Quantum computation in optical lattices via global laser addressing

A scheme for globally addressing a quantum computer is presented along with its realization in an optical lattice set-up 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 realize 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 factorization of the number 15 is given.