



01079nas a2200121   4500008004100000245009300041210006900134260001500203520066100218100002400879700001900903856003500922       2011                        eng d00aApproximating the Turaev-Viro Invariant of Mapping Tori is Complete for  One Clean Qubit0 aApproximating the TuraevViro Invariant of Mapping Tori is Comple  c2011/05/313 a<p>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.</p>1 aJordan, Stephen, P.1 aAlagic, Gorjan  uhttp://arxiv.org/abs/1105.5100