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.