Approximating the Turaev-Viro Invariant of Mapping Tori is Complete for One Clean Qubit

DOI10.1007/978-3-642-54429-3_5zbMath1451.81170arXiv1105.5100OpenAlexW2140469741MaRDI QIDQ3453312

Gorjan Alagic, Stephen P. Jordan

Publication date: 20 November 2015

Published in: Theory of Quantum Computation, Communication, and Cryptography (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.5100

Mathematics Subject Classification ID

Quantum computation (81P68) Quantum algorithms and complexity in the theory of computing (68Q12) Knot polynomials (57K14) Invariants of 3-manifolds (including skein modules, character varieties) (57K31)

Cites Work

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• Topological quantum field theories
• Efficient quantum processing of three-manifold topological invariants
• Quantum computing and quadratically signed weight enumerators
• The two-eigenvalue problem and density of Jones representation of braid groups.
• Simulation of topological field theories by quantum computers
• A modular functor which is universal for quantum computation
• Skein theory and Turaev-Viro invariants
• Computing with highly mixed states
• Estimating Jones polynomials is a complete problem for one clean qubit
• Quantum invariants of knots and 3-manifolds

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