Jordan, Stephen P. and Alagic, Gorjan (2011) Approximating the Turaev-Viro Invariant of Mapping Tori is Complete for One Clean Qubit. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20120713-083236942
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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.
|Item Type:||Report or Paper (Discussion Paper)|
|Additional Information:||This work was done at Institute for Quantum Information, Caltech.|
|Group:||IQIM, Institute for Quantum Information and Matter|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||19 Jul 2012 22:36|
|Last Modified:||26 Dec 2012 15:31|
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