  We implement arbitrary maps between pure states in the 16-dimensional Hilbert
space associated with the ground electronic manifold of Cs. This is
accomplished by driving atoms with phase modulated rf and {\mu}w fields, using
modulation waveforms found via numerical optimization and designed to work
robustly in the presence of imperfections. We evaluate the performance of a
sample of randomly chosen state maps by randomized benchmarking, obtaining an
average fidelity >99%. Our protocol advances state-of-the-art quantum control
and has immediate applications in quantum metrology and tomography.
