Quantum Brachistochrone Curves as Geodesics: Obtaining Accurate Minimum-Time Protocols for the Control of Quantum Systems
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PhysRevLett.114.170501.pdf
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240.89 KB
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Author(s)
Wang, Xiaoting
Allegra, Michele
Jacobs, Kurt
Lloyd, Seth
Lupo, Cosmo
Mohseni, Masoud
Date Issued
April 2015
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Wang, Xiaoting, Michele Allegra, Kurt Jacobs, Seth Lloyd, Cosmo Lupo, and Masoud Mohseni. "Quantum Brachistochrone Curves as Geodesics: Obtaining Accurate Minimum-Time Protocols for the Control of Quantum Systems." Phys. Rev. Lett. 114, 170501 (April 2015). © 2015 American Physical Society
Version
Final published version
Abstract
Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for a wide range of quantum control problems. So far, this potential has not been realized, however, due to the inadequacy of conventional numerical methods to solve it. Here we show that the quantum brachistochrone problem can be recast as that of finding geodesic paths in the space of unitary operators. We expect this brachistochrone-geodesic connection to have broad applications, as it opens up minimal-time control to the tools of geometry. As one such application, we use it to obtain a fast numerical method to solve the brachistochrone problem, and apply this method to two examples demonstrating its power.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Research Laboratory of Electronics
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.114.170501
