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Monotonically convergent optimization in quantum control using Krotov's method.

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  • 1Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany.

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Summary
This summary is machine-generated.

The Konnov-Krotov method enables monotonically convergent quantum control algorithms for complex systems. This approach extends optimal control theory to nonlinear and non-unitary quantum dynamics, improving computational efficiency.

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Area of Science:

  • Quantum Control Theory
  • Non-linear Optimization
  • Computational Physics

Background:

  • Optimal control theory traditionally focused on linear systems.
  • Previous work extended optimal control to the non-linear Schrödinger equation using the Konnov-Krotov method.

Purpose of the Study:

  • To demonstrate monotonically convergent algorithms for a broad range of quantum control problems using the Konnov-Krotov method.
  • To extend the applicability of the method to systems with non-unitary time evolution and complex Hamiltonians.

Main Methods:

  • Application of the Konnov-Krotov non-linear optimization method.
  • Analytical and numerical estimation of second-order non-linear contributions.
  • Comparison of first- and second-order algorithm performance.

Main Results:

  • Monotonic convergence achieved for quantum control problems with non-linear equations of motion and non-unitary evolution.
  • Demonstrated convergence for optimization functionals up to eighth-degree polynomials.
  • Showcased that second-order contributions can accelerate convergence for standard problems.

Conclusions:

  • The Konnov-Krotov method provides robust algorithms for diverse quantum control challenges.
  • The method's flexibility accommodates complex system dynamics and target specifications.
  • Second-order optimization offers enhanced convergence speed in specific quantum control scenarios.