Markov Trace and Markov Property

2011-02-06T17:06:10Z

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!

Answer by Sam Nead for Markov Trace and Markov Property

2011-02-06T18:51:48Z

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.

Markov Trace and Markov Property - MathOverflow

Markov Trace and Markov Property

Answer by Sam Nead for Markov Trace and Markov Property