nLab topological quantum computation with anyons -- references

Topological quantum computation with anyons

Topological quantum computation with anyons

The idea of topological quantum computation via the Chern-Simons theory of anyons (e.g. in the quantum Hall effect) is due to:

Textbook accounts:

Review:

Focus on abelian anyons:

Realization in experiment:

  • Daniel Nigg, Markus Mueller, Esteban A. Martinez, Philipp Schindler, Markus Hennrich, Thomas Monz, Miguel A. Martin-Delgado, Rainer Blatt,

    Experimental Quantum Computations on a Topologically Encoded Qubit, Science 18 Jul 2014: Vol. 345, Issue 6194, pp. 302-305 (arXiv:1403.5426, doi:10.1126/science.1253742)

    (for quantum error correction)

Braid group representations (as topological quantum gates)

On linear representations of braid groups (see also at braid group statistics and interpretation as quantum gates in topological quantum computation):

Review:

in relation to modular tensor categories:

  • Colleen Delaney, Lecture notes on modular tensor categories and braid group representations, 2019 (pdf, pdf)

Braid representations seen inside the topological K-theory of the braid group‘s classifying space:

See also:

  • R. B. Zhang, Braid group representations arising from quantum supergroups with arbitrary qq and link polynomials, Journal of Mathematical Physics 33, 3918 (1992) (doi:10.1063/1.529840)

As quantum gates for topological quantum computation with anyons:

Introduction and review:

Approximating all topological quantum gates by just the weaves among all braids:

Last revised on June 11, 2022 at 12:05:03. See the history of this page for a list of all contributions to it.