nLab braid representation




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

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



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):


in relation to modular tensor categories:

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

Braid representations from the monodromy of the Knizhnik-Zamolodchikov connection on bundles of conformal blocks over configuration spaces of points:

and understood in terms of anyon statistics:

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:

Realization of Fibonacci anyons on quasicrystal-states:

Realization on supersymmetric spin chains:

  • Indrajit Jana, Filippo Montorsi, Pramod Padmanabhan, Diego Trancanelli, Topological Quantum Computation on Supersymmetric Spin Chains [[arXiv:2209.03822]]

Last revised on May 29, 2022 at 13:21:06. See the history of this page for a list of all contributions to it.