Color codes are topological stabilizer codes with unusual transversalityproperties. Here I show that their group of transversal gates is optimal andonly depends on the spatial dimension, not the local geometry. I also introducea generalized, subsystem version of color codes. In 3D they allow thetransversal implementation of a universal set of gates by gauge fixing, whileerror-detecting measurements involve only 4 or 6 qubits.
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