Universal quantum computation with continuous-variable Abelian anyons

Milne, Darran F.; Korolkova, Natalia; Loock, Peter van

doi:10.1103/physreva.85.052325

Cited by 10 publications

(5 citation statements)

References 26 publications

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“…While abelian anyon field theories like those of Eq. ( 42) may be significant in quantum computing [55], it is rather nonabelian statistics that plays the main role in this kind of applications. Despite its limitations, when the Gauss linking number is applied to a 2s−plat configuration, which cannot be destroyed because the 2s points of maxima and minima are kept fixed, some of the nonabelian features of the system are certainly captured.…”

Section: Discussionmentioning

confidence: 99%

Knots, links, anyons and statistical mechanics of entangled polymer rings

et al. 2019

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The field theory approach to the statistical mechanics of a system of N polymer rings linked together is generalized to the case of links that have a fixed number 2s of maxima and minima. Such kind of links are called plats and appear for instance in the DNA of living organisms. The topological states of the link are distinguished using the Gauss linking number. This is a relatively weak link invariant in the case of a general link, but its efficiency improves when 2s−plats are considered. It is proved that, if we restrict ourselves to 2s−plat conformations, the field theoretical model established here is able to take into account also the interactions of topological origin involving three chains simultaneously. It is shown that these three-body interactions have nonvanishing contributions when three or more rings are entangled together, enhancing for instance the attractive forces between monomers. The model can be used to study the statistical mechanics of polymers in confined geometries, for instance when 2s extrema of a few polymer rings are attached to membranes. Its partition function is mapped here into that of a multi-layer electron gas. Such quasi-particle systems are studied in connection with several interesting applications, including high-T c superconductivity and topological quantum computing. At the end an useful connection with the cosh-Gordon equation is shown. *

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Section: Discussionmentioning

confidence: 99%

Knots, links, anyons and statistical mechanics of entangled polymer rings

et al. 2019

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“…CV topological codes require new features such as the direction of edges, signs for anyonic charges, and more complicated string operators, such as fusion rules, and braiding rules. [98] In addition, some other concepts related to it have been proposed in recent years, such as the CV anyon statistics, [76] the graphical calculus for CV states [99] and its application in quantum communication, [100] the CV QC with anyons, [101] the exploration of CV fault-tolerant QC, [102] and topological entanglement entropy. [103] error correction syndrome recognition decode…”

Section: Qec With Five-wave-packet Codementioning

confidence: 99%

Quantum computation and error correction based on continuous variable cluster states*

Hao¹,

Deng²,

Liu³

et al. 2021

Chinese Phys. B

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Measurement-based quantum computation with continuous variables, which realizes computation by performing measurement and feedforward of measurement results on a large scale Gaussian cluster state, provides a feasible way to implement quantum computation. Quantum error correction is an essential procedure to protect quantum information in quantum computation and quantum communication. In this review, we briefly introduce the progress of measurement-based quantum computation and quantum error correction with continuous variables based on Gaussian cluster states. We also discuss the challenges in the fault-tolerant measurement-based quantum computation with continuous variables.

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“…Some CV QEC schemes against displacement errors have been experimentally demonstrated, for example, the nine-wave-packet code [4], the five-wave-packet code [5] and the correcting code with the correlated noisy channels [6]. In addition, some basic concepts related to CV topological QC have been proposed in recent years, such as the CV anyon statistics [45], the graphical calculus for CV states [46], the CV topological codes [47] and its application in quantum communication [48], the CV QC with anyons [49], the exploration of CV fault-tolerant QC [50,51], and topological entanglement entropy [52]. These works established the foundation for the further research of CV topological 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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Universal quantum computation with continuous-variable Abelian anyons

Cited by 10 publications

References 26 publications

Knots, links, anyons and statistical mechanics of entangled polymer rings

Knots, links, anyons and statistical mechanics of entangled polymer rings

Quantum computation and error correction based on continuous variable cluster states*

Topological error correction with a Gaussian cluster state

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