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Gauge Color Codes: Optimal Transversal Gates and Gauge Fixing in Topological Stabilizer Codes

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

preprint2015arXivOpen access
H. Bombin
quant-ph
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H. Bombin

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