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Estimating Turaev-Viro three-manifold invariants is universal for quantum computation
Physical Review A. Atomic, Molecular, and Optical Physics
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 efficientlydoi:10.1103/physreva.82.040302 fatcat:lqcbgycsrrdxvktmmzeshjhgb4