Streamlined quantum computing with macronode cluster states

Continuous-variable cluster states allow for fault-tolerant measurement-based quantum computing when used in tandem with the Gottesman-Kitaev-Preskill (GKP) encoding of a qubit into bosonic mode. For quad-rail-lattice macronode states, whose construction is defined by fixed, low-depth beam splitter network, we show that Clifford gate and GKP error correction can be simultaneously implemented single teleportation step. We give explicit recipes to realize generating set, calculate logical gate-error rates given finite squeezing cluster-state resources. find ${10}^{\ensuremath{-}2}$--${10}^{\ensuremath{-}3}$, compatible thresholds topological codes, achieved 11.9--13.7 dB. The protocol presented eliminates noise present prior schemes puts required fault tolerance range current state-of-the-art optical experiments. Finally, how produce distillable magic directly within state.