Spin(6)≅SU(4) backbone of 6-Majorana braiding yields non-universal Clifford group — E8 Intelligence Research

FINDING: Spin(6)≅SU(4) is the algebraic backbone of 6-Majorana-zero-mode braiding; the 6 MZMs form the 6 of SU(4) (antisymmetric 2-tensor of SO(6)), and braiding generates a finite subgroup of SU(4) that is not universal for SU(4) — it is a Clifford group. MATH: - Local algebra: 2n Majorana operators γ_i satisfy {γ_i,γ_j}=2δ_ij. For n=3 (6 MZMs), the 6 generators span so(6) under commutators. - Isomorphism: so(6) ≅ su(4), via Spin(6) ≅ SU(4). The 6 MZMs transform in the 6 of SO(6), equivalently the 6̄ (antisymmetric 2-index) of SU(4): 4⊗4 = 6 ⊕ 10. - Braiding generators: exchange of MZMs i,j acts as B_ij = exp(π γ_i γ_j /4). These are elements of the Clifford group on 3 qubits (n=3 MZMs pairs → 3 qubits), generated by {H, S, CNOT}-equivalent gates. - Clifford constraint: B_ij are Gaussian (matchgate) operations; by the Gottesman–Knill / Bravyi–Kitaev theorem, braiding alone yields only the Clifford group on n qubits, which is classically simulable and NOT universal. Universality requi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com