Thresholds for Topological Codes in the Presence of Loss

Stace, Thomas M.; Barrett, S. D.; Doherty, Andrew C.

doi:10.1103/physrevlett.102.200501

Cited by 129 publications

(167 citation statements)

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“…8. Our procedure is also related to methods developed to cope with qubit loss in surface codes [36] and similar critical regions have been found in these situations. For the case where P c = 1 the critical value of p ′ x in an infinite square network is then given by H(p ′ x ) = 1/2.…”

Section: Fig 7: A) P ′mentioning

confidence: 99%

Long-distance entanglement generation in two-dimensional networks

Dorner

Jaksch

2010

Phys. Rev. A

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We consider 2D networks composed of nodes initially linked by two-qubit mixed states. In these networks we develop a global error correction scheme that can generate distance-independent entanglement from arbitrary network geometries using rank two states. By using this method and combining it with the concept of percolation we also show that the generation of long distance entanglement is possible with rank three states. Entanglement percolation and global error correction have different advantages depending on the given situation. To reveal the trade-off between them we consider their application on networks containing pure states. In doing so we find a range of pure-state schemes, each of which has applications in particular circumstances: For instance, we can identify a protocol for creating perfect entanglement between two distant nodes. However, this protocol can not generate a singlet between any two nodes. On the other hand, we can also construct schemes for creating entanglement between any nodes, but the corresponding entanglement fidelity is lower.

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Section: Fig 7: A) P ′mentioning

confidence: 99%

Long-distance entanglement generation in two-dimensional networks

Dorner

Jaksch

2010

Phys. Rev. A

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“…The task of determining a threshold for universal QIP depends on proper choice of growth strategy together with a careful audit of the accumulation of unknown errors in that process. We show how to map this cluster state with missing 'edges' to one with missing qubits, thereby making contact with the loss-tolerant thresholds quoted in the prior literature [21][22][23].…”

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confidence: 99%

“…QIP implemented using this topologically protected cluster (TPC) state has a remarkably large tolerance against elementary errors (at rates 1%) during preparation, entangling operations and single qubit measurement. Subsequently, two of us have extended this idea to incorporate the possibility that the lattice contains a significant proportion of missing qubits at known locations (nearly 25% can be missing) [21][22][23].Here we consider the generation of a TPC state when the entangling operations are themselves subject to heralded failures during the cluster state growth process. The result is a lattice with a certain proportion of known failed entanarXiv:1008.1369v1 [quant-ph]…”

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confidence: 99%

“…Fortunately, by simply treating the qubits i and j at each end of the missing bond as though they were lost, and adopting the strategy in [21][22][23], we form products of the damaged parity check operators, yielding super-check operatorsP i =P 1…”

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Fault Tolerant Quantum Computation with Nondeterministic Gates

et al. 2010

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In certain approaches to quantum computing the operations between qubits are non-deterministic and likely to fail. For example, a distributed quantum processor would achieve scalability by networking together many small components; operations between components should assumed to be failure prone. In the logical limit of this architecture each component contains only one qubit. Here we derive thresholds for fault tolerant quantum computation under such extreme paradigms. We find that computation is supported for remarkably high failure rates (exceeding 90%) providing that failures are heralded, meanwhile the rate of unknown errors should not exceed 2 in 10 4 operations.The field of quantum information processing (QIP) has seen many experimental successes, but the challenge of scaling from a few qubits to large scale devices remains unsolved. One can argue that the issue is so crucial that it should dictate the choice of fundamental architecture for the machine. For example, in the concept of distributed QIP a plurality of small components, each similar in complexity to systems already realised experimentally, are networked together to constitute a full scale machine. The components may be trapped atoms or ions, or solid state nanostructures such as quantum dots or NV centres [1]. Each component can be presumed to be under good control, and it is understood that the key task is then to entangle the physically remote components. An attractive method of achieving this entangling operation (EO) is to arrange for each component to emit a photon that is correlated with the internal state of the component, before performing a joint measurement (with the aid of simple linear optical elements) of the photons. A considerable number of such entanglement schemes have been advanced since the first ideas in 1999 [2,3]. An important step was the realisation that photon loss can be detected, or heralded, within such a protocol [4,5]. Generally in these remote entanglement protocols, one is supposed to employ optical measurements that simultaneously observe two, or even four [6], components simultaneously. This principle for generating entanglement has in fact been demonstrated experimentally: first with ensemble systems [7] and subsequently with individual atoms [8].It is understood that the remote EOs may be failure prone. However, these failures are assumed to be heralded: the experimentalist is aware when a failure occurs. The appropriate strategy for dealing with such failures depends on the level of complexity within each component. In the case that each component incorporates multiple qubits then we can nominate one 'logical qubit' and use the other(s) to make repeated attempts at remote entanglement; when we are eventually successful then we can transfer the entanglement to the logical qubits [9,10]. However, many physical systems may have only very limited complexity, and moreover it is always desirable to minimise the required complexity. Therefore it is interesting to consider the case of just one qubit in each compone...

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2012

Advanced Quantum Communications

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Thresholds for Topological Codes in the Presence of Loss

Cited by 129 publications

References 23 publications

Long-distance entanglement generation in two-dimensional networks

Long-distance entanglement generation in two-dimensional networks

Fault Tolerant Quantum Computation with Nondeterministic Gates

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