Optimal control landscapes for quantum observables

Herschel Rabitz, Michael Hsieh, Carey Rosenthal

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


The optimal control of quantum systems provides the means to achieve the best outcome from redirecting dynamical behavior. Quantum systems for optimal control are characterized by an evolving density matrix and a Hermitian operator associated with the observable of interest. The optimal control landscape is the observable as a functional of the control field. The features of interest over this control landscape consist of the extremum values and their topological character. For controllable finite dimensional quantum systems with no constraints placed on the controls, it is shown that there is only a finite number of distinct values for the extrema, dependent on the spectral degeneracy of the initial and target density matrices. The consequences of these findings for the practical discovery of effective quantum controls in the laboratory is discussed.

Original languageEnglish (US)
Article number204107
JournalJournal of Chemical Physics
Issue number20
StatePublished - May 28 2006

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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