Anyonic Braiding and Conformal Field Theory

Question

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

Comments

@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

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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

Answer 1

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).