Effect of randomness on quantum data buses of Heisenberg spin chains

Physical Review B - Condensed Matter and Materials Physics

Volumn 85, Issue 22, 2012, Pages

  Oh, Sangchul ^a   Shim, Yun Pil ^b   Fei, Jianjia ^b   Friesen, Mark ^b   Hu, Xuedong ^a  

^a UNIVERSITY AT BUFFALO   (United States)

^b University of Wisconsin Madison   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84862646500     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.85.224418     Document Type: Article

References (49)

1. D. Loss and D. P. DiVincenzo, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.57.120 57, 120 (1998).
2. J. I. Cirac and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.4091 74, 4091 (1995).
3. A. Imamoḡlu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.4204 83, 4204 (1999).
4. A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.062320 69, 062320 (2004).
5. S. Bose, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.207901 91, 207901 (2003);
6. S. Bose, Contemp. Phys. CTPHAF 0010-7514 10.1080/00107510701342313 48, 13 (2007).
7. M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.187902 92, 187902 (2004).
8. Y. Li, T. Shi, B. Chen, Z. Song, and C.-P. Sun, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.022301 71, 022301 (2005). (Pubitemid 43286527)
9. L. Campos Venuti, C. Degli Esposti Boschi, and M. Roncaglia, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.247206 96, 247206 (2006); (Pubitemid 43938964)
10. L. Campos Venuti, C. Degli Esposti Boschi, and M. Roncaglia, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.060401 99, 060401 (2007). (Pubitemid 47230789)
11. P. Cappellaro, C. Ramanathan, and D. G. Cory, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.250506 99, 250506 (2007).
12. M. Friesen, A. Biswas, X. Hu, and D. Lidar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.230503 98, 230503 (2007). (Pubitemid 47139776)
13. A. Ferreira and J. M. B. Lopes dos Santos, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.034301 77, 034301 (2008). (Pubitemid 351393377)
14. X. Hao and S. Zhu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78. 044302 78, 044302 (2008).
15. C. K. Burrell and T. J. Osborne, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.167201 99, 167201 (2007). (Pubitemid 47587555)
16. J. Allcock and N. Linden, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.110501 102, 110501 (2009).
17. G. A. Alvarez and D. Suter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.230403 104, 230403 (2010).
18. S. Oh, M. Friesen, and X. Hu, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.140403 82, 140403 (R) (2010).
19. Y.-P. Shim, S. Oh, X. Hu, and M. Friesen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.180503 106, 180503 (2011).
20. S. Oh, L.-A. Wu, Y.-P. Shim, J. Fei, M. Friesen, and X. Hu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.84.022330 84, 022330 (2011).
21. S. Oh, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.65.144526 65, 144526 (2002);
22. X. Hu and S. Das Sarma, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.012312 66, 012312 (2002).
23. I. A. Merkulov, A. L. Efros, and M. Rosen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.65.205309 65, 205309 (2002).
24. Y.-P. Shim (unpublished).
25. E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(61)90115-4 16, 407 (1961).
26. A. Auerbach, Interacting Electrons and Quantum Magnetism (Springer-Verlag, New York, 1994).
27. M. A. Ruderman and C. Kittel, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.96.99 96, 99 (1954);
28. T. Kasuya, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.16.45 16, 45 (1956);
29. K. Yoshida, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.106.893 106, 893 (1957).
30. Quantum Annealing and Related Optimization Methods, edited by A. Das and B. K. Chakrabarti (Springer-Verlag, Berlin, 2005).
31. D. Scherrington and S. Kirkpatrick, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.35.1792 35, 1792 (1975).
32. S. F. Edwards and P. W. Anderson, J. Phys. F JPFMAT 0305-4608 10.1088/0305-4608/5/5/017 5, 965 (1975).
33. X. Hu and S. Das Sarma, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.100501 96, 100501 (2006).
34. For static nonuniform exchange couplings, the dynamics of a nonuniform spin bus is not much different from that of a uniform bus. On the other hand, temporally fluctuating exchange couplings or external magnetic fields would lead to decoherence of the spin bus. The bus decoherence dynamics and the full dynamics of a decohering spin bus and qubits are beyond the scope of the current paper. In general, they are dependent on not only the bus spectral properties, but also the environmental spectrum and dynamics.
35. To achieve a strongly coupled spin chain with uniform internode exchange coupling requires careful calibration. While calibration of a single or double quantum dot has been done consistently, calibration for a larger system remains an open experimental question.
36. P. Fulde, Electron Correlations in Molecules and Solids (Springer-Verlag, Berlin, 1991).
37. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (John Wiley & Sons, New York, 1992).
38. H. Bethe, Z. Phys. EPJAFV 1434-6001 10.1007/BF01341708 71, 205 (1931).
39. L. Hulthén, Arkiv Mat. Astron. Fysik A 26, 1 (1938).
40. C. F. Hirjibehedin, C. P. Lutz, and A. J. Heinrich, Science SCIEAS 0036-8075 10.1126/science.1125398 312, 1021 (2006).
41. E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, lapack Users' Guide, 3rd ed. (SIAM, Philadelphia, 1999).
42. C. Kittel, Quantum Theory of Solids (John Wiley & Sons, Inc., New York, 1963).
43. J. C. Bonner and M. E. Fisher, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.135.A640 135, A640 (1964).
44. A. Stathopoulos and J. R. McCombs, ACM Trans. Math. Software 37, 21 (2011).
45. S. R. White, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69. 2863 69, 2863 (1992);
46. S. R. White, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.48.10345 48, 10345 (1993).
47. W. J. Caspers, Spin Systems (World Scientific, Singapore, 1989).
48. W. Nolting and A. Ramakanth, Quantum Theory of Magnetism (Springer-Verlag, Heidelberg, 2009).
49. P. W. Anderson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.109.1492 109, 1492 (1958).