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Braiding defects in topological stabiliser codes has been widely studied as apromising approach to fault-tolerant quantum computing. We present a no-gotheorem that places very strong limitations on the potential of such schemesfor universal fault-tolerant quantum computing in any spatial dimension. Inparticular, we show that, for the natural encoding of quantum information indefects in topological stabiliser codes, the set of logical operatorsimplementable by braiding defects is contained in the Clifford group. Indeed,we show that this remains true even when supplemented with locality-preservinglogical operators.

Braiding defects in topological stabiliser codes of any dimension cannot be universal