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  • Letter
  • Open Access

Accelerated Newton-Raphson GRAPE methods for optimal control

David L. Goodwin1,2,* and Mads Sloth Vinding3,†

  • 1Chemistry Research Laboratory, University of Oxford, Mansfield Road, Oxford OX1 3TA, United Kingdom
  • 2Institute for Biological Interfaces 4 – Magnetic Resonance, Karlsruhe Institute for Technology (KIT), Karlsruhe, Fritz-Haber-Weg 6, 76131, Germany
  • 3Center of Functionally Integrative Neuroscience (CFIN), Department of Clinical Medicine, Aarhus University, DK-8000, Aarhus, Denmark

  • *Present address: Interdisciplinary Nanoscience Center (iNANO), Department of Chemistry, Aarhus University, Aarhus, DK-8000, Denmark; david.goodwin@partner.kit.edu
  • †msv@cfin.au.dk
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Phys. Rev. Research 5, L012042 – Published 22 March, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L012042

Abstract

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.

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Phys. Rev. Research 5, L012042– Published 22 March, 2023
  • Received 21 July 2022
  • Accepted 22 December 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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