Efficient generation of universal two-dimensional cluster states with hybrid systems

We present a scheme to generate two-dimensional cluster state efficiently. The number of the basic gate-entangler-for the operation is in the order of the entanglement bonds of a cluster state, and could be reduced greatly if one uses them repeatedly. The scheme is deterministic and uses few ancilla resources and no quantum memory. It is suitable for large-scale quantum computation and feasible with the current experimental technology.