Graphane with carbon dimer defects: Robust in-gap states and a scalable two-dimensional platform for quantum computation

We study the energy level structures of the defective graphane lattice, where a carbon dimer defect is created by removing the hydrogen atoms on two nearest-neighbor carbon sites. Robust defect states emerge inside the bulk insulating gap of graphane. While for the stoichiometric half-filled system there are two doubly degenerate defect levels, there are four nondegenerate and spin-polarized in-gap defect levels in the system with one electron less than half filling. A universal set of quantum gates can be realized in the defective graphane lattice, by triggering resonant transitions among the defect states via optical pulses and \emph{ac} magnetic fields. The sizable energy separation between the occupied and the empty in-gap states enables precise control at room temperature. The spatial locality of the in-gap states implies a qubit network of extremely high areal density. Based on these results, we propose that graphane as a unique platform could be used to construct the future all-purpose quantum computers.