Majorana 1: Braid Group Math Behind Topological Qubits — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Microsoft's Majorana 1 chip claims topological qubits via Majorana zero modes, but public evidence remains thin; the deeper mathematical structure is in the braid group and non-Abelian anyon statistics. | MATH: Majorana zero modes satisfy γ† = γ, {γi, γj} = 2δij (Clifford algebra). Qubit encoded in parity: iγ1γ2 = ±1. Braiding implements unitary transformations in the braid group Bn, with Fibonacci anyons giving dense gate set via golden ratio τ = (1+√5)/2 ≈ 1.618. Topological protection arises from energy gap Δ, with error rate ∝ exp(−Δ/kBT). | CONNECTION: **Direct geometric harmony**: Fibonacci anyons — the simplest non-Abelian anyons — have quantum dimension φ = (1+√5)/2 = 1.618, exactly the golden ratio. Their fusion rules: φ × φ = 1 + φ. This is the same φ appearing in Penrose tilings (5-fold crystallographic symmetry, forbidden in ordinary crystals) and in the icosahedral root system H3. The braid group B3 maps to the modular group PSL(2,Z), whose fundamental domain has 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: W7204121009
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