Six Majorana Zero Modes Braid into a Three-Qubit Clifford Group — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 30, 2026• 0 citations

Abstract

FINDING: Six Majorana zero modes (MZMs) form three qubit pairs whose braiding generates a finite Clifford-group representation — the minimal non-Abelian platform for universal-adjacent topological quantum computation. | MATH: 2n MZMs → n qubits; 6 MZMs → 3 qubits → Hilbert space dim 2³ = 8. Braid group B₆ (or its image) maps to Clifford group C₃ ⊂ U(8). Ising anyon σ braiding: γᵢ → γⱼ, γⱼ → −γᵢ (i≠j), γₖ → γₖ. Majorana algebra {γᵢ,γⱼ} = 2δᵢⱼ. Fusion: σ×σ = 1 + ψ. Braid generator eigenvalues e^{±iπ/8} (topological phase, related to ν=5/2). | CONNECTION: Clifford group order for n qubits = 2^{n²+2n}·∏(4ᵏ−1); for n=3: 2^{15}·(4−1)(16−1)(64−1) = 32768·3·15·63 = 92,897,280. Braid group B₆ has 6 generators σ₁…σ₅ with relations σᵢσᵢ₊₁σᵢ = σᵢ₊₁σᵢσᵢ₊₁ (Yang–Baxter / braid relation) — a cubic algebraic relation, echoing the 3-fold symmetry of A₂ root system and the 2π/3 rotation in SU(3). The 6 MZMs sit at vertices of an octahedron (6 vertices, 8 faces = 2³ Hilbert states); braiding = SO(6) rota Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23796671

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