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Optimal control landscapes for quantum observables.

Herschel Rabitz1, Michael Hsieh, Carey Rosenthal

  • 1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.

The Journal of Chemical Physics
|June 16, 2006
PubMed
Summary
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Optimal control of quantum systems can be achieved by understanding the control landscape. This study reveals a finite number of distinct extremum values for quantum system controls, simplifying the discovery of effective quantum controls.

Area of Science:

  • Quantum physics
  • Quantum control theory

Background:

  • Optimal control is crucial for manipulating quantum systems.
  • Quantum system dynamics are described by an evolving density matrix.
  • The observable of interest is represented by a Hermitian operator.

Purpose of the Study:

  • To analyze the optimal control landscape of quantum systems.
  • To identify the characteristics of extremum values on this landscape.
  • To determine the factors influencing these extremum values.

Main Methods:

  • Mathematical modeling of quantum systems.
  • Analysis of the observable as a functional of the control field.
  • Investigation of controllable finite dimensional quantum systems.

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Main Results:

  • The optimal control landscape is defined by the observable as a functional of the control field.
  • Extremum values and their topological character are key features.
  • For controllable finite dimensional systems, there's a finite number of distinct extremum values.
  • This number depends on the spectral degeneracy of initial and target density matrices.

Conclusions:

  • The number of distinct extremum values in quantum control is limited and predictable.
  • These findings simplify the search for effective quantum controls in experimental settings.
  • Practical implications for laboratory-based quantum control discovery are discussed.