Second order gradient ascent pulse engineering

Journal of Magnetic Resonance

Volumn 212, Issue 2, 2011, Pages 412-417

  De Fouquieres, P ^a   Schirmer, S G ^a   Glaser, S J ^b   Kuprov, Ilya ^c  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^c UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

BFGS; GRAPE; Optimal control

Indexed keywords

APPROXIMATE GRADIENT; BFGS; BROYDEN-FLETCHER-GOLDFARB-SHANNO; CONTROL DERIVATIVES; CONVERGENCE ACCELERATION; CONVERGENCE RATES; GRADIENT ASCENT; GRAPE; OPTIMAL CONTROLS; QUANTUM SYSTEM; QUASI-NEWTON ALGORITHM; SECOND ORDERS; TEST SYSTEMS;

ALGORITHMS; CONTROL; FRUITS; OPTIMIZATION; QUANTUM ELECTRONICS; QUANTUM OPTICS;

CONVERGENCE OF NUMERICAL METHODS;

ALGORITHM; ARTICLE; ARTIFICIAL NEURAL NETWORK; COMPUTER PROGRAM; ELECTRON SPIN RESONANCE; METHODOLOGY; QUANTUM THEORY; SPIN LABELING; STATISTICAL ANALYSIS;

ALGORITHMS; DATA INTERPRETATION, STATISTICAL; ELECTRON SPIN RESONANCE SPECTROSCOPY; NEURAL NETWORKS (COMPUTER); QUANTUM THEORY; SOFTWARE; SPIN LABELS;

EID: 80053287560     PISSN: 10907807     EISSN: 10960856     Source Type: Journal    
DOI: 10.1016/j.jmr.2011.07.023     Document Type: Article

References (47)

