Microsoft Majorana 1: Topological Qubit Claim Without Demonstrated Logical Qubit — E8 Intelligence Research

FINDING: Microsoft's Majorana 1 chip claims the first scalable topological qubit architecture using Majorana zero modes in InAs/Al hybrid nanowires — a materials/physics claim, not yet a demonstrated logical qubit. MATH: - Topological protection rests on **non-Abelian anyon braiding**. Braid group generators σᵢ satisfy: σᵢσⱼ = σⱼσᵢ for |i−j| ≥ 2 σᵢσᵢ₊₁σᵢ = σᵢ₊₁σᵢσᵢ₊₁ (Yang–Baxter equation) - Majorana operators: γᵢ = γᵢ†, {γᵢ, γⱼ} = 2δᵢⱼ - Qubit encoding from 4 Majoranas: γ₁γ₂γ₃γ₄ = ±1 (parity), giving 2-state Hilbert space - Energy gap Δ ~ 250 μK reported; operating T ~ 20 mK → ratio T/Δ ≈ 0.08 - Nanowire geometry: InAs (semiconductor) + Al (superconductor), lattice mismatch drives proximity-induced pairing - Topological invariant: Pfaffian of the BdG Hamiltonian; ν = sgn[Pf(H(k=0))·Pf(H(k=π))] = −1 for topological phase CONNECTION: - **Crystallographic/lattice**: InAs zincblende (F-43m, tetrahedral T_d point group) interfaced with Al fcc (Fm-3m). The tetrahedral coordination is Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com