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 a bosonic mode. For quad-raillattice macronode cluster states, whose construction is defined by a fixed, low-depth beam splitter network, we show that a Clifford gate and GKP error correction can be simultaneously implemented in a single teleportation step. We give explicit recipes to realize the Clifford generating set, and we calculate the logical gate-error rates given finite squeezing in the cluster-state and GKP resources. We find that logical error rates of 10(-2)-10(-3), compatible with the thresholds of topological codes, can be achieved with squeezing of 11.9-13.7 dB. The protocol presented eliminates noise present in prior schemes and puts the required squeezing for fault tolerance in the range of current state-of-the-art optical experiments. Finally, we show how to produce distillable GKP magic states directly within the cluster state.

Automated summary

Continuous-variable cluster states combined with GKP encoding enable fault-tolerant measurement-based quantum computing. For quad-raillattice macronode cluster states, a Clifford gate and GKP error correction can be simultaneously implemented in a single teleportation step. Logical error rates compatible with the thresholds of topological codes can be achieved with finite squeezing in the resources.