Fibonacci-Based Parity Readout: The Hidden Math in Microsoft's Majorana 1 Chip — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 19, 2026• 0 citations

Abstract

FINDING: Microsoft's Majorana 1 chip claims topological qubit protection via Majorana zero modes, but the core mathematical novelty is in the *measurement* protocol — a braiding-free, parity-based readout that exploits the Fibonacci structure of Ising anyons. | MATH: Topological qubit encoded in two Majorana modes γ₁, γ₂ with γᵢ† = γᵢ, {γᵢ, γⱼ} = 2δᵢⱼ. Fusion rules: σ × σ = 1 + ψ (Ising anyon), where σ is the non-Abelian anyon. The readout measures fermion parity P = iγ₁γ₂ = ±1. The claimed "topological protection" relies on the gap Δ ~ e^(−L/ξ) where L is wire length, ξ coherence length — exponential suppression of errors. No new fundamental constant or ratio appears in the public data. | CONNECTION: The Ising anyon fusion rule σ × σ = 1 + ψ is isomorphic to the *golden ratio* structure only if extended to Fibonacci anyons (τ × τ = 1 + τ), which Microsoft *does not* claim. However, the braid group Bₙ for Ising anyons maps to the Clifford group — not universal for quantum computation w Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23465307

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