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By employing an auxiliary cavity, we investigate the possibility to implement the conditional phase flip (CPF) gate on two atoms confined in separate low-Q cavities by single-photon input-output process, based on the Faraday rotation. This indicates a universal quantum computing available with sophisticated cavity QED techniques. As examples, we carry out generation of cluster states of distant atomic qubits and accomplish a teleportation based on Bell-state measurement in low-Q cavities.

In this paper, we find that topological insulators with time-reversal symmetry and inversion symmetry featuring two-dimensional quantum spin Hall (QSH) state can be divided into 16 classes, which are characterized by four Z2 topological variables ζk = 0, 1 at four points with high symmetry in the Brillouin zone. We obtain the corresponding edge states for each one of these sixteen classes of QSHs. In addition, it is predicted that massless fermionic excitations appear at the quantum phase transition between different QSH states. In the end, we also briefly discuss the three-dimensional case.