A Polynomial Quantum Algorithm for Approximating the Jones Polynomial

@article{Aharonov2006APQ,
  title={A Polynomial Quantum Algorithm for Approximating the Jones Polynomial},
  author={Dorit Aharonov and Vaughan F. R. Jones and Zeph Landau},
  journal={Algorithmica},
  year={2006},
  volume={55},
  pages={395-421}
}
AbstractThe Jones polynomial, discovered in 1984, is an important knot invariant in topology. Among its many connections to various mathematical and physical areas, it is known (due to Witten) to be intimately connected to Topological Quantum Field Theory ( ${\sf{TQFT}}$ ). The works of Freedman, Kitaev, Larsen and Wang provide an efficient simulation of ${\sf{TQFT}}$ by a quantum computer, and vice versa. These results implicitly imply the existence of an efficient (namely, polynomial… 
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