Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
Review
. 2022 Dec 26;380(2239):20210273.
doi: 10.1098/rsta.2021.0273. Epub 2022 Nov 7.

Quantum brachistochrone

Tatsuhiko Koike  1   2
Affiliations
Review

Quantum brachistochrone

Tatsuhiko Koike. Philos Trans A Math Phys Eng Sci. .

Abstract

Quantum brachistochrone (QB) is a quantum analogue of classical brachistochrone (shortest path). It is a solution to the following problem: How can we perform a desired quantum operation (or obtain a desired final quantum state) most quickly, by a time-dependent Hamiltonian subject to given constraints? Finding QB is a fundamental problem in quantum mechanics in its own right. Moreover, it will be useful in the study of quantum information and quantum engineering, such as quantum speed limits and implementations of quantum computers. A general framework for finding QBs, called QB formalism, has been developed. It is based on Pontryagin's maximum principle. We review the basics of the QB formalism, give simple examples, and briefly discuss some related studies. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

Keywords: quantum brachistochrone; quantum control; quantum information; quantum operation; time optimality.

PubMed Disclaimer

Similar articles

  • Dynamical invariant formalism of shortcuts to adiabaticity.
    Takahashi K. Takahashi K. Philos Trans A Math Phys Eng Sci. 2022 Dec 26;380(2239):20220301. doi: 10.1098/rsta.2022.0301. Epub 2022 Nov 7. Philos Trans A Math Phys Eng Sci. 2022. PMID: 36335952 Review.
  • Counterdiabatic formalism of shortcuts to adiabaticity.
    Nakahara M. Nakahara M. Philos Trans A Math Phys Eng Sci. 2022 Dec 26;380(2239):20210272. doi: 10.1098/rsta.2021.0272. Epub 2022 Nov 7. Philos Trans A Math Phys Eng Sci. 2022. PMID: 36335939 Review.
  • Robust electron spin qubit control in a nanowire double quantum dot.
    Lu R, Liu K, Ban Y. Lu R, et al. Philos Trans A Math Phys Eng Sci. 2022 Dec 26;380(2239):20210270. doi: 10.1098/rsta.2021.0270. Epub 2022 Nov 7. Philos Trans A Math Phys Eng Sci. 2022. PMID: 36335949
  • Time-optimal quantum evolution.
    Carlini A, Hosoya A, Koike T, Okudaira Y. Carlini A, et al. Phys Rev Lett. 2006 Feb 17;96(6):060503. doi: 10.1103/PhysRevLett.96.060503. Epub 2006 Feb 15. Phys Rev Lett. 2006. PMID: 16605975
  • Fast-forward scaling theory.
    Masuda S, Nakamura K. Masuda S, et al. Philos Trans A Math Phys Eng Sci. 2022 Dec 26;380(2239):20210278. doi: 10.1098/rsta.2021.0278. Epub 2022 Nov 7. Philos Trans A Math Phys Eng Sci. 2022. PMID: 36335946 Free PMC article. Review.
See all similar articles

LinkOut - more resources