Time-optimal control of SU(2) quantum operations

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 88, Issue 4, 2013, Pages

  Garon, A ^a   Glaser, S J ^a   Sugny, D ^b,c  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b UNIVERSITÉ DE BOURGOGNE   (France)

^c INRIA SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DETUNINGS; EXPLICIT ANALYTICAL SOLUTIONS; OPTIMAL SYNTHESIS; OPTIMAL TRAJECTORIES; QUANTUM OPERATIONS; TARGET STATE; TIME OPTIMAL CONTROL;

OPTIMIZATION;

CONTROL;

EID: 84886256456     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.88.043422     Document Type: Article

References (43)

1. C. Brif, R. Chakrabarti, and H. Rabitz, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/12/7/075008 12, 075008 (2010).
2. S. Rice and M. Zhao, Optimal Control of Quantum Dynamics (Wiley, New York, 2000).
3. M. Shapiro and P. Brumer, Principles of Quantum Control of Molecular Processes (Wiley, New York, 2003).
4. D. J. Tannor, Introduction to Quantum Mechanics: A Time-Dependent Perspective (University Science Books, Sausalito, CA, 2007).
5. T. Viellard, F. Chaussard, D. Sugny, B. Lavorel, and O. Faucher, J. Raman Spectrosc. JRSPAF 0377-0486 10.1002/jrs.1976 39, 694 (2008).
6. M. H. Levitt, Spin Dynamics: Basics of Nuclear Magnetic Resonance (John Wiley & Sons, New York, 2008);
7. R. R. Ernst, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, International Series of Monographs on Chemistry (Oxford University Press, Oxford, 1990).
8. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000).
9. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Mir, Moscow, 1974).
10. B. Bonnard and M. Chyba, Singular Trajectories and Their Role in Control Theory (Springer, New York, 2003), Vol. 40.
11. M. Lapert, Y. Zhang, M. Braun, S. J. Glaser, and D. Sugny, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.083001 104, 083001 (2010);
12. E. Assémat, M. Lapert, Y. Zhang, M. Braun, S. J. Glaser, and D. Sugny, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.82.013415 82, 013415 (2010).
13. U. Boscain and P. Mason, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.2203236 47, 062101 (2006). (Pubitemid 44000483)
14. D. D'Alessandro and M. Dahleh, IEEE Trans. Autom. Control IETAA9 0018-9286 10.1109/9.928587 46, 866 (2001).
15. D. Sugny and C. Kontz, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77. 063420 77, 063420 (2008).
16. N. Khaneja, R. Brockett, and S. J. Glaser, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.032308 63, 032308 (2001). (Pubitemid 33764922)
17. N. Khaneja, S. J. Glaser, and R. Brockett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032301 65, 032301 (2002).
18. B. Bonnard and D. Sugny, SIAM J. Control Optim. SJCODC 0363-0129 10.1137/080717043 48, 1289 (2009).
19. B. Bonnard, M. Chyba, and D. Sugny, IEEE Trans. Autom. Control IETAA9 0018-9286 10.1109/TAC.2009.2031212 54, 2598 (2009).
20. N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, and S. J. Glaser, J. Magn. Reson. JMARF3 1090-7807 10.1016/j.jmr.2004.11.004 172, 296 (2005). (Pubitemid 40072534)
21. T. E. Skinner, T. O. Reiss, B. Luy, N. Khaneja, and S. J. Glaser, J. Magn. Reson. JMARF3 1090-7807 10.1016/S1090-7807(03)00153-8 163, 8 (2003).
22. R. Kosloff, S. A. Rice, P. Gaspard, S. Tersigni, and D. Tannor, Chem. Phys. CMPHC2 0301-0104 10.1016/0301-0104(89)90012-8 139, 201 (1989).
23. J. Werschnik and E. K. U. Gross, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/40/18/R01 40, R175 (2007). (Pubitemid 350049320)
24. D. M. Reich, M. Ndong, and C. P. Koch, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.3691827 136, 104103 (2012).
25. R. Tycko, Adv. Magn. Reson. 9780-1202 10.1016/S1057-2732(13)70005-6 15, 1 (1990).
26. M. H. Levitt, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2831927 128, 052205 (2008). (Pubitemid 351598411)
27. B. Luy, K. Kozbar, T. E. Skinner, N. Kaneja, and S. J. Glaser, J. Magn. Reson. JMARF3 1090-7807 10.1016/j.jmr.2005.06.002 176, 179 (2005). (Pubitemid 41336685)
28. K. Kobzar, S. Ehni, T. E. Skinner, S. J. Glaser, and B. Luy, J. Magn. Reson. JMARF3 1090-7807 10.1016/j.jmr.2012.09.013 225, 142 (2012).
29. M. Lapert, J. Salomon, and D. Sugny, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.85.033406 85, 033406 (2012).
30. M. A. Janich, R. F. Schulte, M. Schwaiger, and S. J. Glaser, J. Magn. Reson. 213, 126 (2011).
31. M. A. Janich, M. A. McLean, R. Noeske, S. J. Glaser, and R. F. Schulte, J. Magn. Reson. JMARF3 1090-7807 10.1016/j.jmr.2012.08.003 223, 129 (2012).
32. J. P. Palao and R. Kosloff, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.062308 68, 062308 (2003).
33. T. Schulte-Herbrüggen, A. Spörl, N. Khaneja, and S. J. Glaser, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.042331 72, 042331 (2005). (Pubitemid 41776318)
34. N. Khaneja, B. Heitmann, A. Spörl, H. Yuan, T. Schulte- Herbrüggen, and S. J. Glaser, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.012322 75, 012322 (2007). (Pubitemid 46155084)
35. U. Boscain and Y. Chitour, SIAM J. Control Optim. SJCODC 0363-0129 10.1137/S0363012904441532 44, 111 (2005).
36. E. Kirillova, T. Hoch, and K. Spindler, WSEAS Trans. Math. 7, 687 (2008).
37. K. M. Fonseca Romero, G. Useche Laverde, and F. Torres Ardila, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/36/3/317 36, 841 (2003).
38. M. Wenin and W. Pötz, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.022319 74, 022319 (2006). (Pubitemid 44274284)
39. R. Wu, C. Li, and Y. Wang, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(02)00141-X 295, 20 (2002).
40. A. D. Boozer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.85.012317 85, 012317 (2012).
41. I. I. Rabi, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.49.324 49, 324 (1936).
42. I. I. Rabi, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.51.652 51, 652 (1937).
43. A. Garon, S. J. Glaser, and D. Sugny (unpublished).