Bott Periodicity, Clifford Algebras, and Majorana Zero Modes in Topological Quantum Computing — E8 Intelligence Research

FINDING: Bott periodicity (period 8) classifies real Clifford algebras Cl(p,q) and governs the tenfold way of topological phases; Majorana zero modes obey non-Abelian Ising anyon braiding, the physical substrate for topological qubits. | MATH: Cl(p+8,q) ≅ Cl(p,q) ⊗ M₁₆(ℝ); real Bott clock period 8, complex period 2. Classification table: Cl(n,0) for n mod 8 → {ℝ, ℂ, ℍ, ℍ⊕ℍ, M₂(ℍ), M₄(ℂ), M₈(ℝ), M₈(ℝ)⊕M₈(ℝ)}. Tenfold way (Altland–Zirnbauer): 10 symmetry classes = 2 complex (A, AIII) + 8 real (AI, BDI, D, DIII, AII, CII, C, CI), indexed by Cartan labels and KO-dimension mod 8. Ising anyon braiding: σ_i σ_{i+1} σ_i = σ_{i+1} σ_i σ_{i+1} (braid group B_n), with σ_i² = e^{iπ/4}·(1 + iγ_iγ_{i+1})/√2 acting on Majorana pairs. Majorana operators: {γ_i, γ_j} = 2δ_ij, γ_i† = γ_i. Fusion: γ×γ = 1 + ψ (vacuum + fermion). Braiding phase for Ising anyons: R = e^{iπ/8} (topological phase, not universal alone — needs magic state distillation). | CONNECTION: Bott periodicity 8 = the same 8-fold structu Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com