@article {1401, title = {Approximating Turaev-Viro 3-manifold invariants is universal for quantum computation }, journal = {Physical Review A}, volume = {82}, year = {2010}, month = {2010/10/8}, abstract = { 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 decidable by a quantum computer. Thus approximating certain Turaev-Viro invariants of manifolds presented by Heegaard splittings is a universal problem for quantum computation. This establishes a novel relation between the task of distinguishing non-homeomorphic 3-manifolds and the power of a general quantum computer. }, doi = {10.1103/PhysRevA.82.040302}, url = {http://arxiv.org/abs/1003.0923v1}, author = {Gorjan Alagic and Stephen P. Jordan and Robert Koenig and Ben W. Reichardt} }