Antidot lattices, defined on a two-dimensional electron gas at a
semiconductor heterostructure, are a well-studied class of man-made structures
with intriguing physical properties. We point out that a closely related
system, graphene sheets with regularly spaced holes ("antidots"), should
display similar phenomenology, but within a much more favorable energy scale, a
consequence of the Dirac fermion nature of the states around the Fermi level.
Further, by leaving out some of the holes one can create defect states, or
pairs of coupled defect states, which can function as hosts for electron spin
qubits. We present a detailed study of the energetics of periodic graphene
antidot lattices, analyze the level structure of a single defect, calculate the
exchange coupling between a pair of spin qubits, and identify possible avenues
for further developments.Comment: 4 pages, 5 figures, accepted for publication in Phys. Rev. Let
