---
_id: '65746'
abstract:
- lang: eng
  text: This paper presents a class of structure-preserving numerical methods for
    quantum optimal control problems, based on commutator-free Cayley integrators.
    Starting from the Krotov framework, we reformulate the forward and backward propagation
    steps using Cayley-type schemes that preserve unitarity and symmetry at the discrete
    level. This approach eliminates the need for matrix exponentials and commutators,
    leading to significant computational savings while maintaining higher-order accuracy.
    We first recall the standard linear setting and then extend the formulation to
    nonlinear Schrödinger and Gross-Pitaevskii equations using a Cayley-polynomial
    interpolation strategy. Numerical experiments on state-transfer problems illustrate
    that the CF-Cayley method achieves the same accuracy as high-order exponential
    or Cayley-Magnus schemes at substantially lower cost, especially for longtime
    or highly oscillatory dynamics. In the nonlinear regime, the structure-preserving
    properties of the method ensure stability and norm conservation, making it a robust
    tool for large-scale quantum control simulations. The proposed framework thus
    bridges geometric integration and optimal control, offering an efficient and reliable
    alternative to existing exponential-based propagators.
author:
- first_name: Boris Edgar
  full_name: Wembe Moafo, Boris Edgar
  id: '95394'
  last_name: Wembe Moafo
  orcid: 0000-0002-6085-8071
- first_name: Usman
  full_name: Ali, Usman
  last_name: Ali
- first_name: Torsten
  full_name: Meier, Torsten
  id: '344'
  last_name: Meier
  orcid: 0000-0001-8864-2072
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
citation:
  ama: 'Wembe Moafo BE, Ali U, Meier T, Ober-Blöbaum S. Cayley Commutator-free Methods
    for Krotov-Type Algorithms in Quantum Optimal Control. In: ; 2026. doi:<a href="https://doi.org/10.48550/ARXIV.2603.11697">10.48550/ARXIV.2603.11697</a>'
  apa: Wembe Moafo, B. E., Ali, U., Meier, T., &#38; Ober-Blöbaum, S. (2026). <i>Cayley
    Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal Control</i>.
    European Control Conference, Reykjavík, Iceland. <a href="https://doi.org/10.48550/ARXIV.2603.11697">https://doi.org/10.48550/ARXIV.2603.11697</a>
  bibtex: '@inproceedings{Wembe Moafo_Ali_Meier_Ober-Blöbaum_2026, title={Cayley Commutator-free
    Methods for Krotov-Type Algorithms in Quantum Optimal Control}, DOI={<a href="https://doi.org/10.48550/ARXIV.2603.11697">10.48550/ARXIV.2603.11697</a>},
    author={Wembe Moafo, Boris Edgar and Ali, Usman and Meier, Torsten and Ober-Blöbaum,
    Sina}, year={2026} }'
  chicago: Wembe Moafo, Boris Edgar, Usman Ali, Torsten Meier, and Sina Ober-Blöbaum.
    “Cayley Commutator-Free Methods for Krotov-Type Algorithms in Quantum Optimal
    Control,” 2026. <a href="https://doi.org/10.48550/ARXIV.2603.11697">https://doi.org/10.48550/ARXIV.2603.11697</a>.
  ieee: 'B. E. Wembe Moafo, U. Ali, T. Meier, and S. Ober-Blöbaum, “Cayley Commutator-free
    Methods for Krotov-Type Algorithms in Quantum Optimal Control,” presented at the
    European Control Conference, Reykjavík, Iceland, 2026, doi: <a href="https://doi.org/10.48550/ARXIV.2603.11697">10.48550/ARXIV.2603.11697</a>.'
  mla: Wembe Moafo, Boris Edgar, et al. <i>Cayley Commutator-Free Methods for Krotov-Type
    Algorithms in Quantum Optimal Control</i>. 2026, doi:<a href="https://doi.org/10.48550/ARXIV.2603.11697">10.48550/ARXIV.2603.11697</a>.
  short: 'B.E. Wembe Moafo, U. Ali, T. Meier, S. Ober-Blöbaum, in: 2026.'
conference:
  end_date: 2026-07-10
  location: Reykjavík, Iceland
  name: European Control Conference
  start_date: 2026-07-07
date_created: 2026-06-01T09:38:06Z
date_updated: 2026-06-01T09:40:38Z
department:
- _id: '94'
doi: 10.48550/ARXIV.2603.11697
language:
- iso: eng
status: public
title: Cayley Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal
  Control
type: conference
user_id: '95394'
year: '2026'
...