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Control of the quantum systems and some ideas of the optimal control theory

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Abstract

The mathematical theory of control of the quantum systems relies on some ideas of the optimal control theory. They were analyzed and developed with regard to the specifics of such systems. The field of application of the control design algorithms was expanded, their efficiency and speed were increased.

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References

  1. Rabitz, H., Control of Microworld Chemical and Physical Processes, in Encyclopedia of Computational Chemistry, Chichester: Wiley, 1998, vol. 1, pp. 573–580.

    Google Scholar 

  2. Krotov, V.F., Global Methods in Optimal Control Theory, New York: Marcel Dekker, 1996.

    MATH  Google Scholar 

  3. Kelley, H.J., Gradient Theory of Optimal Flight Paths, ARS J., 1960, vol. 30, pp. 947–954.

    MATH  Google Scholar 

  4. Eneev, T.M., Application of the Gradient Method to the Optimal Control Theory, Kosm. Issled., 1966, vol. 4, no. 5, pp. 651–669.

    Google Scholar 

  5. Bryson, A.E. and Ho, Y.Ch., Applied Optimal Control, Washington: Hemisphere, 1975.

    Google Scholar 

  6. Krotov, V.F. and Fel’dman, I.N., Iterative Method for Solution of Technical and Economic Processes, in Model. tekhniko-ekonomicheskikh protsessov (Models of Technical and Economic Processes), Moscow: Akad. Nauk SSSR, 1978, pp. 22–35.

    Google Scholar 

  7. Krotov, V.F. and Fel’dman, I.N., Iterative Method of Solving the Problems of Optimal Control, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1983, no. 2, pp. 162–167.

  8. Konnov, A.I. and Krotov, V.F., On the Global Methods of Successive Improvement of Controllable Processes, Avtom. Telemekh., 1999, no. 10, pp. 77–88.

  9. Kazakov, V.A. and Krotov, V.F., Optimal Control of Light-Matter Interaction, Avtom. Telemekh., 1987, no. 4, pp. 9–15.

  10. Krotov, V.F., Global Methods to Improve Control and Optimal Control of Resonance Interaction of Light and Matter, in Lecture Notes in Control and Information Sciences, New York: Springer, 1988, vol. 121, pp. 267–298.

    Google Scholar 

  11. Somloi, J., Kazakov, V.A., and Tannor, D.J., Controlled Dissociation of I2 via Optical Transitions Between the X and B Electronic States, Chemistry Physics, 1993, vol. 172, pp. 85–98.

    Article  Google Scholar 

  12. Somloi, J., Kazakov, V.A., and Tannor, D.J., Physical Review A, 1993, vol. 60.

  13. Rangan, C. and Bucksbaum, P.H., Optimally Shaped Terahertz Pulses for Phase Retrievial in a Rydbergatom Data Register, Physical Rev. A, 2001, vol. 64.

  14. Sklarz, S.E. and Tannor, D.J., Loading a Bose-Einstein Condensate Onto an Optical Lattice: An Application of Optimal Control Theory to the Nonlinear Shroedinger Equation, Physical Rev. A, 2002, vol. 66.

  15. Calarco, T., Dorner, U., Julienne, P.S., et al., Quantum Computations with Atoms in Optical Lattices: Marker Qubits and Molecular Interactions, Physical Rev. A, 2004, vol. 70.

  16. Khaneja, N., Reiss, T., Rehlet, C., Shulte-Herbrueggen, T., and Glaster, S.J., Optical Control of Coupled Spin Dynamics: Design of NMR Pulse Sequences by Gradient Ascent Algorithms, J. Magnet. Reson., 2005, vol. 172, pp. 296–305.

    Article  Google Scholar 

  17. Gorshkov, A.V., Calarco, T., Lukin, M.D., and Sorensen, A.S., Photon Storage in Λ-optically Dense Atomic Media, Physical Rev. A, 2008, vol. 77.

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Original Russian Text © V.F. Krotov, 2009, published in Avtomatika i Telemekhanika, 2009, No. 3, pp. 15–23.

This work was supported in part by the Program no. 15 “Problems of Analysis and Design of the Integrated Control Systems of Complex Plants Operating Under Uncertainty” of the Department of Power Engineering, Machine Building, Mechanics, and Control Processes, Russian Academy of Sciences.

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Krotov, V.F. Control of the quantum systems and some ideas of the optimal control theory. Autom Remote Control 70, 357–365 (2009). https://doi.org/10.1134/S0005117909030035

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  • DOI: https://doi.org/10.1134/S0005117909030035

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