%0 Journal Article %J Physical Review A %D 2010 %T Approximating Turaev-Viro 3-manifold invariants is universal for quantum computation %A Gorjan Alagic %A Stephen P. Jordan %A Robert Koenig %A Ben W. Reichardt %X 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. %B Physical Review A %V 82 %8 2010/10/8 %G eng %U http://arxiv.org/abs/1003.0923v1 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.82.040302