Topologically protected gates for quantum computation with non-Abelian anyons in the Pfaffian quantum Hall state

Physical Review B - Condensed Matter and Materials Physics

Volumn 74, Issue 23, 2006, Pages

  Georgiev, Lachezar S ^a  

^a INSTITUTE FOR NUCLEAR RESEARCH AND NUCLEAR ENERGY   (Bulgaria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33845801623     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.74.235112     Document Type: Article

References (31)

1. F. Wilczek, Fractional Statistics and Anyon Superconductivity (World Scientific, Singapore, 1990).
2. J. P. Eisenstein, K. B. Cooper, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.076801 88, 076801 (2002).
3. J. S. Xia, W. Pan, C. L. Vicente, E. D. Adams, N. S. Sullivan, H. L. Stormer, D. C. Tsui, L. N. Pfeiffer, K. W. Baldwin, and K. W. West, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.176809 93, 176809 (2004).
4. R. H. Morf, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.1505 80, 1505 (1998).
5. E. H. Rezayi and F. D. M. Haldane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.4685 84, 4685 (2000).
6. N. Read and D. Green, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.61. 10267 61, 10267 (2000).
7. D. A. Ivanov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86. 268 86, 268 (2001).
8. G. Moore and N. Read, Nucl. Phys. B NUPBBO 0550-3213 360, 362 (1991).
9. R. de Picciotto, M. Reznikov, M. Meiblum, V. Umansky, G. Bunin, and D. Mahalu, Nature (London) NATUAS 0028-0836 10.1038/38241 389, 162 (1997).
10. F. E. Camino, W. Zhou, and V. J. Goldman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.246802 95, 246802 (2005).
11. A. Stern and B. I. Halperin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.016802 94, 016802 (2006).
12. P. Bonderson, A. Kitaev, and K. Shtengel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.016803 96, 016803 (2006).
13. L. S. Georgiev and M. R. Geller, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.205310 73, 205310 (2006).
14. P. Bonderson, K. Shtengel, and J. K. Slingerland, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.016401 97, 016401 (2006).
15. S. B. Chung and M. Stone, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.245311 73, 245311 (2006).
16. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
17. A. Kitaev, Ann. Phys. ANPYA2 0003-3804 303, 2 (2003).
18. M. Freedman, M. Larsen, and Z. Wang, Commun. Math. Phys. CMPHAY 0010-3616 227, 605 (2002).
19. S. Das Sarma, M. Freedman, and C. Nayak, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.166802 94, 166802 (2005).
20. M. Freedman, C. Nayak, and K. Walker, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.245307 73, 245307 (2006).
21. L. H. Kauffman and S. J. Lomonaco, Jr., New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/6/1/134 6, 134 (2004).
22. D. V. Averin and V. J. Goldman, Solid State Commun. SSCOA4 0038-1098 10.1016/S0038-1098(01)00447-1 121, 25 (2002).
23. L. S. Georgiev hep-th/0611340 (unpublished).
24. N. Read, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1530369 44, 558 (2003).
25. S. Bravyi and A. Kitaev, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.022316 71, 022316 (2005).
26. C. Nayak and F. Wilczek, Nucl. Phys. B NUPBBO 0550-3213 479, 529 (1996).
27. P. Di Francesco, P. Mathieu, and D. Sénéchal, Conformal Field Theory (Springer-Verlag, New York, 1997).
28. L. S. Georgiev, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(02) 01076-3 651, 331 (2003).
29. Y. Ji, Y. Chung, D. Sprinzak, M. Heiblum, D. Mahalu, and H. Shtrikman, Nature (London) NATUAS 0028-0836 10.1038/nature01503 422, 415 (2003).
30. J. S. Birman, Braids, Links and Mapping Class Groups, 82nd ed. (Princeton University Press, Princeton, NJ, 1974).
31. The CNOT gate can be obtained from CZ with the help of the Hadamard gate acting on the target qubit.