Hamiltonian Engineering for Quantum Systems

  • Sonia G. Schirmer
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 366)


We describe different strategies for using a semi-classical controller to engineer Hamiltonians for quantum systems to solve control problems such as quantum state or process engineering and optimization of observables.


Quantum System Control Pulse Drift Term Rotate Wave Approximation Quantum Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Albertini F, D’Alessandro D (2001) Notions of controllability for quantum-mechanical systems electronic preprint
  2. 2.
    D’Alessandro D (2000) Algorithms for quantum control based on decompositions of Lie groups. In: Proceedings of the 39th IEEE Conference on Decision and Control. IEEE New York, pages 1074–1075Google Scholar
  3. 3.
    Judson R S, Rabitz H (1992) Teaching lasers to control molecules. Phys. Rev. Lett. 68: 1500CrossRefGoogle Scholar
  4. 4.
    Maday Y, Turinici G (2003) New formulations of monotonically convergent quantum control algorithms. J. Chem. Phys. 118(18): 8191CrossRefGoogle Scholar
  5. 5.
    Pearson B J et al. (2001) Coherent control using adaptive learning algorithms. Phys. Rev. A 63: 063412CrossRefGoogle Scholar
  6. 6.
    Ramakrishna V et al. (2000) Quantum control by decompositions of SU(2). Phys. Rev. A 62: 053409CrossRefGoogle Scholar
  7. 7.
    Ramakrishna V et al. (2000) Explicit generation of unitary transformations in a single atom or molecule. Phys. Rev. A 61: 032106CrossRefGoogle Scholar
  8. 8.
    Sa Earp H A, Pachos J K (2005) A constructive algorithm for the cartan decomposition of SU(2n). J. Math. Phys. 46: 1CrossRefGoogle Scholar
  9. 9.
    Schirmer S G et al. (2002) Constructive control of quantum systems using factorization of unitary operators. J. Phys. A 35: 8315–8339zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Schirmer S G, Leahy J V, Solomon A I (2002) Degrees of controllability for quantum systems and applications to atomic systems. J. Phys. A 35: 4125zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Shore B W (1990) Theory of coherent atomic excitation. John Wiley & Sons, New YorkGoogle Scholar
  12. 12.
    Tarn T J, Clark J W, Lucarelli D J (2000) Controllability of quantum-mechanical systems with continuous spectra. In: Proceedings of the 39th IEEE Conference on Decision and Control. IEEE, New York, pages 2803–2809Google Scholar
  13. 13.
    Wiseman H M (1994) Quantum theory of continuous feedback. Phys. Rev. A 49: 2133CrossRefGoogle Scholar
  14. 14.
    Yanagisawa M, Kimura H (2003) Transfer function approach to quantum control. IEEE Trans. Autom. Control 48: 2107 and 2121CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Sonia G. Schirmer
    • 1
  1. 1.Dept of Applied Mathematics & Theoretical PhysicsUniversity of CambridgeCambridgeUK

Personalised recommendations