  We consider the possibility of performing linear optical quantum computation
making use of extra photonic degrees of freedom. In particular we focus on the
case where we use photons as quadbits. The basic 2-quadbit cluster state is a
hyper-entangled state across polarization and two spatial mode degrees of
freedom. We examine the non-deterministic methods whereby such states can be
created from single photons and/or Bell pairs, and then give some mechanisms
for performing higher-dimensional fusion gates.
