Cluster states prepared by using hot trapped ions

We propose a scheme for the preparation of one-dimensional andtwo-dimensional cluster states by using hot trapped ions. The schemeis based on the interaction between two ions and bichromaticradiation. The vibrational mode in our protocol is only virtuallyexcited so that the system is insensitive to the thermal field. Inaddition, we only use two levels of ions as qubits and thesuccessful probability may achieve 100%.