Landscape for optimal control of quantum-mechanical unitary transformations

Herschel Rabitz, Michael Hsieh, Carey Rosenthal

Research output: Contribution to journalArticlepeer-review

82 Scopus citations


The optimal creation of a targeted unitary transformation W is considered under the influence of an external control field. The controlled dynamics produces the unitary transformation U and the goal is to seek a control field that minimizes the cost JU. The optimal control landscape is the cost J as a functional of the control field. For a controllable quantum system with N states and without restrictions placed on the controls, the optimal control landscape is shown to have extrema with N+1 possible distinct values, where the desired transformation at U=W is a minimum and the maximum value is at UW. The other distinct N1 extrema values of J are saddle points. The results of this analysis have significance for the practical construction of unitary transformations.

Original languageEnglish (US)
Article number052337
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number5
StatePublished - Nov 2005

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


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