PreprintarXiv licencearXiv
One generation of the Standard Model as a quantum error-correcting code
Abstract
Together with a right-handed neutrino, the fermions of one generation of the Standard Model are labelled by five bits, a combinatorial structure tied to anomaly cancellation. We make this precise. Anomaly cancellation is the vanishing of a cubic form, the defining property of triorthogonal codes, the quantum error-correcting codes behind magic state distillation. Removing the right-handed neutrino gives a [[15,1,3]]p code for every prime p, including the Bravyi-Kitaev code for p = 2. For qutrits it is the unique shortest distance-three triorthogonal code.
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BibTeX
@misc{prakash2026generation,
title = {{One generation of the Standard Model as a quantum error-correcting code}},
author = {Shiroman Prakash and K. L. Ramya},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21879},
eprint = {2610.21879},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21879},
}
RIS
TY - UNPB
TI - One generation of the Standard Model as a quantum error-correcting code
AU - Shiroman Prakash
AU - K. L. Ramya
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21879
UR - https://arxiv.org/abs/2610.21879
AB - Together with a right-handed neutrino, the fermions of one generation of the Standard Model are labelled by five bits, a combinatorial structure tied to anomaly cancellation. We make this precise. Anomaly cancellation is the vanishing of a cubic form, the defining property of triorthogonal codes, the quantum error-correcting codes behind magic state distillation. Removing the right-handed neutrino gives a [[15,1,3]]_p code for every prime p, including the Bravyi-Kitaev code for p = 2. For qutrits it is the unique shortest distance-three triorthogonal code.
ER -