Abstract: We complete quantum information processing tasks based on a cavity-assisted single photon input-output process in a low-Q cavity. The polarization states of two photons are encoded into a logical qubit, which is immune to collective-rotating noise.First we construct the hybrid controlled-phased-flip gate between an atom and a single logic qubit. Then, we realize the CNOT gate of two logical qubits. Finally, we achieve entanglement preparation of logical qubits and the quantum state transfer from an atom to a logical qubit.