  Maximally entangled bipartite unitary operators or gates find various
applications from quantum information to being building blocks of minimal
models of many-body quantum chaos, and have been referred to as "dual
unitaries". Dual unitary operators that can create the maximum average
entanglement when acting on product states have to satisfy additional
constraints. These have been called "2-unitaries" and are examples of perfect
tensors that can be used to construct absolutely maximally entangled states of
four parties. Hitherto, no systematic method exists, in any local dimension,
which result in the formation of such special classes of unitary operators. We
outline an iterative protocol, a nonlinear map on the space of unitary
operators, that creates ensembles whose members are arbitrarily close to being
dual unitaries, while for qutrits and ququads we find that a slightly modified
protocol yields a plethora of 2-unitaries. We further characterize the dual
unitary operators via their entangling power and the 2-unitaries via the
distribution of entanglement created from unentangled states.
