Streamlined quantum computing with macronode cluster states

TL;DR

This paper demonstrates a method for efficient, fault-tolerant quantum computing using macronode cluster states with GKP encoding, achieving low logical error rates with current optical technology.

Contribution

It introduces a protocol that combines Clifford gates and GKP error correction in a single step, reducing noise and lowering the squeezing requirements for fault tolerance.

Findings

Logical error rates of 10^{-2} to 10^{-3} are achievable.

Squeezing levels of 11.9-13.7 dB are sufficient for fault-tolerant operation.

The protocol enables direct production of distillable GKP magic states within the cluster state.

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.