Topological quantum computing

Steve Flammia from the University of New Mexico has been visiting, and has been giving us a great series of tutorial talks on topological quantum computing. Steve has prepared a webpage for his tutorials (to be expanded as the tutorials go on), which you may wish to look at if you’re interested in learning the subject.


  1. It would be interesting if knot invariants actually ended up having an application, eg in topological quantum computing!

    I havn’t had the time to properly understand topological quantum computing (being trained as a maths person and all that), however I do know about knot invariants and quantum groups etc, and the potential of topological quantum computing is very interesting!

  2. I haven’t followed the work closely, but do know that there is a sense in which computing the Jones polynomial is complete for quantum computing. (I.e., it can be regarded as a canonical problem for quantum computing, to which all the others can be reduced). Start from quant-ph/0605181 and work backwards!

  3. I’ll check it out when I have time – I only started understanding it in the scientific american article a few months ago – it sounded as if you could compute something, somehow, by creating a braid to encode the computation, and then calculating the Jones polynomial for the braid, which is a pretty straightforward thing to do, conceptually. (Just taking the quantum trace of a matrix).

  4. Thanks for the reference, Michael. When I read the sci am article, I wondered about the relation between calculating a knot polynomial and using that to simulate a quantum computer, and this is discussed in this article.

    Reading my previous comment – of course, doing something conceptually can be easy. Actually doing it may be difficult! (eg multiplying all the matrices representing the braidings in a braid and then taking the quantum trace of the resultant).

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