|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)|
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.