  Constructing compact quantum circuits for universal quantum gates on
solid-state systems is crucial for quantum computing. We present some compact
quantum circuits for a deterministic solid-state quantum computing, including
the CNOT, Toffoli, and Fredkin gates on the diamond nitrogen-vacancy centers
confined inside cavities, achieved by some input-output processes of a single
photon. Our quantum circuits for these universal quantum gates are simple and
economic. Moreover, additional electron qubits are not employed, but only a
single-photon medium. These gates have a long coherent time. We discuss the
feasibility of these universal solid-state quantum gates, concluding that they
are feasible with current technology.
