Magic-Angle Photonic Quantum Computing: Geometric Decoherence Protection, the Trisection Qutrit, and Falsifiable Predictions from a (3+3) Spacetime Framework

We apply the (3+3) spacetime framework [1, 6] — a six-dimensional Einstein–Aether construction with three spatial and three temporal dimensions, the third time dimension compactified as a discrete two-sphere S² with N_cells = 2¹⁵² Planck-area cells — to photonic quantum computing. The framework identifies the photon as a null arc (a c-vector configuration with v_T = v_t₂ = v_t₃ = 0 and v_spatial = c) corresponding to the n = 0 Kaluza–Klein zero-mode on S². From this single identification three Level-1 structural results follow: (i) the photon's polarization Poincaré sphere is geometrically the third time dimension's S²; single-qubit gates are physical S² rotations and the Born rule is Malus's law as S² projection; (ii) photons inherit no t₃-winding decoherence channels, with cosmological coherence floor τ_cosm = 1/H₀ ≈ 14.5 Gyr [§14bis.46.4 of 6] and practical decoherence by photon loss as t₃ entrainment; (iii) the cross-Kerr nonlinearity scales as χ⁽³⁾ ∼ α² = 5.3 × 10⁻⁵ from two successive c-vector rotations each of amplitude √α.

We give a self-contained derivation in §5.4 of the χ⁽³⁾ ∼ α² scaling from the Lagrangian-level photon-photon-via-radion vertex L = −(g₀/4) Φ² F_{μν} F^{μν}|_node with bare coupling g₀ = (4/9) ε_ZPE², through radion integration-out at optical frequencies, to the four-loop running g₀ → α (drawing on §16–§17 of [6]). Sections 5.5–5.9 establish the structural form of the nodal-cone TPA-suppression factor η_node: the breathing-mode contribution at the cone vanishes geometrically because the Y_{2,0}(ϑ_node) = 0 identity that defines the cone latitude also eliminates the breathing's metric perturbation there (§5.7); the higher-multipole tail is bounded at η_node|_higher ≲ 10⁻⁵ using the framework's identified spectrum from [6] (§5.8); and the same Z₃ symmetry that organises SU(3), three-generation fermion structure, and tribimaximal PMNS mixing also protects the qutrit basis at the trisection vertices (§5.9). Combining these structural results with anchored medium-specific estimates for silicon-on-insulator (K_medium ≈ 0.10–0.20), silicon nitride (0.03–0.08, lowest), and thin-film lithium niobate (0.05–0.15) (Appendix B), the framework predicts η_node ≈ K_medium ≈ 0.03–0.20 across candidate platforms — silicon nitride is identified as the optimal platform — dominated entirely by medium contributions rather than framework-vacuum dynamics, and decisively testable by the §6.7 thermal MZI experiment (2027–2030). The magic-angle latitude ϑ_node = arccos(1/√3) = 54.74° is the same magic angle as in NMR magic-angle spinning, and the underlying physics (averaging-out of Y_{2,0} dipolar interactions) is structurally identical.

Six engineering proposals leverage these results: null-arc qubit encoding; the nodal-cone LOQC architecture (qubits at the magic-angle latitude where Y_{2,0} vanishes and the leading TPA channel is suppressed); (3+3) measurement protocols with t₃-entrainment-strength control; trisection qutrit photonic computing (log₂ 3 ≈ 1.585 bits per photon, with Z₃-symmetric coherence protection giving η_qutrit ≈ 0.06–0.21 comparable to qubit η_node — a 58.5% information-density gain at essentially no extra coherence cost); boson sampling reframed as null-arc network interference; and a nodal-cone photonic-crystal integrated chip. Three testable predictions are organised into a year-resolved 2026–2030+ falsifiability timeline (§6.7). All claims are explicitly tagged Level 1 (geometric, derived), Level 2 (anchored prefactor), or Level 3 (engineering speculation); the room-temperature fault-tolerance projection of §9 is an explicit Level-3 conditional argument with dependency chain made explicit. A self-contained framework digest is given in §1.7; readers unfamiliar with the (3+3) programme can read §1.7 alone to decide whether to continue.