Resources required for topological quantum factoring

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 81, Issue 6, 2010, Pages

  Baraban, M ^a   Bonesteel, N E ^b   Simon, S H ^c  

^a Yale University   (United States)

^b Florida State University   (United States)

^c UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BIT NUMBERS; DISTILLATION ALGORITHM; DISTILLATION METHOD; MODULAR EXPONENTIATION; PHYSICAL PARAMETERS; QUANTUM COMPUTATION; SHOR'S ALGORITHMS;

COMPUTATIONAL LINGUISTICS; DISTILLATION; QUANTUM COMPUTERS;

TOPOLOGY;

EID: 77953705468     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.81.062317     Document Type: Article

References (27)

1. P. Shor, Proceedings of the 35th Annual Symposium on Foundations of Computer Science, edited by, S. Goldwasser, (IEEE Computer Society, Los Alamitos, 1994), pp. 124-134.
2. C. Nayak, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.80.1083 80, 1083 (2008).
3. A. Kitaev, Ann. Phys. APNYA6 0003-4916 10.1016/S0003-4916(02)00018-0 303, 2 (2003).
4. G. Moore and N. Read, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550- 3213(91)90407-O 360, 362 (1991).
5. S. Das Sarma, C. Nayak, and S. Tewari, Phys. Rev. B NUPBBO 1098-0121 10.1103/PhysRevB.73.220502 73, 220502 (R) (2006).
6. V. Gurarie, L. Radzihovsky, and A. V. Andreev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.230403 94, 230403 (2005);
7. S. Tewari, S. Das Sarma, C. Nayak, C. Zhang, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.010506 98, 010506 (2007);
8. N. R. Cooper and G. V. Shlyapnikov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.155302 103, 155302 (2009).
9. L. Fu and C. L. Kane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.096407 100, 096407 (2008);
10. J. D. Sau, R. M. Lutchyn, S. Tewari, and S. Das Sarma, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.040502 104, 040502 (2010);
11. P. A. Lee, e-print arXiv: 0907.2681 (2009).
12. S. Bravyi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.042313 73, 042313 (2006).
13. N. Read and E. H. Rezayi, Phys. Rev. B PLRAAN 1098-0121 10.1103/PhysRevB.59.8084 59, 8084 (1999);
14. E. H. Rezayi and N. Read, Phys. Rev. B PLRAAN 1098-0121 10.1103/PhysRevB.79.075306 79, 075306 (2009).
15. M. A. Levin and X. G. Wen, Phys. Rev. B PLRAAN 1098-0121 10.1103/PhysRevB.71.045110 71, 045110 (2005);
16. P. Fendley, Ann. Phys. APNYA6 0003-4916 10.1016/j.aop.2008.04.011 323, 3113 (2008).
17. This model assumes uncorrelated and phase coherent random errors. Additionally, for Fibonacci anyons the errors must add incoherently. If any of these conditions are not met, a worst case situation would require gates with accuracy of O (1 / N 2).
18. D. Beckman, A. N. Chari, S. Devabhaktuni, and J. Preskill, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.1034 54, 1034 (1996).
19. M. A. Nielsen and I. L. Chuang, Quantum Computing and Quantum Information (Cambridge University Press, Cambridge, 2000).
20. S. Bravyi and A. Kitaev, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.022316 71, 022316 (2005).
21. M. Baraban, G. Zikos, N. Bonesteel, and S. H. Simon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.076801 103, 076801 (2009).
22. M. W. Keller, Science SCIEAS 0036-8075 10.1126/science.285.5434.1706 285, 1706 (1999).
23. M. H. Freedman and Z. Wang, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.032322 75, 032322 (2007).
24. L. Hormozi, G. Zikos, N. E. Bonesteel, and S. H. Simon, Phys. Rev. B PLRAAN 1098-0121 10.1103/PhysRevB.75.165310 75, 165310 (2007).
25. M. Burrello, H. Xu, G. Mussardo, and X. Wan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.160502 104, 160502 (2010);
26. R. Mosseri, J. Phys. A: Math. Theor. PRLTAO 1751-8113 10.1088/1751-8113/41/17/175302 41, 175302 (2008).
27. P. Bonderson (unpublished).