By utilizing strong optical resonant interactions in arrays of atoms with electric dipole transitions, we show how to synthesize collective optical responses that correspond to those formed by arrays of magnetic dipoles and other multipoles. Optically active magnetism with the strength comparable with that of electric dipole transitions is achieved in collective excitation eigenmodes of the array. By controlling the atomic level shifts, an array of spectrally overlapping, crossed electric and magnetic dipoles can be excited, providing a physical realization of a nearly reflectionless quantum Huygens’surface with the full 2π phase control of the transmitted light that allows for extreme wavefront engineering even at a single photon level. We illustrate this by creating a superposition of two different orbital angular momentum states of light from an ordinary input state that has no orbital angular momentum.