  A scheme for globally addressing a quantum computer is presented along with
its realisation in an optical lattice setup of one, two or three dimensions.
The required resources are mainly those necessary for performing quantum
simulations of spin systems with optical lattices, circumventing the necessity
for single qubit addressing. We present the control procedures, in terms of
laser manipulations, required to realise universal quantum computation. Error
avoidance with the help of the quantum Zeno effect is presented and a scheme
for globally addressed error correction is given. The latter does not require
measurements during the computation, facilitating its experimental
implementation. As an illustrative example, the pulse sequence for the
factorisation of the number fifteen is given.
