2 research outputs found
Topological fault-tolerance in cluster state quantum computation
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.Comment: 20 pages, 12 figure
Optical generation of matter qubit graph states
We present a scheme for rapidly entangling matter qubits in order to create
graph states for one-way quantum computing. The qubits can be simple 3-level
systems in separate cavities. Coupling involves only local fields and a static
(unswitched) linear optics network. Fusion of graph state sections occurs with,
in principle, zero probability of damaging the nascent graph state. We avoid
the finite thresholds of other schemes by operating on two entangled pairs, so
that each generates exactly one photon. We do not require the relatively slow
single qubit local flips to be applied during the growth phase: growth of the
graph state can then become a purely optical process. The scheme naturally
generates graph states with vertices of high degree and so is easily able to
construct minimal graph states, with consequent resource savings. The most
efficient approach will be to create new graph state edges even as qubits
elsewhere are measured, in a `just in time' approach. An error analysis
indicates that the scheme is relatively robust against imperfections in the
apparatus.Comment: 10 pages in 2 column format, includes 4 figures. Problems with
figures resolve