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Updated: Aug 23, 2025

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Quantum brachistochrone.

Tatsuhiko Koike1,2

  • 1Department of Physics and Quantum Computing Center, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama 223-8522, Japan.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|November 6, 2022
PubMed
Summary
This summary is machine-generated.

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Researchers explored the quantum brachistochrone (QB), the fastest quantum operation path. This work reviews the QB formalism, crucial for quantum information and computing advancements.

Area of Science:

  • Quantum Mechanics
  • Quantum Information Science
  • Quantum Engineering

Background:

  • The quantum brachistochrone (QB) is the quantum mechanical analog of the classical brachistochrone problem, focusing on the shortest time to achieve a quantum state transformation.
  • Finding the optimal path for quantum operations is crucial for advancing quantum technologies.

Purpose of the Study:

  • To review the fundamental problem of finding the quantum brachistochrone (QB).
  • To introduce and explain the general framework, known as the QB formalism, for identifying QBs.
  • To highlight the relevance of QBs in quantum information and quantum engineering.

Main Methods:

  • The study reviews the basics of the QB formalism.
  • The formalism is based on Pontryagin's maximum principle.
Keywords:
quantum brachistochronequantum controlquantum informationquantum operationtime optimality

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Last Updated: Aug 23, 2025

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  • Simple examples illustrating the QB formalism are provided.

    • Main Results:

    • A general framework (QB formalism) for finding quantum brachistochrones has been established.
    • The QB formalism provides a method to determine the fastest possible quantum operations under given constraints.
    • The review includes illustrative examples of QB applications.

    Conclusions:

    • The quantum brachistochrone problem is fundamental to quantum mechanics.
    • The QB formalism offers a powerful tool for optimizing quantum operations.
    • Understanding QBs is essential for progress in quantum speed limits and quantum computing implementations.