Standard model particles linked to quantum error correcting codes
One generation of the Standard Model as a quantum error-correcting code
Information Theory
Summary
Particles in one generation of the Standard Model, along with a right-handed neutrino, can be represented using five bits in a way that links to quantum error correction. The authors show this bit pattern corresponds exactly to a special kind of quantum code used to fix errors in quantum computing. Removing the right-handed neutrino gives a known quantum error-correcting code that protects quantum information across different systems. This connection ties deep physics properties to quantum computing methods.
What this means in practice
- •For quantum hardware developers: Use the unique structure of the Standard Model related codes to design efficient quantum error-correcting schemes for protecting quantum hardware operations.
- •For quantum software engineers: Incorporate triorthogonal codes from particle physics insights into quantum software layers to improve magic state distillation for fault-tolerant quantum algorithms.
A theory result. No direct application yet.
Authors
Shiroman Prakash, K. L. Ramya
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.