  We propose a scalable approach to building cluster states of matter qubits
using coherent states of light. Recent work on the subject relies on the use of
single photonic qubits in the measurement process. These schemes can be made
robust to detector loss, spontaneous emission and cavity mismatching but as a
consequence the overhead costs grow rapidly, in particular when considering
single photon loss. In contrast, our approach uses continuous variables and
highly efficient homodyne measurements. We present a two-qubit scheme, with a
simple bucket measurement system yielding an entangling operation with success
probability 1/2. Then we extend this to a three-qubit interaction, increasing
this probability to 3/4. We discuss the important issues of the overhead cost
and the time scaling. This leads to a "no-measurement" approach to building
cluster states, making use of geometric phases in phase space.
