  We give a detailed account of the one-way quantum computer, a scheme of
quantum computation that consists entirely of one-qubit measurements on a
particular class of entangled states, the cluster states. We prove its
universality, describe why its underlying computational model is different from
the network model of quantum computation and relate quantum algorithms to
mathematical graphs. Further we investigate the scaling of required resources
and give a number of examples for circuits of practical interest such as the
circuit for quantum Fourier transformation and for the quantum adder. Finally,
we describe computation with clusters of finite size.
