Topological fault-tolerance in cluster state quantum computation

TLDR

The paper proposes a fault‑tolerant one‑way quantum computer based on a three‑dimensional cluster state. Topological protection is achieved by selecting boundary conditions on the cluster, with equivalence transformations simplifying circuits, and by reducing the scheme to two dimensions by treating one spatial axis as time. The scheme attains a 0.75 % error threshold per source and requires only poly‑logarithmic overhead in circuit size.

Abstract

We describe a fault-tolerant version of the one-way quantum computer using a cluster state in three spatial dimensions. Topologically protected quantum gates are realized by choosing appropriate boundary conditions on the cluster. We provide equivalence transformations for these boundary conditions that can be used to simplify fault-tolerant circuits and to derive circuit identities in a topological manner. The spatial dimensionality of the scheme can be reduced to two by converting one spatial axis of the cluster into time. The error threshold is 0.75% for each source in an error model with preparation, gate, storage and measurement errors. The operational overhead is poly-logarithmic in the circuit size.