Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Albertini F, D’Alessandro D (2001) Notions of controllability for quantum-mechanical systems electronic preprint http://arxiv.org/abs/quant-ph/0106128
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 1074–1075
Judson R S, Rabitz H (1992) Teaching lasers to control molecules. Phys. Rev. Lett. 68: 1500
Maday Y, Turinici G (2003) New formulations of monotonically convergent quantum control algorithms. J. Chem. Phys. 118(18): 8191
Pearson B J et al. (2001) Coherent control using adaptive learning algorithms. Phys. Rev. A 63: 063412
Ramakrishna V et al. (2000) Quantum control by decompositions of SU(2). Phys. Rev. A 62: 053409
Ramakrishna V et al. (2000) Explicit generation of unitary transformations in a single atom or molecule. Phys. Rev. A 61: 032106
Sa Earp H A, Pachos J K (2005) A constructive algorithm for the cartan decomposition of SU(2n). J. Math. Phys. 46: 1
Schirmer S G et al. (2002) Constructive control of quantum systems using factorization of unitary operators. J. Phys. A 35: 8315–8339
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: 4125
Shore B W (1990) Theory of coherent atomic excitation. John Wiley & Sons, New York
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 2803–2809
Wiseman H M (1994) Quantum theory of continuous feedback. Phys. Rev. A 49: 2133
Yanagisawa M, Kimura H (2003) Transfer function approach to quantum control. IEEE Trans. Autom. Control 48: 2107 and 2121
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schirmer, S.G. (2007). Hamiltonian Engineering for Quantum Systems. In: Allgüwer, F., et al. Lagrangian and Hamiltonian Methods for Nonlinear Control 2006. Lecture Notes in Control and Information Sciences, vol 366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73890-9_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-73890-9_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73889-3
Online ISBN: 978-3-540-73890-9
eBook Packages: EngineeringEngineering (R0)