1. F.L. Lewis, and V.L. Syrmos Optimal Control 1995 Wiley
2. L.S. Pontryagin, V.G. Boltyanski, R.V. Gamkrelidze, and E.F. Mischenko Mathematical Theory of Optimal Processes 1961 Nauka Moscow
3. V.F. Krotov Global Methods in Optimal Control Theory 1996 Marcel Dekker New York
4. C.P. Koch, M. Ndong, and R. Kosloff Two-photon coherent control of femtosecond photoassociation Faraday Discuss. 142 2009 389 402
5. C.P. Koch, J.P. Palao, R. Kosloff, and F. Masnou-Seeuws Stabilization of ultracold molecules using optimal control theory Phys. Rev. A 70 2004 013402
6. J.P. Palao, R. Kosloff, and C.P. Koch Protecting coherence in optimal control theory: state-dependent constraint approach Phys. Rev. A 77 2008
7. N.I. Gershenzon, K. Kobzar, B. Luy, S.J. Glaser, and T.E. Skinner Optimal control design of excitation pulses that accommodate relaxation J. Magn. Reson. 188 2007 330 336 (Pubitemid 47562811)
8. T.O. Levante, T. Bremi, and R.R. Ernst Pulse-sequence optimization with analytical derivatives. Application to deuterium decoupling in oriented phases J. Magn. Reson. 121 1996 167 177 (Pubitemid 126751790)
9. N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, and S.J. Glaser Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms J. Magn. Reson. 172 2005 296 305 (Pubitemid 40072534)
10. K. Kobzar, T.E. Skinner, N. Khaneja, S.J. Glaser, and B. Luy Exploring the limits of broadband excitation and inversion: II. Rf-power optimized pulses J. Magn. Reson. 194 2008 58 66
11. Z. Tošner, S.J. Glaser, N. Khaneja, and N.C. Nielsen Effective Hamiltonians by optimal control: solid-state NMR double-quantum planar and isotropic dipolar recoupling J. Chem. Phys. 125 2006 184502
12. Z. Tošner, T. Vosegaard, C. Kehlet, N. Khaneja, S.J. Glaser, and N.C. Nielsen Optimal control in NMR spectroscopy: numerical implementation in SIMPSON J. Magn. Reson. 197 2009 120 134
13. N. Khaneja, R. Brockett, and S.J. Glaser Time optimal control in spin systems Phys. Rev. A 63 2001 323081
14. N. Khaneja, T. Reiss, B. Luy, and S.J. Glaser Optimal control of spin dynamics in the presence of relaxation J. Magn. Reson. 162 2003 311 319
15. T. Calarco, M.A. Cirone, M. Cozzini, A. Negretti, A. Recati, and E. Charron Quantum control theory for decoherence suppression in quantum gates Int. J. Quant. Inf. 5 2007 207 213
16. T. Caneva, M. Murphy, T. Calarco, R. Fazio, S. Montangero, V. Giovannetti, and G.E. Santoro Optimal control at the quantum speed limit Phys. Rev. Lett. 103 2009
17. U.V. Poulsen, S. Sklarz, D. Tannor, and T. Calarco Correcting errors in a quantum gate with pushed ions via optimal control Phys. Rev. A 82 2010 012339
18. N. Khaneja, B. Heitmann, A. Spörl, H. Yuan, T. Schulte- Herbrüggen, and S.J. Glaser Shortest paths for efficient control of indirectly coupled qubits Phys. Rev. A 75 2007 012322
19. A. Spörl, T. Schulte-Herbrüggen, S.J. Glaser, V. Bergholm, M.J. Storcz, J. Ferber, and F.K. Wilhelm Optimal control of coupled Josephson qubits Phys. Rev. A 75 2007 012302
20. V.F. Krotov Quantum system control optimization Dokl. Math. 78 2008 949 952
21. V.F. Krotov, and I.N. Fel'dman Iterative method for solving optimal control problems Eng. Cyber. 21 1983 123 130 (Pubitemid 14590169)
22. S. Machnes, U. Sander, S.J. Glaser, P.d. Fouquieres, A. Gruslys, S. Schirmer, T. Schulte-Herbrueggen, Comparing, optimising and benchmarking quantum control algorithms in a unifying programming framework. Available from: < http://link.aps.org/doi/10.1103/PhysRevA.84.022305 >.
23. H. Mabuchi, and N. Khaneja Principles and applications of control in quantum systems Int. J. Rob. Nonl. Con. 15 2005 647 667 (Pubitemid 41568321)
24. L.S. Pontryagin Mathematical Theory of Optimal Processes 1964 Pergamon Press
25. B. Luy, K. Kobzar, T.E. Skinner, N. Khaneja, and S.J. Glaser Construction of universal rotations from point-to-point transformations J. Magn. Reson. 176 2005 179 186 (Pubitemid 41336685)
26. K. Kobzar, B. Luy, N. Khaneja, and S.J. Glaser Pattern pulses: design of arbitrary excitation profiles as a function of pulse amplitude and offset J. Magn. Reson. 173 2005 229 235 (Pubitemid 40352446)
27. N. Pomplun, B. Heitmann, N. Khaneja, and S.J. Glaser Optimization of electron-nuclear polarization transfer Appl. Magn. Reson. 34 2008 331 346
28. T.E. Skinner, T.O. Reiss, B. Luy, N. Khaneja, and S.J. Glaser Application of optimal control theory to the design of broadband excitation pulses for high-resolution NMR J. Magn. Reson. 163 2003 8 15
29. R.R. Ernst, G. Bodenhausen, A. Wokaun, Principles of nuclear magnetic resonance in one and two dimensions, Clarendon, 1987.
30. F.J. Dyson The radiation theories of Tomonaga, Schwinger, and Feynman Phys. Rev. 75 1949 486 502
31. I. Kuprov, and C.T. Rodgers Derivatives of spin dynamics simulations J. Chem. Phys. 131 2009 234108
32. R.S. Dumont, S. Jain, and A. Bain Simulation of many-spin system dynamics via sparse matrix methodology J. Chem. Phys. 106 1997 5928 5936 (Pubitemid 127580693)
33. H.J. Hogben, M. Krzystyniak, G.T.P. Charnock, P.J. Hore, and I. Kuprov Spinach - A software library for simulation of spin dynamics in large spin systems J. Magn. Reson. 208 2011 179 194
34. T.C. Fung Computation of the matrix exponential and its derivatives by scaling and squaring Int. J. Numer. Meth. Eng. 59 2004 1273 1286 (Pubitemid 38335657)
35. G.E. Forsythe, and W.R. Wasow Finite-difference Methods for Partial Differential Equations 1960 John Wiley and Sons New York; London
36. M.D. Canon, C.D. Cullum, and E. Polak Theory of Optimal Control and Mathematical Programming 1970 McGraw-Hill New York, London
37. E. Polak Historical survey of computational methods in optimal control Siam Rev. 15 1973 553 584
38. D. Tabak, Kuo, and B.C.-i. Kuo Optimal Control by Mathematical Programming 1971 Prentice-Hall Englewood Cliffs, NJ
39. A. Barclay, P.E. Gill, and J. Ben Rosen SQP methods and their application to numerical optimal control, variational calculus Optim. Contr. Appl. 124 1998 207 222
40. M. Hinze, and K. Kunisch Second order methods for optimal control of time-dependent fluid flow SIAM J. Contr. Optim. 40 2002 925 946 (Pubitemid 34692286)
41. E. Balsa-Canto, J.R. Banga, A.A. Alonso, and V.S. Vassiliadis Efficient optimal control of bioprocesses using second-order information Ind. Eng. Chem. Res. 39 2000 4287 4295
42. R. Fletcher Practical Methods of Optimization second ed. 1987 Wiley
43. W.C. Davidon Variable metric method for minimization SIAM J. Opt. 1 1991 1 17
44. R.H. Byrd, J. Nocedal, and R.B. Schnabel Representations of quasi-Newton matrices and their use in limited memory methods Math. Program. 63 1994 129 156
45. D.C. Liu, and J. Nocedal On the limited memory BFGS method for large scale optimization Math. Progr. 45 1989 503 528 (Pubitemid 20660315)
46. T.F. Coleman, and Y. Li On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds Math. Program. 67 1994 189 224
47. T.F. Coleman, and Y.Y. Li An interior trust region approach for nonlinear minimization subject to bounds Siam J. Optim. 6 1996 418 445