We propose how to prepare four remote logical qubits, with each in a separate cavity and encoded in the decoherence-free subspace by two atoms, into various entangled states. By means of the cavity-assisted photon scattering, we can link the four remote logical qubits in different cavities to be, respectively,
W state, Greenberger-Horne-Zeilinger state, and cluster state, which are important in view of the distributed quantum information processing. The generation of the latter two entangled states can be theoretically generalized to many-qubit cases. Because our qubits are defined in dephasing-free subspace, our scheme is immune to dephasing during or even after the entanglement preparation.
We propose a many-qubit network with cavity QED by encoding qubits in decoherence-free subspace, based on which we can implement many-logic-qubit conditional gates by means of cavity-assisted interaction with single-photon pulses. Our scheme could not only resist collective dephasing errors, but also much reduce the implementational steps compared to conventional methods doing the same job, and we can also complete communications between two arbitrary nodes. We show the details by implementing a three-logic-qubit Toffoli gate and explore the experimental feasibility and challenge based on currently achievable cavity QED technologies.