  We propose a feasible scheme to achieve quantum computation based on
geometric manipulation of ensembles of atoms, and analyze it for neutral
rubidium atoms magnetically trapped in planoconcave microcavities on an atom
chip. The geometric operations are accomplished by optical excitation of a
single atom into a Rydberg state in a constant electric field. Strong
dipole-dipole interactions and incident lasers drive the dark state of the atom
ensembles to undergo cyclic evolutions that realize a universal set of quantum
gates. Such geometric manipulation turns out naturally to protect the qubits
from the errors induced by non-uniform laser illumination as well as cavity
loss. The gate performance and decoherence processes are assessed by numerical
simulation.
