In the 1990s Aravind proposed that topological links can be used to classify different patterns of quantum entanglement. One way this connection can be investigated is through an appropriate quantum mechanical definition of knots. I will start from the category theory definition of a TQFT and derive a relation between measures of quantum entanglement and topological invariants of links. We will see how patterns of quantum entanglement emerge in the TQFT picture. Meanwhile, complexity is a complementary measure of quantum correlations. In the TQFT case, it can also be related to topological invariants. I will discuss a few definitions of complexity for several families of knots and links.