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.
We describe a fault-tolerant one-way quantum computer on cluster states in
three dimensions. The presented scheme uses methods of topological error
correction resulting from a link between cluster states and surface codes. The
error threshold is 1.4% for local depolarizing error and 0.11% for each source
in an error model with preparation-, gate-, storage- and measurement errors.Comment: 26 page
The quantum computing scheme described by Raussendorf et. al (2007), when viewed as a cluster state computation, features a 3-D cluster state, novel adjustable strength error correction capable of correcting general errors through the correction of Z errors only, a threshold error rate approaching 1% and low overhead arbitrarily long-range logical gates. In this work, we review the scheme in detail framing the discussion solely in terms of the required 3-D cluster state and its stabilizers.
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