Transversality Versus Universality for Additive Quantum Codes

@article{Zeng2011TransversalityVU,
  title={Transversality Versus Universality for Additive Quantum Codes},
  author={Bei Zeng and Andrew W. Cross and Isaac L. Chuang},
  journal={IEEE Transactions on Information Theory},
  year={2011},
  volume={57},
  pages={6272-6284}
}
Logic gates can be performed on data encoded in quantum code blocks such that errors introduced by faulty gates can be corrected. The important class of transversal gates acts bitwise between corresponding qubits of code blocks and thus limits error propagation. If any quantum gate could be implemented using transversal gates, the set would be universal. We study the structure of GF(4)-additive quantum codes and prove that no universal set of transversal logic gates exists for these codes. This… 

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