An efficient triangular configuration of macronode measurements on quad-rail lattice cluster states implements arbitrary beamsplitter networks, and composite configurations implement general Gaussian unitaries and a compact multimode shear subgroup.
(34) The commutability comes from the fact that the trans- formation matrix of a beamsplitter is a real matrix in Eq
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Configuration design of multimode Gaussian operations on continuous-variable quad-rail lattice cluster states
An efficient triangular configuration of macronode measurements on quad-rail lattice cluster states implements arbitrary beamsplitter networks, and composite configurations implement general Gaussian unitaries and a compact multimode shear subgroup.