  Metasurfaces mold the flow of classical light waves by engineering
sub-wavelength patterns from dielectric or metallic thin films. We describe and
analyze a method in which quantum operator-valued reflectivity can be used to
control both spatio-temporal and quantum properties of transmitted and
reflected light. Such a quantum metasurface is realized by preparing and
manipulating entangled superposition states of atomically thin reflectors.
Specifically, we show that such a system allows for massively parallel quantum
operations between atoms and photons and for the generation of highly
non-classical states of light, including photonic GHZ and cluster states
suitable for quantum information processing. We analyze the influence of
imperfections and decoherence, as well as specific implementations based on
atom arrays excited into Rydberg states. Finally, the extension to quantum
metamaterials and emulations of quantum gravitational background for light are
discussed.
