  We present two paradigms relating algebraic, topological and quantum
computational statistics for the topological model for quantum computation. In
particular we suggest correspondences between the computational power of
topological quantum computers, computational complexity of link invariants and
images of braid group representations. While at least parts of these paradigms
are well-known to experts, we provide supporting evidence for them in terms of
recent results. We give a fairly comprehensive list of known examples and
formulate two conjectures that would further support the paradigms.
