Performance of deterministic dynamical decoupling schemes: Concatenated and periodic pulse sequences

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 75, Issue 6, 2007, Pages

  Khodjasteh, Kaveh ^a   Lidar, Daniel A ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR ANALYSIS; HAMILTONIANS; PARAMETER ESTIMATION; QUANTUM THEORY;

CONCATENATED DECOUPLING; DYNAMICAL DECOUPLING; QUANTUM STATES;

ELECTRON ENERGY LEVELS;

EID: 34347336632     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.75.062310     Document Type: Article

References (60)

1. W. H. Zurek, Phys. Today PHTOAD 0031-9228 10.1103/PhysRevD.24.151610. 1103/PhysRevD.26.1862 44, 36 (1991).
2. R. Freeman, Spin Choreography: Basic Steps in High Resolution NMR (Oxford University Press, Oxford, 1998).
3. L. M. K. Vandersypen and I. L. Chuang, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.76.1037 76, 1037 (2004).
4. L. Viola, E. Knill, and S. Lloyd, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.2417 82, 2417 (1999).
5. L. Viola and S. Lloyd, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58. 2733 58, 2733 (1998).
6. P. Facchi, S. Tasaki, S. Pascazio, H. Nakazato, A. Tokuse, and D. A. Lidar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.022302 71, 022302 (2005).
7. K. Shiokawa and D. A. Lidar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.030302 69, 030302 (R) (2004).
8. M. S. Byrd and D. A. Lidar, Quantum Inf. Process. QIPUAT 1570-0755 10.1023/A:1019697017584 1, 19 (2002).
9. L. P. Pryadko and P. Sengupta, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.085321 73, 085321 (2006).
10. P. Facchi, D. A. Lidar, and S. Pascazio, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.032314 69, 032314 (2004).
11. L. Viola and E. Knill, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.060502 94, 060502 (2005).
12. L. F. Santos and L. Viola, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.150501 97, 150501 (2006).
13. L. Viola and L. F. Santos, J. Mod. Opt. JMOPEW 0950-0340 (to be published).
14. O. Kern and G. Alber, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.250501 95, 250501 (2005).
15. P. Zanardi, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(99)00365-5 258, 77 (1999).
16. W. Magnus, Commun. Pure Appl. Math. CPMAMV 0010-3640 10.1002/cpa. 3160070404 7, 649 (1954).
17. K. Khodjasteh and D. A. Lidar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.180501 95, 180501 (2005).
18. M. Suzuki, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01609348 51, 183 (1976).
19. D. A. Lidar and K. B. Whaley, in Irreversible Quantum Dynamics, Vol. 622 of Lecture Notes in Physics (Springer, Berlin, 2003), p. 83.
20. This is not the only possibility; one may consider controlling the environment as well. See, e.g., A. Pechen and H. Rabitz, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.062102 73, 062102 (2006).
21. L.-A. Wu, M. S. Byrd, and D. A. Lidar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.127901 89, 127901 (2002).
22. M. S. Byrd, D. A. Lidar, L.-A. Wu, and P. Zanardi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.052301 71, 052301 (2005).
23. P. Sengupta and L. P. Pryadko, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.037202 95, 037202 (2005).
24. P. C. Moan and J. A. Oteo, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1330198 42, 501 (2001).
25. A. V. Khaetskii, D. Loss, and L. Glazman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.186802 88, 186802 (2002).
26. L. Viola and E. Knill, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.037901 90, 037901 (2003).
27. U. Haeberlen, High Resolution NMR in Solids, Advances in Magnetic Resonance Series, Supplement 1 (Academic, New York, 1976).
28. L. F. Santos and L. Viola, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.062303 72, 062303 (2005).
29. W. Yao, R. B. Liu, and L. J. Sham, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.077602 98, 077602 (2007).
30. The sequence of operations used in Ref. corresponds to the concatenated CPMG sequence explicitly given in Appendix.
31. G. S. Uhrig, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98. 100504 98, 100504 (2007).
32. R. Bhatia, Matrix Analysis, No. 169 in Graduate Texts in Mathematics (Springer-Verlag, New York, 1997).
33. B. M. Terhal and G. Burkard, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.012336 71, 012336 (2005).
34. I. A. Merkulov, Al. L. Efros, and M. Rosen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.205309 65, 205309 (2002).
35. W. A. Coish, V. N. Golovach, J. C. Egues, and D. Loss, Phys. Status Solidi B PSSBBD 0370-1972 10.1002/pssb.200642348 243, 3658 (2006).
36. R. de Sousa, N. Shenvi, and K. B. Whaley, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.045330 72, 045330 (2006).
37. H. Y. Carr and E. M. Purcell, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.94.630 94, 630 (1954).
38. S. Meiboom and D. Gill, Rev. Sci. Instrum. RSINAK 0034-6748 10.1063/1.1716296 29, 6881 (1958).
39. W. M. Witzel and S. Das Sarma, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.077601 98, 077601 (2007).
40. T. J. Osborne, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97. 157202 97, 157202 (2006).
41. W. Zhang, V. V. Dobrovitski, L. F. Santos, L. Viola, and B. N. Harmon, eprint arXiv:cond-mat/0701507.
42. N. Hatano and M. Suzuki, eprint arXiv:math-ph/0506007.
43. K. R. Brown, A. W. Harrow, and I. L. Chuang, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.052318 70, 052318 (2004).
44. R. C. Thompson, Linear Multilinear Algebra 19, 187 (1986).
45. A. M. Childs, H. L. Haselgrove, and M. A. Nielsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.052311 68, 052311 (2003).
46. K. Khodjasteh and D. A. Lidar (in preparation).
47. E. Knill, R. Laflamme, and W. Zurek, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 10.1098/rspa.1998.0166 454, 365 (1998).
48. D. Aharonov, A. Kitaev, and J. Preskill, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.050504 96, 050504 (2006).
49. P. Aliferis, D. Gottesman, and J. Preskill, Quantum Inf. Comput. QICUAW 1533-7146 6, 97 (2006).
50. M. S. Byrd and D. A. Lidar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.047901 89, 047901 (2002).
51. M. S. Byrd and D. A. Lidar, J. Mod. Opt. JMOPEW 0950-0340 10.1080/0950034021000011428 50, 1285 (2003).
52. K. Khodjasteh and D. A. Lidar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.022322 68, 022322 (2003).
53. A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.405 78, 405 (1997).
54. D. Gottesman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.1862 54, 1862 (1996).
55. A. M. Steane, in Introduction to Quantum Computation and Information, edited by, H. K. Lo, S. Popescu, and, T. P. Spiller, (World Scientific, Singapore, 1999), pp. 184-212.
56. R. Alicki, D. A. Lidar, and P. Zanardi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.052311 73, 052311 (2006).
57. R. Alicki, eprint arXiv:quant-ph/0702050.
58. B. Rahn, A. C. Doherty, and H. Mabuchi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.032304 66, 032304 (2002).
59. J. Fern, J. Kempe, S. Simic, and S. Sastry, IEEE Trans. Autom. Control IETAA9 0018-9286 10.1109/TAC.2006.871942 51, 448 (2006).
60. M. W. Reinsch, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.533250 41, 2434 (2000).