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PreprintCC BY 4.0arXiv

Hybrid Clifford Codes via Operator Algebra Quantum Error Correction and Projective Representation Theory

  • Jonas Eidesen
  • David W. Kribs
  • Andrew Nemec
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Abstract

Clifford codes are a natural generalization of quantum stabilizer codes based primarily on representation theory. This class of codes has previously been extended to the setting of quantum subsystem codes. We formulate a two-fold generalization of Clifford codes, for both the hybrid classical and quantum information and projective representation theory settings. This leads to new classes of hybrid subspace and subsystem Clifford codes. We extend the fundamental representation theoretic quantum error correction theorem to include these codes, based on the operator algebra quantum error correction framework. We also discuss several examples throughout the presentation, of both stabilizer and non-stabilizer type.

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Cite

BibTeXRIS
BibTeX
@misc{eidesen2026hybrid,
  title = {{Hybrid Clifford Codes via Operator Algebra Quantum Error Correction and Projective Representation Theory}},
  author = {Jonas Eidesen and David W. Kribs and Andrew Nemec},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2606.02531},
  eprint = {2606.02531},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.02531},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Hybrid Clifford Codes via Operator Algebra Quantum Error Correction and Projective Representation Theory
AU  - Jonas Eidesen
AU  - David W. Kribs
AU  - Andrew Nemec
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2606.02531
UR  - https://arxiv.org/abs/2606.02531
AB  - Clifford codes are a natural generalization of quantum stabilizer codes based primarily on representation theory. This class of codes has previously been extended to the setting of quantum subsystem codes. We formulate a two-fold generalization of Clifford codes, for both the hybrid classical and quantum information and projective representation theory settings. This leads to new classes of hybrid subspace and subsystem Clifford codes. We extend the fundamental representation theoretic quantum error correction theorem to include these codes, based on the operator algebra quantum error correction framework. We also discuss several examples throughout the presentation, of both stabilizer and non-stabilizer type.
ER  -