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  Anyonic Braiding and Conformal Field Theory

+ 4 like - 0 dislike

I am looking for resources (both pedagogical and newer research articles) on the connection between topological quantum computation and conformal field theory. In particular, a CFT description of anyonic braiding, fractional statistics, and/or the braid group of which assumes basic knowledge of conformal field theory and topological quantum computation. Does anyone know any good resources on this subject?

This post imported from StackExchange Physics at 2015-06-20 08:29 (UTC), posted by SE-user Joshuah Heath
asked Jun 10, 2015 in Resources and References by Joshuah Heath (70 points) [ no revision ]
retagged Jun 20, 2015
@CuriousOne I already did a Google search, and (other than a book on Amazon I can't get access to right now) I only found that the fusing and braiding of anyons is identical to a 2d rotational conformal field theory. I was really looking for a more descriptive covering of the topic.

This post imported from StackExchange Physics at 2015-06-20 08:29 (UTC), posted by SE-user Joshuah Heath
Have you looked at the review arxiv.org/abs/0707.1889, which is by now a standard reference in the field? Section III D is about the relation between Chern-Simons theory, CFT and quantum Hall states and I think that is a good place to start.

This post imported from StackExchange Physics at 2015-06-20 08:29 (UTC), posted by SE-user Meng Cheng

1 Answer

+ 3 like - 0 dislike

Here are some important papers 

Fault-tolerant quantum computation by anyons (Kitaev 2003)

Computing with quantum knots (Collins 2006)

Non-Abelian anyons and topological quantum computation  (Nayak et al. 2008)

Measurement-only topological quantum computation via anyonic interferometry (Bonderson et al. 2009)

 an online book 

Introduction to topological quantum computation (Pachos 2012)

and an introduction 

An Anyon Primer (Rao 1992).

answered Jun 20, 2015 by Arnold Neumaier (15,787 points) [ revision history ]
edited Oct 28, 2016 by Arnold Neumaier

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