Exact correctability of fusion-space codes is equivalent to fibrewise Knill–Laflamme conditions on syndrome-admissible footprint algebras, with a conditional Peierls threshold for growing families and explicit Ising examples of diagnostic versus syndrome measurements.
Topological fault-tolerance in cluster state quantum computation
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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.
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A diagrammatic field theory of quantum error correction
Exact correctability of fusion-space codes is equivalent to fibrewise Knill–Laflamme conditions on syndrome-admissible footprint algebras, with a conditional Peierls threshold for growing families and explicit Ising examples of diagnostic versus syndrome measurements.