  We present a scheme for correcting qubit loss error while quantum computing
with neutral atoms in an addressable optical lattice. The qubit loss is first
detected using a quantum non-demolition measurement and then transformed into a
standard qubit error by inserting a new atom in the vacated lattice site. The
logical qubit, encoded here into four physical qubits with the
Grassl-Beth-Pellizzari code, is reconstructed via a sequence of one projective
measurement, two single-qubit gates, and three controlled-NOT operations. No
ancillary qubits are required. Both quantum non-demolition and projective
measurements are implemented using a cavity QED system which can also detect a
general leakage error and thus allow qubit loss to be corrected within the same
framework. The scheme can also be applied in quantum computation with trapped
ions or with photons.
