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. © 2014 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Jordan, S. P., & Alagic, G. (2014). Approximating the Turaev-Viro invariant of mapping tori is complete for one clean qubit. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6745 LNCS, pp. 53–72). Springer Verlag. https://doi.org/10.1007/978-3-642-54429-3_5
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