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Generalized monotonically convergent algorithms for solving quantum optimal control problems.

Yukiyoshi Ohtsuki1, Gabriel Turinici, Herschel Rabitz

  • 1Department of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan. ohtsuki@mcl.chem.tohoku.ac.jp

The Journal of Chemical Physics
|July 23, 2004
PubMed
Summary
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New algorithms improve optimal pulse design by reducing complex cost functionals to two basic ones. These methods ensure monotonic convergence, overcoming issues like "trapping" and enhancing control system design.

Area of Science:

  • Quantum control
  • Optimal control theory
  • Computational chemistry

Background:

  • Designing optimal control pulses is crucial for manipulating quantum systems.
  • Existing algorithms face challenges with complex cost functionals and convergence.
  • Product space formulation simplifies diverse cost functionals.

Purpose of the Study:

  • To extend monotonically convergent algorithms for generalized pulse design equations.
  • To analyze the convergence behavior of new algorithms in various scenarios.
  • To investigate the impact of relaxation on pulse design convergence.

Main Methods:

  • Reduction of cost functionals to two basic types using product spaces.
  • Extension of monotonically convergent algorithms.

Related Experiment Videos

  • Numerical implementation in four-level model systems.
  • Analysis of convergence using trajectory plots.

    • Main Results:

    • The extended algorithms demonstrate monotonic convergence.
    • Numerical tests in four-level systems confirm algorithm performance.
    • "Trapping" identified as a cause of slow convergence.
    • Relaxation processes were shown to mitigate unfavorable convergence behavior.

    Conclusions:

    • The developed algorithms provide a robust method for optimal pulse design.
    • Understanding convergence behavior, including trapping, is key to effective control.
    • Relaxation can be leveraged to improve the efficiency of quantum control pulse design.