  The cluster state model for quantum computation [Phys. Rev. Lett. 86, 5188]
outlines a scheme that allows one to use measurement on a large set of
entangled quantum systems in what is known as a cluster state to undertake
quantum computations. The model itself and many works dedicated to it involve
using entangled qubits. In this paper we consider the issue of using entangled
qudits instead. We present a complete framework for cluster state quantum
computation using qudits, which not only contains the features of the original
qubit model but also contains the new idea of adaptive computation: via a
change in the classical computation that helps to correct the errors that are
inherent in the model, the implemented quantum computation can be changed. This
feature arises through the extra degrees of freedom that appear when using
qudits. Finally, for prime dimensions, we give a very explicit description of
the model, making use of mutually unbiased bases.
