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 gate using fewer qubits and with a better minimum distance than is possible with the best known stabilizer codes.
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