Quantum computing in optical lattices

Summary form only given. Controlled cold collisions of atoms in optical lattices allow implementations of highly parallel entanglement operations and quantum gates. Applications include quantum computing with efficient quantum error correction. Existing experimental techniques for cooling and trapping of atoms in optical lattices, combined with the physics of ultracold collisions (BEC) offer a new perspective for quantum information experiments. We propose the use of cold controlled collisions of atoms, trapped in the ground state of the lattice wells, as a mechanism to introduce dynamic phase shifts depending on the state of the atoms. In conventional lattices with random occupation of the lattice sites, this mechanism can be used, for example, for spectroscopic studies of entangled Bell and GHZ states. In lattices with ordered filling structures, which have been discussed theoretically (Mott insulator phase), highly parallel entanglement operations could be implemented, corresponding to a novel class of quantum gates. We show that these (multi-qubit) quantum gates can be employed for efficient quantum error correction and discuss how the parallelism in an optical lattice could be used for quantum computation in general.