  We present two deterministic schemes for constructing a CNOT gate and a
Toffoli gate on photon-atom and photon-atom-atom hybrid quantum systems
assisted by bad cavities, respectively. They are achieved by cavity-assisted
photon scattering and work in the intermediate coupling region with bad
cavities, which relaxes the difficulty of their implementation in experiment.
Also, bad cavities are feasible for fast quantum operations and reading out
information. Compared with previous works, our schemes do not need any
auxiliary qubits and measurements. Moreover, the schematic setups for these
gates are simple, especially that for our Toffoli gate as only a quarter wave
packet is used to interact the photon with each of the atoms every time. These
atom-cavity systems can be used as the quantum nodes in long-distance quantum
communication as their relatively long coherence time is suitable for
multi-time operations between the photon and the system. Our calculations show
that the average fidelities and efficiencies of our two universal hybrid
quantum gates are high with current experimental technology.
