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