Cayley Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal Control Wembe Moafo, Boris Edgar Ali, Usman Meier, Torsten Ober-Blöbaum, Sina 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. 2026 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject text http://purl.org/coar/resource_type/c_5794 https://ris.uni-paderborn.de/record/65746 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> eng info:eu-repo/semantics/altIdentifier/doi/10.48550/ARXIV.2603.11697 info:eu-repo/semantics/closedAccess