One generation of the Standard Model as a quantum error-correcting code

Shiroman Prakash; K. L. Ramya

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arXiv · 2610.21879

One generation of the Standard Model as a quantum error-correcting code

Shiroman Prakash·K. L. Ramya

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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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Shiroman Prakash, K. L. Ramya. 2026-10-15. One generation of the Standard Model as a quantum error-correcting code. https://arxiv.org/abs/2610.21879

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