  In this paper we consider a two-dimensional metamaterial comprising an array
of qubits (two level quantum objects). Here we show that a two-dimensional
quantum metamaterial may be controlled, e.g. via the application of a magnetic
flux, so as to provide controllable refraction of an input signal. Our results
are consistent with a material that could be quantum birefringent (beam
splitter) or not dependent on the application of this control parameter. We
note that quantum metamaterials as proposed here may be fabricated from a
variety of current candidate technologies from superconducting qubits to
quantum dots. Thus the ideas proposed in this work would be readily testable in
existing state of the art laboratories.
