Abstract
Perfect tensors are the tensors corresponding to the absolutely maximally entangled states, a special type of quantum states of interest in quantum information theory. We establish a method to compute parameterized families of perfect tensors in (C^d)^⊗ 4 using exponential maps from Lie theory. With this method, we find explicit examples of non-classical perfect tensors in (C³)^⊗ 4. In particular, we answer an open question posted by \.Zyczkowski et al.