Quantum knitting

Laser Physics

Volumn 16, Issue 11, 2006, Pages 1582-1594

  Garnerone, S ^a,c   Marzuoli, A ^b,c   Rasetti, M ^a,c  

^a POLITECNICO DI TORINO   (Italy)

^b UNIVERSITY OF PAVIA   (Italy)

^c ISI FOUNDATION   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATION THEORY; COMPUTATIONAL COMPLEXITY; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING; TOPOLOGY;

JONES POLYNOMIAL; QUANTUM ALGORITHMS; QUANTUM KNITTING; QUANTUM PHYSICS;

QUANTUM THEORY;

EID: 33751537680     PISSN: 1054660X     EISSN: 15556611     Source Type: Journal    
DOI: 10.1134/S1054660X06110120     Document Type: Article

References (28)

1. E. Witten, Commun. Math. Phys. 121, 351 (1989).
2. V. F. R. Jones, Bull. Am. Math. Soc. 12, 103 (1985).
3. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, London, 2000).
4. F. Y. Wu, Rev. Mod. Phys. 64, 1099 (1992).
5. C. Gomez, M. Ruiz-Altaba, and G. Sierra, Quantum Group in Two-Dimensional Physics (Cambridge Univ. Press, Cambridge, 1996).
6. D. Aharonov, V. F. R. Jones, and Z. Landau, "A Polynomial Quantum Algorithm for Approximating the Jones Polynomial," quant-ph/0511096 (2005).
7. M. Bordewich, M. Freedman, L. Lovasz, and D. Welsh, "Approximate Counting and Quantum Computation," submitted to Combinatorics, Probability and Computing (2006).
8. S. Garnerone, A. Marzuoli, and M. Rasetti, J. Phys.: Conf. Ser. 33, 95 (2006).
9. S. Garnerone, A. Marzuoli, and M. Rasetti, "Quantum Automata, Braid Group and Link Polynomials," quant-ph/0601169 (2006).
10. P. Wocjan and J. Yard, "The Jones Polynomial: Quantum Algorithms and Applications to Quantum Complexity Theory," quant-ph/0603069 (2006).
11. D. Rolfsen, Knots and Links (Publish or Perish, Berkeley, CA, 1976).
12. J. S. Birman, Braids, Links, and Mapping Class Groups (Princeton Univ. Press, Princeton, 1974).
13. J. S. Birman and T. E. Brendle, "Braids: A Survey," mathGT/0409205 (2004).
14. W. B. R. Lickorish, An Introduction to Knot Theory (Springer, New York, 1997).
15. W. Magnus, A. Karrass, and D. Solitar, Combinatorial Group theory, 2nd ed. (Dover, New York, 1976).
16. I. Anshel, M. Anshel, and D. Goldfeld, Math. Res. Lett. 6, 1 (1999).
17. P. Freyd, D. Yetter, J. Hoste, et al., Bull. Am. Math. Soc. 12, 183 (1985).
18. V. F. R. Jones, "The Jones Polynomial," http://math.berkeley. edu/vfr/.
19. R. Kirby and R. Melvin, Invent. Math. 105, 473 (1991).
20. H. R. Morton and P. Strickland, Math. Proc. Cambridge Philos. Soc. 109, 83 (1991).
21. P. Ramadevi, T. R. Govindarajan, and R. K. Kaul, Mod. Phys. Lett. A 9, 3205 (1994).
22. R. K. Kaul, Commun. Math. Phys. 162, 289 (1994).
23. F. Jaeger, D. L. Vertigan, and D. J. A. Welsh, Math. Proc. Cambridge Philos. Soc. 108, 35 (1990).
24. M. H. Freedman, Proc. Natl. Acad. Sci. USA 95, 98 (1998).
25. M. H. Freedman, M. Larsen, and Z. Wang, Commun. Math. Phys. 227, 605 (2002).
26. A. Marzuoli and M. Rasetti, Ann. Phys. 318, 345 (2005).
27. S. Garnerone, A. Marzuoli, and M. Rasetti, "Quantum Algorithm" (J. Phys. A, in press).
28. S. J. Lomonaco and L. H. Kauffman, "Topological Quantum Computing and the Jones Polynomial," quant-ph/0605004 (2006).