  Cluster states are an essential component in one-way quantum computation
protocols. We present two schemes to generate addressable continuous-variable
cluster states from quadrature squeezed cylindrically polarized modes. By
including polarization in addition to the transverse spatial degree of freedom,
elementary cluster states can be created in which four cluster nodes
co-propagate within one paraxial vector beam. This approach is fundamentally
compatible with existing time-multiplexed schemes that have been used to create
the largest cluster states to date. We implement a proof-of-principle
experiment of one of the proposed schemes and verify its feasibility by
measuring the quantum correlations between the different nodes of the cluster
state.
