| Title | Approximating the Turaev-Viro Invariant of Mapping Tori is Complete for One Clean Qubit |
| Publication Type | Conference Proceedings |
| Year of Publication | 2011 |
| Authors | Jordan, SP, Alagic, G |
| Conference Name | In Proceedings of the Sixth Conference on Theory of Quantum Computation, Communication and Cryptography (TQC11) |
| Date Published | 2011/05/31 |
| Abstract | 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. |
| URL | http://arxiv.org/abs/1105.5100 |
