  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 $(\mathbb{C}^d)^{\otimes 4}$ using exponential maps from Lie
theory. With this method, we find explicit examples of non-classical perfect
tensors in $(\mathbb{C}^3)^{\otimes 4}$. In particular, we answer an open
question posted by \.Zyczkowski et al.
