nLab
braid representation

Contents

Contents

Idea

A braid representation is a linear representation of a braid group.

In topological quantum computation on anyons, braid representations serve as quantum gates.

References

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)

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:

Last revised on July 12, 2021 at 17:11:01. See the history of this page for a list of all contributions to it.