  One of the fundamental conditions for one-way quantum computation (1WQC) is
the ability to make sequential measurements on isolated qubits that comprise
the highly entangled resource for 1WQC, the cluster state. This has been a
significant impediment in the implementation of 1WQC with ultracold atoms
confined in optical lattices, because the width of the measuring lasers is
generally much greater than the atomic (qubit) spacing. We demonstrate that
deterministic 1WQC is nevertheless possible, with a polynomial increase in the
number of operations, as long as the center of the beams can be positioned with
high accuracy. Extending the number of cluster atoms, the scheme is also able
to compensate for accidental measurements of an arbitrary number of nearby
qubits.
