Cluster-state preparation in thermal cavities without single-qubit operation

A potential scheme is proposed for generating cluster states of many atoms in cavity quantum electradynamics (QED), in which an unorthodox encoding is employed with the ground state being qubit \left\vert 0\right\rangle while two closely spaced upper states being qubit \left\vert 1\right\rangle . Throughout the scheme the cavities can be in thermal states but are only virtually excited. We show how to create the cluster states by performing a two-step but no single-qubit operation. Discussion is also carried out on the experimental feasibility of our scheme.