01327nas a2200157 4500008004100000245009200041210006900133260001400202490000700216520082400223100001901047700002401066700001901090700002301109856003701132 2010 eng d00aApproximating Turaev-Viro 3-manifold invariants is universal for quantum computation
0 aApproximating TuraevViro 3manifold invariants is universal for q c2010/10/80 v823 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 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.
1 aAlagic, Gorjan1 aJordan, Stephen, P.1 aKoenig, Robert1 aReichardt, Ben, W. uhttp://arxiv.org/abs/1003.0923v1