Journal
PHYSICAL REVIEW A
Volume 82, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.82.040302
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Funding
- Sherman Fairchild Foundation
- NSF [PHY-0803371, PHY05-51164]
- Swiss National Science Foundation (SNF) [PA00P2-126220]
- NSERC
- ARO
- Direct For Mathematical & Physical Scien
- Division Of Physics [0803371] Funding Source: National Science Foundation
- Swiss National Science Foundation (SNF) [PA00P2_126220] Funding Source: Swiss National Science Foundation (SNF)
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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)-dimensional 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 relation between the task of distinguishing nonhomeomorphic 3-manifolds and the power of a general quantum computer.
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