Jordan, Stephen P. and Alagic, Gorjan (2011) Approximating the Turaev-Viro Invariant of Mapping Tori is Complete for One Clean Qubit. . (Submitted) https://resolver.caltech.edu/CaltechAUTHORS:20120713-083236942
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Abstract
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) | ||||||
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| Additional Information: | This work was done at Institute for Quantum Information, Caltech. | ||||||
| Group: | UNSPECIFIED, Institute for Quantum Information and Matter | ||||||
| Record Number: | CaltechAUTHORS:20120713-083236942 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20120713-083236942 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 32408 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Tony Diaz | ||||||
| Deposited On: | 19 Jul 2012 22:36 | ||||||
| Last Modified: | 04 Jun 2020 10:14 |
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