  Standard quantum computation is based on sequences of unitary quantum logic
gates which process qubits. The one-way quantum computer proposed by
Raussendorf and Briegel is entirely different. It has changed our understanding
of the requirements for quantum computation and more generally how we think
about quantum physics. This new model requires qubits to be initialized in a
highly-entangled cluster state. From this point, the quantum computation
proceeds by a sequence of single-qubit measurements with classical feedforward
of their outcomes. Because of the essential role of measurement a one-way
quantum computer is irreversible. In the one-way quantum computer the order and
choices of measurements determine the algorithm computed. We have
experimentally realized four-qubit cluster states encoded into the polarization
state of four photons. We fully characterize the quantum state by implementing
the first experimental four-qubit quantum state tomography. Using this cluster
state we demonstrate the feasibility of one-way quantum computing through a
universal set of one- and two-qubit operations. Finally, our implementation of
Grover's search algorithm demonstrates that one-way quantum computation is
ideally suited for such tasks.
