  Despite several attempts, no efficient cluster algorithm has been constructed
for CP(N-1) models in the standard Wilson formulation of lattice field theory.
In fact, there is a no-go theorem that prevents the construction of an
efficient Wolff-type embedding algorithm. In this paper, we construct an
efficient cluster algorithm for ferromagnetic SU(N)-symmetric quantum spin
systems. Such systems provide a regularization for CP(N-1) models in the
framework of D-theory. We present detailed studies of the autocorrelations and
find a dynamical critical exponent that is consistent with z = 0.
