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Hey guys,

I'm a computer science student attempting to understand a quantum algorithm that uses braid theory - something I'm completely unfamiliar. I've getting through the algorithm but I can't find any simple explanations of the following terms:

  • Markov Trace
  • Markov Property

For example, the following article tells me what a Markov trace is but it's out of my zone a bit:

@ARTICLE{markov, author = {{Orellana}, R. and {Ram}, A.}, title = "{Affine braids, Markov traces and the category O}", journal = {ArXiv Mathematics e-prints}, eprint = {arXiv:math/0401317}, keywords = {Representation Theory}, year = 2004, month = jan, adsurl = {http://adsabs.harvard.edu/abs/2004math......1317O}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} }

Can anyone explain what they are very simply? Thank you :).

EDIT: Sorry for being not specific enough, this is the paper I'm referring to:

@article{tutte, Author = {Aharonov D and Arad I and Eban E and Landau Z}, Journal = {Arxiv preprint quant-ph/0702008}, Title = {Polynomial Quantum Algorithms for Additive approximations of the Potts model and other Points of the Tutte Plane}, Year = {2007}}

I'm trying to get my head around how the Tutte polynomial is approximated using tensor networks in quantum computing. This is perhaps too specific now!

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  • $\begingroup$ Perhaps say what you are trying to read. That way MO would know which Markov property is being referred to... $\endgroup$
    – Sam Nead
    Commented Feb 6, 2011 at 17:37
  • $\begingroup$ I've made an EDIT - see original post. Thank you :). $\endgroup$
    – ale
    Commented Feb 6, 2011 at 18:26

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I think you want section 2.11 of reference [6] of the paper you are looking at, namely "A Polynomial Quantum Algorithm for Approximating the Jones Polynomial" at the arxiv.

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