Accelerated Newton-Raphson GRAPE methods for optimal control
A Hessian-based state-to-state optimal control method in Liouville space is presented to mitigate previously undesirable polynomial scaling of Hessian computation time. This method, an improvement to the state-of-the-art Newton-Raphson gradient ascent pulse engineering (GRAPE) method, is derived wit...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-03-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.L012042 |
| _version_ | 1797210487824318464 |
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| author | David L. Goodwin Mads Sloth Vinding |
| author_facet | David L. Goodwin Mads Sloth Vinding |
| author_sort | David L. Goodwin |
| collection | DOAJ |
| description | A Hessian-based state-to-state optimal control method in Liouville space is presented to mitigate previously undesirable polynomial scaling of Hessian computation time. This method, an improvement to the state-of-the-art Newton-Raphson gradient ascent pulse engineering (GRAPE) method, is derived with respect to two exact time-propagator derivative calculation techniques, auxiliary matrix and efficient spin control using analytical Lie algebraic derivatives (ESCALADE) methods. We observed that compared to the best current implementation of the Newton-Raphson GRAPE method, for an ensemble of two-level systems, with realistic conditions, our auxiliary matrix and ESCALADE Hessians can be 4–200 and 70–600 times faster, respectively. Additionally, the Newton-Raphson GRAPE method using ESCALADE is presented in a Liouville space for higher-level systems and with the derivation of x-, y-, and z-control propagator derivatives, also extending the application of ESCALADE and the recent quantum optimal control by adaptive low-cost algorithm (QOALA) method for coupled systems. |
| first_indexed | 2024-04-24T10:11:23Z |
| format | Article |
| id | doaj.art-0d4f6c98854b4ad8bf5149cee5d1a5a7 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:11:23Z |
| publishDate | 2023-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-0d4f6c98854b4ad8bf5149cee5d1a5a72024-04-12T17:29:29ZengAmerican Physical SocietyPhysical Review Research2643-15642023-03-0151L01204210.1103/PhysRevResearch.5.L012042Accelerated Newton-Raphson GRAPE methods for optimal controlDavid L. GoodwinMads Sloth VindingA Hessian-based state-to-state optimal control method in Liouville space is presented to mitigate previously undesirable polynomial scaling of Hessian computation time. This method, an improvement to the state-of-the-art Newton-Raphson gradient ascent pulse engineering (GRAPE) method, is derived with respect to two exact time-propagator derivative calculation techniques, auxiliary matrix and efficient spin control using analytical Lie algebraic derivatives (ESCALADE) methods. We observed that compared to the best current implementation of the Newton-Raphson GRAPE method, for an ensemble of two-level systems, with realistic conditions, our auxiliary matrix and ESCALADE Hessians can be 4–200 and 70–600 times faster, respectively. Additionally, the Newton-Raphson GRAPE method using ESCALADE is presented in a Liouville space for higher-level systems and with the derivation of x-, y-, and z-control propagator derivatives, also extending the application of ESCALADE and the recent quantum optimal control by adaptive low-cost algorithm (QOALA) method for coupled systems.http://doi.org/10.1103/PhysRevResearch.5.L012042 |
| spellingShingle | David L. Goodwin Mads Sloth Vinding Accelerated Newton-Raphson GRAPE methods for optimal control Physical Review Research |
| title | Accelerated Newton-Raphson GRAPE methods for optimal control |
| title_full | Accelerated Newton-Raphson GRAPE methods for optimal control |
| title_fullStr | Accelerated Newton-Raphson GRAPE methods for optimal control |
| title_full_unstemmed | Accelerated Newton-Raphson GRAPE methods for optimal control |
| title_short | Accelerated Newton-Raphson GRAPE methods for optimal control |
| title_sort | accelerated newton raphson grape methods for optimal control |
| url | http://doi.org/10.1103/PhysRevResearch.5.L012042 |
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