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