  Using a braid group representation based on the Temperley-Lieb algebra, we
construct braid quantum gates that could generate entangled $n$-partite
$D$-level qudit states. $D$ different sets of $D^n\times D^n$ unitary
representation of the braid group generators are presented. With these
generators the desired braid quantum gates are obtained. We show that the
generalized GHZ states, which are maximally entangled states, can be obtained
directly from these braid quantum gates without resorting to further local
unitary transformations. We also point out an interesting observation, namely
for a general multi-qudit state there exists a unitary braid quantum gate based
on the Temperley-Lieb algebra that connects it from one of its component basis
states, if the coefficient of the component state is such that the square of
its norm is no less than $1/4$.
