  We describe in detail the application of four qubit cluster states, built on
the simultaneous entanglement of two photons in the degrees of freedom of
polarization and linear momentum, for the realization of a complete set of
basic one-way quantum computation operations. These consist of arbitrary single
qubit rotations, either probabilistic or deterministic, and simple two qubit
gates, such as a c-not gate for equatorial qubits and a universal c-phase (CZ)
gate acting on arbitrary target qubits. Other basic computation operations,
such as the Grover's search and the Deutsch's algorithms, have been realized by
using these states. In all the cases we obtained a high value of the operation
fidelities. These results demonstrate that cluster states of two photons
entangled in many degrees of freedom are good candidates for the realization of
more complex quantum computation operations based on a larger number of qubits.
