@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}
}