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

```@inproceedings{Jordan2011ApproximatingTT,
title={Approximating the Turaev-Viro Invariant of Mapping Tori is Complete for One Clean Qubit},
author={Stephen P. Jordan and Gorjan Alagic},
booktitle={TQC},
year={2011}
}```
• Published in TQC 24 May 2011
• Mathematics
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…
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