Time-optimal synthesis of unitary transformations in a coupled fast and slow qubit system

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 77, Issue 3, 2008, Pages

  Zeier, Robert ^a   Yuan, Haidong ^b   Khaneja, Navin ^a  

^a HARVARD UNIVERSITY   (United States)

^b Massachusetts Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DATA PROCESSING; DOMAIN DECOMPOSITION METHODS; MATHEMATICAL TRANSFORMATIONS; OPTIMAL CONTROL SYSTEMS; SPIN DYNAMICS;

CANONICAL DECOMPOSITION; SPIN SYSTEMS; TIME-OPTIMAL CONTROL PROBLEM; UNITARY TRANSFORMATIONS;

QUANTUM COMPUTERS;

EID: 41449091379     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.77.032332     Document Type: Article

References (59)

1. M. A. Nielsen, M. R. Dowling, M. Gu, and A. C. Doherty, Science SCIEAS 0036-8075 10.1126/science.1121541 311, 1133 (2006).
2. M. A. Nielsen, Quantum Inf. Comput. 6, 213 (2006). 0890-5401
3. M. A. Nielsen, M. R. Dowling, M. Gu, and A. C. Doherty, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.062323 73, 062323 (2006).
4. N. Khaneja, R. Brockett, and S. J. Glaser, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.032308 63, 032308 (2001).
5. N. Khaneja and S. J. Glaser, Chem. Phys. CMPHC2 0301-0104 10.1016/S0301-0104(01)00318-4 267, 11 (2001).
6. T. O. Reiss, N. Khaneja, and S. J. Glaser, J. Magn. Reson. JMARF3 1090-7807 10.1006/jmre.2001.2480 154, 192 (2002).
7. G. Vidal, K. Hammerer, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.237902 88, 237902 (2002).
8. K. Hammerer, G. Vidal, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.062321 66, 062321 (2002).
9. A. M. Childs, H. L. Haselgrove, and M. A. Nielsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.052311 68, 052311 (2003).
10. R. Zeier, M. Grassl, and T. Beth, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.032319 70, 032319 (2004).
11. N. Khaneja, F. Kramer, and S. J. Glaser, J. Magn. Reson. JMARF3 1090-7807 10.1016/j.jmr.2004.11.023 173, 116 (2005).
12. H. Yuan and N. Khaneja, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.040301 72, 040301 (R) (2005).
13. H. Yuan and N. Khaneja, in Proceedings of the 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference, Seville, Spain (IEEE, Piscataway, NJ, 2005), pp. 8006-8011.
14. J. Swoboda, e-print arXiv:quant-ph/0601131v1.
15. H. Yuan and N. Khaneja, Syst. Control Lett. SCLEDC 0167-6911 10.1016/j.sysconle.2005.10.004 55, 501 (2006).
16. H. Yuan, Ph.D. thesis, Harvard University, 2006.
17. G. Dirr, U. Helmke, K. Haper, M. Kleinsteuber, and Y. Liu, J. Global Optim. 35, 443 (2006). 0925-5001
18. R. M. Zeier, Ph.D. thesis, Universität Karlsruhe, 2006 (unpublished).
19. N. Khaneja, S. J. Glaser, and R. Brockett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032301 65, 032301 (2002).
20. T. O. Reiss, N. Khaneja, and S. J. Glaser, J. Magn. Reson. JMARF3 1090-7807 10.1016/S1090-7807(03)00245-3 165, 95 (2003).
21. N. Khaneja, T. O. Reiss, C. Kehlet, T. Schulte-Herbraggen, and S. J. Glaser, J. Magn. Reson. JMARF3 1090-7807 10.1016/j.jmr.2004.11.004 172, 296 (2005).
22. T. Schulte-Herbraggen, A. SpÃrl, N. Khaneja, and S. J. Glaser, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.042331 72, 042331 (2005).
23. H. Yuan and N. Khaneja, Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, CA, 2006 (IEEE, Piscataway, NJ, 2006), pp. 3117-3120.
24. N. Khaneja, B. Heitmann, A. SpÃrl, H. Yuan, T. Schulte-Herbraggen, and S. J. Glaser, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.012322 75, 012322 (2007).
