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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 of a 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 problem belonging to the class BQP, i.e. such that it can be computed with bounded error in polynomial time using quantum resources.
  • 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 of a 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 problem belonging to the class BQP, i.e. such that it can be computed with bounded error in polynomial time using quantum resources. (en)
Title
  • A permanent formula for the Jones polynomial
  • A permanent formula for the Jones polynomial (en)
skos:prefLabel
  • A permanent formula for the Jones polynomial
  • A permanent formula for the Jones polynomial (en)
skos:notation
  • RIV/00216208:11320/11:10104296!RIV12-MSM-11320___
http://linked.open...avai/predkladatel
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(1M0545), Z(MSM0021620838)
http://linked.open...iv/cisloPeriodika
  • 4
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 184050
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/11:10104296
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Quantum computing; Approximation; State sums; Jones polynomial; permanent (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [D3CADCA99227]
http://linked.open...i/riv/nazevZdroje
  • Advances in Applied Mathematics
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 47
http://linked.open...iv/tvurceVysledku
  • Loebl, Martin
  • Moffat, Iain
http://linked.open...ain/vavai/riv/wos
  • 000295445300001
http://linked.open...n/vavai/riv/zamer
issn
  • 0196-8858
number of pages
http://bibframe.org/vocab/doi
  • 10.1016/j.aam.2011.03.003
http://localhost/t...ganizacniJednotka
  • 11320
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