The BQP-hardness of approximating the Jones Polynomial

@article{Aharonov2006TheBO,
  title={The BQP-hardness of approximating the Jones Polynomial},
  author={Dorit Aharonov and Itai Arad},
  journal={CoRR},
  year={2006},
  volume={abs/quant-ph/0605181}
}
Following the work by Kitaev, Freedman and Wang [1], Aharonov, Jones and Landau [3] recently gave an explicit and efficient quantum algorithm for approximating the Jones polynomial of the plat closure of a braid, at the kth root of unity, for constant k. The universality proof of Freedman, Larsen and Wang [2] implies that the problem which these algorithms solve is BQP-hard. The fact that this is the only non-trivial BQP-complete problem known today motivates a deep investigation of this topic… CONTINUE READING
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