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

TitleApproximating Turaev-Viro 3-manifold invariants is universal for quantum computation
Publication TypeJournal Article
Year of Publication2010
AuthorsAlagic, G, Jordan, SP, Koenig, R, Reichardt, BW
JournalPhysical Review A
Date Published2010/10/8

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

Short TitlePhys. Rev. A