Approximating Turaev-Viro 3-manifold invariants is universal for quantum computation

  title={Approximating Turaev-Viro 3-manifold invariants is universal for quantum computation},
  author={Gorjan Alagic and Stephen P. Jordan and Robert K{\"o}nig and Ben Reichardt},
  journal={Physical Review A},
The Turaev-Viro invariants are scalar topological invariants of compact, orientable 3-manifolds. We give a quantum algorithm for additively approximating Turaev-Viro invariants of a manifold presented by a Heegaard splitting. The algorithm is motivated by the relationship between topological quantum computers and (2+1)-D topological quantum field theories. Its accuracy is shown to be nontrivial, as the same algorithm, after efficient classical preprocessing, can solve any problem efficiently… Expand

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