We introduce a new strongly driven dispersive atom-cavity interaction and develop a new scheme for implementing the nontrivial entangling gates for two logical qubits in decoherence-free subspaces (DFSs). Our scheme combines the robust advantages of DFS and the geometric phase. Moreover, only two neighboring physical qubits, which encode a logical qubit, are required to undergo the collective dephasing in our scheme.

• Received 30 March 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.200501