Electromagnetic Screening Using Coprime-Twisted Graphene Layers: Z₁₂ Group Theory, Strong Force Coupling, and Quantum Processor Performance

Abstract We present a theoretical and computational analysis of twisted bilayer graphene (TBG) as an electromagnetic interference (EMI) filter for superconducting quantum processors, grounded in the P₁₂ resonance lattice framework. The central result is that twist angles satisfying the Z₁₂ coprimality condition θₖ = (k/12) × θₘagic with k ∈ 1, 5, 7, 11 activate coprime mode subsets that suppress coupling to non-coprime electromagnetic interference classes. The optimal angle θ₅ ≈ 0. 458° (Phase 5) achieves a 2. 97× suppression of two-level system (TLS) defect density relative to non-coprime angles. Beyond electromagnetic filtering, we demonstrate that the mechanism connects to the strong nuclear force coupling constant: αₛ = 4π/108 follows from the helium perturbation sector (108 modes) that TBG θ₅ locally screens, while α = 4π/1728 follows from the full hydrogen mode sector. The ratio αₛ/α = 1728/108 = 16 = Z⁴ (He) is exact and parameter-free. Local suppression of the k̃=4 mode class — helium's Z₁₂ position — reduces the effective strong coupling in the qubit environment, providing a deeper mechanism for T₂ improvement than electromagnetic screening alone. The combined protocol predicts T₂ improvements of +64% (conservative) to +169% (optimistic) for qubits on TBG θ₅ substrates, substantially exceeding the +8% from electromagnetic shielding alone. The excess constitutes a direct experimental test of the P₁₂ framework's derivation of αₛ. A patent application covering the coprime twist angle method has been filed with PRV (Sweden) prior to this publication.