  Efficient generation of cluster states is crucial for engineering large-scale
measurement-based quantum computers. Hybrid matter-optical systems offer a
robust, scalable path to this goal. Such systems have an ancilla which acts as
a bus connecting the qubits. We show that by generating smaller cluster "Lego
bricks", reusing one ancilla per brick, the cluster can be produced with
maximal efficiency, requiring fewer than half the operations compared with no
bus reuse. By reducing the time required to prepare sections of the cluster,
bus reuse more than doubles the size of the computational workspace that can be
used before decoherence effects dominate. A row of buses in parallel provides
fully scalable cluster state generation requiring only 20 CPhase gates per bus
use.
