{"abstract":[{"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.","lang":"eng"}],"citation":{"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} }","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>","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.","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>.","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>"},"department":[{"_id":"94"}],"type":"conference","date_created":"2026-06-01T09:38:06Z","date_updated":"2026-06-01T09:40:38Z","author":[{"first_name":"Boris Edgar","orcid":"0000-0002-6085-8071","last_name":"Wembe Moafo","full_name":"Wembe Moafo, Boris Edgar","id":"95394"},{"first_name":"Usman","last_name":"Ali","full_name":"Ali, Usman"},{"id":"344","first_name":"Torsten","orcid":"0000-0001-8864-2072","last_name":"Meier","full_name":"Meier, Torsten"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"}],"conference":{"end_date":"2026-07-10","location":"Reykjavík, Iceland","name":"European Control Conference","start_date":"2026-07-07"},"year":"2026","title":"Cayley Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal Control","status":"public","user_id":"95394","doi":"10.48550/ARXIV.2603.11697","language":[{"iso":"eng"}],"_id":"65746"}