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!



Markov Trace and Markov Property
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](http://arxiv.org/abs/quant-ph/0511096v2).


