TY - Generic T1 - Approximating the Turaev-Viro Invariant of Mapping Tori is Complete for One Clean Qubit T2 - In Proceedings of the Sixth Conference on Theory of Quantum Computation, Communication and Cryptography (TQC11) Y1 - 2011 A1 - Stephen P. Jordan A1 - Gorjan Alagic AB -

The Turaev-Viro invariants are scalar topological invariants of three-dimensional manifolds. Here we show that the problem of estimating the Fibonacci version of the Turaev-Viro invariant of a mapping torus is a complete problem for the one clean qubit complexity class (DQC1). This complements a previous result showing that estimating the Turaev-Viro invariant for arbitrary manifolds presented as Heegaard splittings is a complete problem for the standard quantum computation model (BQP). We also discuss a beautiful analogy between these results and previously known results on the computational complexity of approximating the Jones polynomial.

JA - In Proceedings of the Sixth Conference on Theory of Quantum Computation, Communication and Cryptography (TQC11) UR - http://arxiv.org/abs/1105.5100 ER -