Schemes for generating the cluster states in microwave cavity QED

We propose two experimental schemes to generate the cluster states in the context of microwave cavity quantum electrodynamics (QED). In the first scheme to prepare many cavities into the cluster states, we encode the vacuum state and one-photon state of the microwave cavity as the logic zero and one of the qubits. The second scheme is to prepare many atoms into the cluster states, where qubits are represented by the states of Rydberg atoms. Both schemes require the resonant atom-cavity interaction so that the quantum dynamics operates at a high speed, which is important in view of decoherence.