Coulomb coupling and the role of symmetries in quantum-dot arrays for cellular automata

Using a group-theoretical analysis of the symmetries of a quantum dot array, we investigate the role of defects on the energetics of the system and the resulting charge configurations (or polarization of the cell). We find that for the typical four- or five-element geometries proposed, even small asymmetries introduced by defects in the system, or variations in the local electrostatic environment, can give rise to large effects on the polarization of the ground state and the corresponding low-energy excitations. These shifts art: likely to produce important effects in the operation of the cellular automata proposed using these quantum dots, in particular, we find that the sensitivity to polarization changes induced by a driver cell decreases dramatically, and the polarization values are no longer fully defined. These effects would both force the use of stronger driving fields, and may also complicate the dynamical behavior of the cellular automata.