conference paper Boris Edgar Wembe Moafo author 953940000-0002-6085-8071 Usman Ali author Torsten Meier author 3440000-0001-8864-2072 Sina Ober-Blöbaum author 16494 94 department European Control Conference 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. 2026Reykjavík, Iceland eng 10.48550/ARXIV.2603.11697 B.E. Wembe Moafo, U. Ali, T. Meier, S. Ober-Blöbaum, in: 2026. 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>. 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> 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>. 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> @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} } 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>. 657462026-06-01T09:38:06Z2026-06-01T09:40:38Z