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High fidelity and robustness in population inversion is very desirable formany quantum control applications. We expand composite pulse schemes developedfor two-level dynamics, and present an analytic solution for the coherentevolution of an N-level quantum system with SU(2) symmetry, for achieving highfidelity and robust population inversion, which outperforms common solutions inN-level dynamics. Our approach offers a platform for accurate steering of thepopulation transfer in physical multi-level systems, which is crucial forfidelity in quantum computation and achieving fundamental excitations innuclear magnetic resonances and atomic physics. We also introduce and discussthe geometrical trajectories of these dynamics on the Majorana sphere as aninterpretation, allowing to gain physical insight on the dynamics of many-bodyor high-dimensional quantum systems.

Composite Pulses in N-level Systems with SU(2) Symmetry and their Geometrical Representation on the Majorana Sphere