Streamlined quantum computing with macronode cluster states

Abstract

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-rail-lattice 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.

16 pages, 2 figures, 2 tables

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• Switching-free time-domain optical quantum computation with quantum teleportation
• Quantum Volume for Photonic Quantum Processors
• Equivalent noise properties of scalable continuous-variable cluster states
• A complete continuous-variable quantum computation architecture based on the 2D spatiotemporal cluster state
• End-to-end switchless architecture for fault-tolerant photonic quantum computing
• Logical channel for heralded and pure loss with the Gottesman-Kitaev-Preskill code
• Logical channels in approximate Gottesman-Kitaev-Preskill error correction