Majorana Braiding Generates Single-Qubit Clifford Group of Order 24 — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Majorana zero modes realize non-Abelian anyons whose braiding generates a finite subgroup of the Clifford group — specifically the single-qubit Clifford group of order 24, isomorphic to the binary tetrahedral group 2T. | MATH: Braiding operators B_ij = exp(π γ_i γ_j / 4); Majorana algebra {γ_i, γ_j} = 2δ_ij; single-qubit Clifford group |C₁| = 24 = 2³·3; 2T ≅ SL(2,3) ⊂ SU(2), order 24; 24 = 4! = 2·12 = binary tetrahedral order; braid group B_n → Clifford via Burau/Ising representation; Ising anyon fusion σ×σ = 1+ψ; R-matrix eigenvalues e^{±iπ/8} (silver ratio phase). | CONNECTION: 24 = order of binary tetrahedral group 2T, the double cover of A₄ (tetrahedral rotation group, order 12). Tetrahedron = 4 vertices, 6 edges, 4 faces → 4+6+4 = 14, but 2T doubles to 24. 24 = 2·12 = 2·(tetrahedral rotations). Also 24 = 4! = permutations of 4 elements (S₄ has order 24; 2T ⊂ S₄ as normal subgroup). The braid phase e^{iπ/8} has |phase| = π/8 = 22.5° = 360°/16, linking to 16-fold symmetry ( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225123085