In recent years, there has been heightened interest in quantum teleportation,
which allows for the transfer of unknown quantum states over arbitrary
distances. Quantum teleportation not only serves as an essential ingredient in
long-distance quantum communication, but also provides enabling technologies
for practical quantum computation. Of particular interest is the scheme
proposed by Gottesman and Chuang [Nature \textbf{402}, 390 (1999)], showing
that quantum gates can be implemented by teleporting qubits with the help of
some special entangled states. Therefore, the construction of a quantum
computer can be simply based on some multi-particle entangled states, Bell
state measurements and single-qubit operations. The feasibility of this scheme
relaxes experimental constraints on realizing universal quantum computation.
Using two different methods we demonstrate the smallest non-trivial module in
such a scheme---a teleportation-based quantum entangling gate for two different
photonic qubits. One uses a high-fidelity six-photon interferometer to realize
controlled-NOT gates and the other uses four-photon hyper-entanglement to
realize controlled-Phase gates. The results clearly demonstrate the working
principles and the entangling capability of the gates. Our experiment
represents an important step towards the realization of practical quantum
computers and could lead to many further applications in linear optics quantum
information processing.Comment: 10 pages, 6 figure