  We report an experimental realization of one-way quantum computing on a
two-photon four-qubit cluster state. This is accomplished by developing a
two-photon cluster state source entangled both in polarization and spatial
modes. With this special source, we implemented a highly efficient Grover's
search algorithm and high-fidelity two qubits quantum gates. Our experiment
demonstrates that such cluster states could serve as an ideal source and a
building block for rapid and precise optical quantum computation.
