  Through a combination of laser beams, we engineer a two-dimensional optical
lattice of Mexican hat potentials able to host atoms in its ring-shaped wells.
When tunneling can be ignored (at high laser intensities), we show that a
well-defined qubit can be associated with the states of the atoms trapped in
each of the rings. Each of these two-level systems can be manipulated by a
suitable configuration of Raman laser beams imprinting a synthetic flux onto
each Mexican hat cell of the lattice. Overall, we believe that the system has
the potential to form a scalable architecture for atomtronic flux qubits.
