A permanent formula for the Jones polynomial

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10104296" target="_blank" >RIV/00216208:11320/11:10104296 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.aam.2011.03.003" target="_blank" >http://dx.doi.org/10.1016/j.aam.2011.03.003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aam.2011.03.003" target="_blank" >10.1016/j.aam.2011.03.003</a>

Result language
angličtina
Original language name
A permanent formula for the Jones polynomial
Original language description
The permanent of a square matrix is defined in a way similar to the determinant, but without using signs. The exact computation of the permanent is hard, but there are Monte Carlo algorithms that can estimate general permanents. Given a planar diagram ofa link L with n crossings, we define a 7n x 7n matrix whose permanent equals the Jones polynomial of L. This result, accompanied with recent work of Freedman, Kitaev, Larsen and Wang (2003) [8], provides a Monte Carlo algorithm for any decision problembelonging to the class BQP, i.e. such that it can be computed with bounded error in polynomial time using quantum resources.
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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