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Related Experiment Videos

Time-optimal quantum evolution.

Alberto Carlini1, Akio Hosoya, Tatsuhiko Koike

  • 1Department of Physics, Tokyo Institute of Technology, Tokyo, Japan. carlini@th.phys.titech.ac.jp

Physical Review Letters
|April 12, 2006
PubMed
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Researchers developed a method to find the fastest quantum system evolution and optimal Hamiltonian using variational principles. This approach, analogous to classical mechanics, solves for the Hamiltonian under specific constraints.

Area of Science:

  • Quantum Mechanics
  • Optimal Control Theory
  • Theoretical Physics

Background:

  • Controlling quantum systems efficiently is crucial for quantum technologies.
  • Finding time-optimal paths and control Hamiltonians is a complex challenge.
  • Existing methods may not cover all constraint scenarios for quantum evolution.

Purpose of the Study:

  • To establish a general framework for determining time-optimal quantum evolution.
  • To identify the optimal Hamiltonian for transitioning between specified quantum states.
  • To provide a method applicable to various constraints on available Hamiltonians.

Main Methods:

  • Formulation based on the variational principle, drawing parallels to classical brachistochrone problems.
  • Reduction of the optimal control problem to a formal equation for the Hamiltonian.

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  • Analysis of Hamiltonian constraints defining the set of permissible controls.

    • Main Results:

    • A general framework for time-optimal quantum control is presented.
    • The optimal Hamiltonian is derived as a function of constraint functions.
    • Explicit optimal solutions are found for specific, illustrative constraint examples.

    Conclusions:

    • The proposed variational approach offers a systematic way to solve time-optimal quantum control problems.
    • The framework is versatile and can be adapted to different physical constraints.
    • This work provides a foundation for designing faster and more efficient quantum operations.