Data-driven control of a single-qubit system based on unitary evolution reconstruction

We present a data-driven framework for controlling a single qubit based on experimental data, without requiring explicit Hamiltonian models. Two modeling approaches are studied. The indirect approach identifies an affine model of the qubit dynamics and employs it for control design, while the direct approach uses a Hankel matrix representation to generate feasible control actions directly from recorded trajectories. We provide stability guarantees and verify both formulations in simulation, demonstrating that data-driven predictive control can effectively steer a qubit to the desired target state under input constraints.