A fault-tolerant one-way quantum computer

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

Loss tolerant linear optical quantum memory by measurement-based quantum computing

We give a scheme for loss tolerantly building a linear optical quantum memory which itself is tolerant to qubit loss. We use the encoding recently introduced in Varnava et al 2006 Phys. Rev. Lett. 97 120501, and give a method for efficiently achieving this. The entire approach resides within the 'one-way' model for quantum computing (Raussendorf and Briegel 2001 Phys. Rev. Lett. 86 5188–91; Raussendorf et al 2003 Phys. Rev. A 68 022312). Our results suggest that it is possible to build a loss tolerant quantum memory, such that if the requirement is to keep the data stored over arbitrarily long times then this is possible with only polynomially increasing resources and logarithmically increasing individual photon life-times

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

A direct approach to fault-tolerance in measurement-based quantum computation via teleportation

International audienceWe discuss a simple variant of the one-way quantum computing model [R. Raussendorf and H.-J. Briegel, PRL 86, 5188, 2001], called the Pauli measurement model, where measurements are restricted to be along the eigenbases of the Pauli X and Y operators, while auxiliary qubits can be prepared both in the $\ket{+_{\pi\over 4}}:={1/\sqrt{2}}(\ket{0}+e^{i{\pi\over 4}}\ket{1})$ state, and the usual $\ket{+}:={1/ \sqrt{2}}(\ket{0}+\ket{1})$ state. We prove the universality of this quantum computation model, and establish a standardization procedure which permits all entanglement and state preparation to be performed at the beginning of computation. This leads us to develop a direct approach to fault-tolerance by simple transformations of the entanglement graph and preparation operations, while error correction is performed naturally via syndrome-extracting teleportations

Brokered Graph State Quantum Computing

We describe a procedure for graph state quantum computing that is tailored to fully exploit the physics of optically active multi-level systems. Leveraging ideas from the literature on distributed computation together with the recent work on probabilistic cluster state synthesis, our model assigns to each physical system two logical qubits: the broker and the client. Groups of brokers negotiate new graph state fragments via a probabilistic optical protocol. Completed fragments are mapped from broker to clients via a simple state transition and measurement. The clients, whose role is to store the nascent graph state long term, remain entirely insulated from failures during the brokerage. We describe an implementation in terms of NV-centres in diamond, where brokers and clients are very naturally embodied as electron and nuclear spins.Comment: 5 pages, 3 figure