Quantum brachistochrone curves as geodesics: Obtaining accurate minimum-time protocols for the control of quantum systems

Xiaoting Wang; Michele Allegra; Kurt Jacobs; Seth Lloyd; Cosmo Lupo; Masoud Mohseni

doi:10.1103/PhysRevLett.114.170501

Quantum brachistochrone curves as geodesics: Obtaining accurate minimum-time protocols for the control of quantum systems

Xiaoting Wang, Michele Allegra, Kurt Jacobs, Seth Lloyd, Cosmo Lupo, Masoud Mohseni

Computer Science

Research output: Contribution to journal › Letter › peer-review

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.

Original language	English
Article number	170501
Journal	Physical Review Letters
Volume	114
Issue number	17
DOIs	https://doi.org/10.1103/PhysRevLett.114.170501
Publication status	Published - 28 Apr 2015

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AU - Lloyd, Seth

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AU - Mohseni, Masoud

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AB - 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.

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Quantum brachistochrone curves as geodesics: Obtaining accurate minimum-time protocols for the control of quantum systems

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