25. H. Yuan, S. J. Glaser, and N. Khaneja, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.012316 76, 012316 (2007).
26. M. Mehring, J. Mende, and W. Scherer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.153001 90, 153001 (2003).
27. F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.076401 92, 076401 (2004).
28. F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.130501 93, 130501 (2004).
29. M. Mehring, W. Scherer, and A. Weidinger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.206603 93, 206603 (2004).
30. J. Mende, Ph.D. thesis, Universität Stuttgart, 2005.
31. A. Heidebrecht, J. Mende, and M. Mehring, Solid State Nucl. Magn. Reson. SSNRE4 0926-2040 10.1016/j.ssnmr.2005.09.015 29, 90 (2006).
32. R. Rahimi Darabad, Ph.D. thesis, Osaka University, 2006.
33. M. Mehring and J. Mende, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.052303 73, 052303 (2006).
34. T. Gaebel, Nat. Phys. ZZZZZZ 1745-2473 2, 408 (2006).
35. N. B. Manson, J. P. Harrison, and M. J. Sellars, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.104303 74, 104303 (2006).
36. A. Heidebrecht, J. Mende, and M. Mehring, Fortschr. Phys. FPYKA6 0015-8208 10.1002/prop.200610312 54, 788 (2006).
37. F. Jelezko and J. Wrachtrup, Phys. Status Solidi A PSSABA 0031-8965 10.1002/pssa.200671403 203, 3207 (2006).
38. J. Wrachtrup and F. Jelezko, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/18/21/S08 18, S807 (2006).
39. L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, Science SCIEAS 0036-8075 10.1126/science.1131871 314, 281 (2006).
40. A. Heidebrecht, Ph.D. thesis, Universität Stuttgart, 2006.
41. D. D. Awschalom and M. E. FlattÃ, Nat. Phys. ZZZZZZ 1745-2473 3, 153 (2007).
42. M. V. Gurudev Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, Science SCIEAS 0036-8075 10.1126/science.1139831 316, 1312 (2007).
43. S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces (American Mathematical Society, Providence, 2001), reprinted with corrections.
44. A. W. Knapp, Lie Groups Beyond an Introduction, 2nd ed. (Birkhäuser, Boston, 2002).
45. R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Clarendon Press, Oxford, 1997), reprinted with corrections.
46. A. Schweiger and G. Jeschke, Principles of Pulse Electron Paramagnetic Resonance (Oxford University Press, Oxford, 2001).
47. V. Jurdjevic and H. J. Sussmann, J. Differ. Equations JDEQAK 0022-0396 10.1016/0022-0396(72)90035-6 12, 313 (1972).
48. S. S. Bullock, Quantum Inf. Comput. 4, 396 (2004). 0890-5401
49. S. S. Bullock and G. K. Brennen, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1723701 45, 2447 (2004).
50. S. S. Bullock, G. K. Brennen, and D. P. OâLeary, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1900293 46, 062104 (2005).
51. H. N. S. Earp and J. K. Pachos, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.2008210 46, 082108 (2005).
52. Y. Nakajima, Y. Kawano, and H. Sekigawa, Quantum Inf. Comput. 6, 67 (2006). 0890-5401
53. C. Van Loan, Numer. Math. NUMMA7 0029-599X 10.1007/BF01389653 46, 479 (1985).
54. G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd ed. (The Johns Hopkins University Press, Baltimore, 1989).
55. C. C. Paige and M. Wei, Linear Algebr. Appl. LAAPAW 0024-3795 208-209, 303 (1994).
56. M. D. Shuster, J. Astronaut. Sci. JALSA6 0021-9142 41, 439 (1993).
57. N. Khaneja, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.032326 76, 032326 (2007).
58. J. S. Hodges, J. C. Yang, C. Ramanathan, and D. G. Cory, arXiv:0707.2956v1.
59. A. W. Marshall and I. Olkin, Inequalities: Theory of Majorization and Its Applications (Academic Press, New York, 1979).