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

A potential scheme is proposed for generating cluster states of manyatoms in cavity quantum electradynamics (QED), in which an unorthodoxencoding is employed with the ground state being qubit $leftvert0rightrangle $ while two closely spaced upper states being qubit$leftvert 1rightrangle $. Throughout the scheme the cavities canbe in thermal states but are only virtually excited. We show how tocreate the cluster states by performing a two-step but nosingle-qubit operation. Discussion is also carried out on theexperimental feasibility of our scheme.