Spin networks and anyonic topological computing

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 6244, Issue , 2006, Pages

  Kauffman, Louis H ^a   Lomonaco Jr , Samuel J ^b  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

^b Baltimore County   (United States)

Author keywords

Braiding; Knotting; Linking; Spin network; Temperley Lieb algebra; Unitary representation

Indexed keywords

COMPUTATION THEORY; OPTICAL COMMUNICATION; TOPOLOGY;

BRAIDING; KNOTTING; LINKING; SPIN NETWORK; TEMPERLEY - LIEB ALGEBRA; UNITARY REPRESENTATION;

QUANTUM THEORY;

EID: 33747332832     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.666291     Document Type: Conference Paper

References (14)

1. M. Freedman, A magnetic model with a possible Chern-Simons phase, quant-ph/0110060vl 9 Oct 2001, (2001), preprint
2. M. Freedman, Topologicat Views on Computational Complexity, Documenta Mathematica - Extra Volume ICM, 1998, pp. 453-464.
3. M. Freedman, M. Larsen, and Z. Wang, A modular functor which is universal for quantum computation, quant-ph/0001108v2, 1 Feb 2000.
4. M. H. Freedman, A. Kitaev, Z. Wang, Simulation of topological field theories by quantum computers, Commun. Math. Phys., 227, 587-603 (2002), quant-ph/0001071.
5. M. Freedman, Quantum computation and the localization of modular functors, quant-ph/0003128.
6. V.F.R. Jones, A polynomial invariant for links via von Neumann algebras, Bull. Amer. Math. Soc. 129 (1985). 103-112.
7. L.H. Kauffman, State models and the Jones polynomial, Topology 26 (1987), 395-407.
8. L.H. Kauffman, Temperley - Lieb Recoupling Theory and Invariants of Three-Manifolds. Princeton University Press, Annals Studies 114 (1994).
9. L. H. Kauffman and S. J. Lomonaco Jr., Braiding Operators are Universal Quantum Gates, New Journal of Physics 6 (2004) 134, pp. 1-39.
10. A. Kitaev, Anyons in an exactly solved model and beyond, arXiv.cond-mat/0506438 vl 17 June 2005.
11. A. Marzuoli and M. Rasetti, Spin network quantum simulator, Physics Letters A 306 (2002) 79-87.
12. R. Penrose, Angular momentum: An approach to Combinatorial Spacetime, In Quantum Theory and Beyond, edited by T. Bastin, Cambridge University Press (1969).
13. J. Preskill, Topological computing for beginners, (slide presentation), Lecture Notes for Chapter 9 - Physics 219 - Quantum Computation, http://www.iqi.caltech.edu/preskill/ph219
14. F. Wilczek, Fractional Statistics and Anyon Superconductivity, World Scientific Publishing Company (1990).