Markov Trace and Markov Property - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T03:28:15Z http://mathoverflow.net/feeds/question/54537 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/54537/markov-trace-and-markov-property Markov Trace and Markov Property vivid-colours 2011-02-06T17:06:10Z 2011-02-06T18:51:48Z <p>Hey guys,</p> <p>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:</p> <ul> <li>Markov Trace</li> <li>Markov Property</li> </ul> <p>For example, the following article tells me what a Markov trace is but it's out of my zone a bit:</p> <p>@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} }</p> <p>Can anyone explain what they are very simply? Thank you :).</p> <p>EDIT: Sorry for being not specific enough, this is the paper I'm referring to:</p> <p>@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}}</p> <p>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!</p> http://mathoverflow.net/questions/54537/markov-trace-and-markov-property/54548#54548 Answer by Sam Nead for Markov Trace and Markov Property Sam Nead 2011-02-06T18:51:48Z 2011-02-06T18:51:48Z <p>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 <a href="http://arxiv.org/abs/quant-ph/0511096v2" rel="nofollow">arxiv</a>.</p>