Quantum Fourier Transforms and the Complexity of Link Invariants for Quantum Doubles of Finite Groups

@article{Krovi2012QuantumFT,
  title={Quantum Fourier Transforms and the Complexity of Link Invariants for Quantum Doubles of Finite Groups},
  author={Hari Krovi and Alexander Russell},
  journal={Communications in Mathematical Physics},
  year={2012},
  volume={334},
  pages={743-777}
}
  • H. Krovi, A. Russell
  • Published 4 October 2012
  • Mathematics
  • Communications in Mathematical Physics
Knot and link invariants naturally arise from any braided Hopf algebra. We consider the computational complexity of the invariants arising from an elementary family of finite-dimensional Hopf algebras: quantum doubles of finite groups [denoted $${{\mathsf{D}(G)}}$$D(G), for a group G]. These induce a rich family of knot invariants and, additionally, are directly related to topological quantum computation.Regarding algorithms for these invariants, we develop quantum circuits for the quantum… 
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