Creating Ensembles of Dual Unitary and Maximally Entangling Quantum Evolutions

Maximally entangled bipartite unitary operators or gates find various applications from quantum information to many-body physics wherein they are building blocks of minimal models of quantum chaos. In the latter case, they are 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 results 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. For qutrits and ququads we find that a slightly modified protocol yields a plethora of 2-unitaries.