theory resulting in gravity coupled to an anti-symmetric tensor and dilaton.
