Abstract
Continuous variable measurement-based quantum computation on cluster states has in recent years shown great potential for scalable, universal, and fault-tolerant quantum computation when combined with the Gottesman-Kitaev-Preskill (GKP) code and quantum error correction. However, no complete fault-tolerant architecture exists that includes everything from cluster state generation with finite squeezing to gate implementations with realistic noise and error correction. In this work, we propose a simple architecture for the preparation of a cluster state in three dimensions in which gates by gate teleportation can be efficiently implemented. To accommodate scalability, we propose architectures that allow for both spatial and temporal multiplexing, with the temporal encoded version requiring as little as two squeezed light sources. Due to its three-dimensional structure, the architecture supports topological qubit error correction, while GKP error correction is efficiently realized within the architecture by teleportation. To validate fault-tolerance, the architecture is simulated using surface-GKP codes, including noise from GKP-states as well as gate noise caused by finite squeezing in the cluster state. We find a fault-tolerant squeezing threshold of 12.7 dB with room for further improvement.
Highlights
In measurement-based quantum computation (MBQC), gates are implemented by projective measurements on a multimode entangled cluster state, circumventing the complex coherent unitary dynamics required in conventional gate-based quantum computation [1]
As a result, when the topological surface code is combined with GKP error correction in the surface-GKP code [29], we find a squeezing threshold of 17.3 dB
We propose a simple but complete and scalable architecture for optical CV MBQC that includes quadrature noise correction and qubit error correction using topological codes
Summary
In measurement-based quantum computation (MBQC), gates are implemented by projective measurements on a multimode entangled cluster state, circumventing the complex coherent unitary dynamics required in conventional gate-based quantum computation [1]. Fukui et al [18] suggested a scheme for fault-tolerant MBQC based on topological error correction, but their scheme assumes the availability of a highly complex 3D cluster state of encoded qubits. The suggested architecture is based on spatial encoding, rendering the amount of spatial resources required very large (as this number scales linearly with the computation size) Their scheme relies on a very large number of experimentally challenging online swap and sum gates, which they assume to be ideal. We propose a simple, scalable, and complete architecture for topological MBQC and validate the fault tolerance of the computation scheme. We validate the fault tolerance of the full scheme by a thorough simulation that includes both noise in the GKP qubits and, unlike previous work, gate noise caused by finite squeezing in the cluster state.
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