Topological cluster state quantum computing

Fowler, Austin G.; Goyal, Kovid

doi:10.26421/qic9.9-10-1

Cited by 37 publications

(65 citation statements)

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“…The state |C L is currently the best available choice, to the best of our knowledge, to make linear-optical platform fault tolerant; it can tolerate qubit loss [49,50], probabilistic entangling operations [14,45] and, dephasing and depolarizing noises [30,31,51], all of which are peculiar to the platform. Furthermore, QEC and gate operations on |C L is topological in nature and thus offers the highest fault tolerance in the platforms where interactions are restricted to those of the nearest neighbors [52].…”

Section: Protocolmentioning

confidence: 99%

“…An isolated dephasing error is detected by two check operators adjacent to the qubit. Generally, an error chain of dephasing errors is detected by two check operators located at its ends [30,31,51,66]. However, error chains connecting two opposite boundaries are not detectable, since there are no check operators at their ends.…”

Section: Appendix B: Simulation Of Qecmentioning

confidence: 99%

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All-photonic architectural roadmap for scalable quantum computing using Greenberger-Horne-Zeilinger states

Omkar,

Lee,

Teo

et al. 2021

Preprint

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Linear optical quantum computing is beset by the lack of deterministic entangling operations besides photon loss. Motivated by advancements at the experimental front in deterministic generation of various kinds of multiphoton entangled states, we propose an architecture for linear-optical quantum computing that harnesses the availability of three-photon Greenberger-Horne-Zeilinger (GHZ) states. Our architecture and its subvariants use polarized photons in GHZ states, polarization beam splitters, delay lines, optical switches and on-off detectors. We concatenate topological quantum error correction code with three-qubit repetition codes and estimate that our architecture can tolerate remarkably high photon-loss rate of 11.5%; this makes a drastic change that is at least an order higher than those of known proposals. Further, considering three-photon GHZ states as resources, we estimate the resource overheads to perform gate operations with an accuracy of 10 −6 (10 −15 ) to be 2.0 × 10 6 (5.6 × 10 7 ). Compared to other all-photonic schemes, our architecture is also resource-efficient. In addition, the resource overhead can be even further improved if larger GHZ states are available. Given its striking enhancement in the photon loss threshold and the recent progress in generating multiphoton entanglement, our scheme will make scalable photonic quantum computing a step closer to reality.

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Section: Protocolmentioning

confidence: 99%

Section: Appendix B: Simulation Of Qecmentioning

confidence: 99%

All-photonic architectural roadmap for scalable quantum computing using Greenberger-Horne-Zeilinger states

Omkar,

Lee,

Teo

et al. 2021

Preprint

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“…It has been shown that, cluster states whenever the underlying interaction graph can be embedded in a threedimensional cell structure, the so-called cell complex [10], can be used for QEC and fault-tolerant QC [11][12][13]. With a large cell complex, the quantum algorithms can be realized by suitable braiding-like manipulation of the defects [11]. It is based on the property that some topological quantum correlations hold on defect-enclosing closed surfaces.…”

Section: Introductionmentioning

confidence: 99%

“…We can use the redundancy of the cell complex to protect the topological correlations against local errors [12]. By using the topological properties of the cluster states, we can realize the topological QC and the active topological error correction (TEC) at the same time [11][12][13]. This topological QC will lead to a higher error threshold [14,15] and high tolerating loss rates [16] in the scalable QC.…”

Section: Introductionmentioning

confidence: 99%

Topological error correction with a Gaussian cluster state

Hao,

Wang,

Wang

et al. 2021

Preprint

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Topological error correction provides an effective method to correct errors in quantum computation. It allows quantum computation to be implemented with higher error threshold and high tolerating loss rates. We present a topological a error correction scheme with continuous variables based on an eight-partite Gaussian cluster state. We show that topological quantum correlation between two modes can be protected against a single quadrature phase displacement error occurring on any mode and some of two errors occurring on two modes. More interestingly, some cases of errors occurring on three modes can also be recognised and corrected, which is different from the topological error correction with discrete variables. We show that the final error rate after correction can be further reduced if the modes are subjected to identical errors occurring on all modes with equal probability. The presented results provide a feasible scheme for topological error correction with continuous variables and it can be experimentally demonstrated with a Gaussian cluster state.

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“…The recent use of topological techniques in the cluster state quantum computation scheme [1,2] has lead to some very encouraging fault tolerant threshold predictions. The initial estimate for the computational basis error threshold was 0.75% [1,2], but it is believed this could reach as high as 1% [3], making this architecture a serious contender for scalable quantum computing [4]. This scheme encodes qubits as defects in a three dimensional cluster state, constructing the necessary qubit gates via topological operations on the surface of the code.…”

Section: Introductionmentioning

confidence: 99%

Coherent state topological cluster state production

Myers¹,

Ralph²

2011

New J. Phys.

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We present results illustrating the construction of 3D topological cluster states with coherent state logic. Such a construction would be ideally suited to wave-guide implementations of quantum optical processing. We investigate the use of a ballistic csign gate, showing that given large enough initial cat states, it is possible to build large 3D cluster states. We model X and Z basis measurements by displaced photon number detections and x-quadrature homodyne detections, respectively. We investigate whether teleportation can aid cluster state construction and whether the introduction of located loss errors fits within the topological cluster state framework.

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Topological cluster state quantum computing

Cited by 37 publications

References 1 publication

All-photonic architectural roadmap for scalable quantum computing using Greenberger-Horne-Zeilinger states

All-photonic architectural roadmap for scalable quantum computing using Greenberger-Horne-Zeilinger states

Topological error correction with a Gaussian cluster state

Coherent state topological cluster state production

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