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Permutation-Invariant Quantum Codes with Transversal Generalized Phase Gates

Quantum Physics 2024-10-08 v3

Abstract

With respect to the transversal gate group (an invariant of quantum codes), we demonstrate that non-additive codes can outperform stabilizer codes. We do this by constructing spin codes that correspond to permutation-invariant multiqubit codes that can implement generalized phase gates transversally. Of particular note, we construct permutation-invariant quantum codes that implement a transversal TT gate using fewer qubits and with a better minimum distance than is possible with the best known stabilizer codes.

Keywords

Cite

@article{arxiv.2310.17652,
  title  = {Permutation-Invariant Quantum Codes with Transversal Generalized Phase Gates},
  author = {Eric Kubischta and Ian Teixeira},
  journal= {arXiv preprint arXiv:2310.17652},
  year   = {2024}
}

Comments

Changed title and abstract to more accurately reflect the contents of the paper. Changed to IEEE transactions formatting. Added more complete proofs of all major results. Added more references

R2 v1 2026-06-28T13:03:07.606Z