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

Multi-qudit states generated by unitary braid quantum gates based on Temperley-Lieb algebra