  Important developments in fault-tolerant quantum computation using the
braiding of anyons have placed the theory of braid groups at the very
foundation of topological quantum computing. Furthermore, the realization by
Kauffman and Lomonaco that a specific braiding operator from the solution of
the Yang-Baxter equation, namely the Bell matrix, is universal implies that in
principle all quantum gates can be constructed from braiding operators together
with single qubit gates. In this paper we present a new class of braiding
operators from the Temperley-Lieb algebra that generalizes the Bell matrix to
multi-qubit systems, thus unifying the Hadamard and Bell matrices within the
same framework. Unlike previous braiding operators, these new operators
generate {\it directly}, from separable basis states, important entangled
states such as the generalized Greenberger-Horne-Zeilinger states, cluster-like
states, and other states with varying degrees of entanglement.
