We show that measurement-based quantum computation on scalable
continuous-variable (CV) cluster states admits more quantum-circuit flexibility
and compactness than similar protocols for standard square-lattice CV cluster
states. This advantage is a direct result of the macronode structure of these
states---that is, a lattice structure in which each graph node actually
consists of several physical modes. These extra modes provide additional
measurement degrees of freedom at each graph location, which can be used to
manipulate the flow and processing of quantum information more robustly and
with additional flexibility that is not available on an ordinary lattice.Comment: (v2) consistent with published version; (v1) 11 pages (9 figures
