CaltechAUTHORS
  A Caltech Library Service

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

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

[img]
Preview
PDF - Submitted Version
See Usage Policy.

302Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20120713-083236942

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)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1105.5100arXivUNSPECIFIED
Additional Information:This work was done at Institute for Quantum Information, Caltech.
Group:IQIM, Institute for Quantum Information and Matter
Record Number:CaltechAUTHORS:20120713-083236942
Persistent URL:http://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:26 Dec 2012 15:31

Repository Staff Only: item control page