Quantum Brachistochrone Curves as Geodesics: Obtaining Accurate Minimum-Time Protocols for the Control of Quantum Systems
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, d...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2015
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| Online Access: | http://hdl.handle.net/1721.1/96838 https://orcid.org/0000-0002-5227-4009 |
| _version_ | 1826214481192026112 |
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| author | Wang, Xiaoting Allegra, Michele Jacobs, Kurt Lloyd, Seth Lupo, Cosmo Mohseni, Masoud |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Wang, Xiaoting Allegra, Michele Jacobs, Kurt Lloyd, Seth Lupo, Cosmo Mohseni, Masoud |
| author_sort | Wang, Xiaoting |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T16:06:25Z |
| format | Article |
| id | mit-1721.1/96838 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:06:25Z |
| publishDate | 2015 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/968382022-10-02T06:20:54Z Quantum Brachistochrone Curves as Geodesics: Obtaining Accurate Minimum-Time Protocols for the Control of Quantum Systems Wang, Xiaoting Allegra, Michele Jacobs, Kurt Lloyd, Seth Lupo, Cosmo Mohseni, Masoud Massachusetts Institute of Technology. Department of Mechanical Engineering Massachusetts Institute of Technology. Research Laboratory of Electronics Wang, Xiaoting Allegra, Michele Lloyd, Seth Lupo, Cosmo 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. National Science Foundation (U.S.) (Project PHY-1005571) United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-11-1-0268) National Science Foundation (U.S.) (Project CCF-1350397) 2015-04-29T13:17:37Z 2015-04-29T13:17:37Z 2015-04 2015-01 2015-04-28T22:00:05Z Article http://purl.org/eprint/type/JournalArticle 0031-9007 1079-7114 http://hdl.handle.net/1721.1/96838 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 https://orcid.org/0000-0002-5227-4009 en http://dx.doi.org/10.1103/PhysRevLett.114.170501 Physical Review Letters Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Wang, Xiaoting Allegra, Michele Jacobs, Kurt Lloyd, Seth Lupo, Cosmo Mohseni, Masoud Quantum Brachistochrone Curves as Geodesics: Obtaining Accurate Minimum-Time Protocols for the Control of Quantum Systems |
| title | Quantum Brachistochrone Curves as Geodesics: Obtaining Accurate Minimum-Time Protocols for the Control of Quantum Systems |
| title_full | Quantum Brachistochrone Curves as Geodesics: Obtaining Accurate Minimum-Time Protocols for the Control of Quantum Systems |
| title_fullStr | Quantum Brachistochrone Curves as Geodesics: Obtaining Accurate Minimum-Time Protocols for the Control of Quantum Systems |
| title_full_unstemmed | Quantum Brachistochrone Curves as Geodesics: Obtaining Accurate Minimum-Time Protocols for the Control of Quantum Systems |
| title_short | Quantum Brachistochrone Curves as Geodesics: Obtaining Accurate Minimum-Time Protocols for the Control of Quantum Systems |
| title_sort | quantum brachistochrone curves as geodesics obtaining accurate minimum time protocols for the control of quantum systems |
| url | http://hdl.handle.net/1721.1/96838 https://orcid.org/0000-0002-5227-4009 |
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