Phosphorus-31 Nuclear Spin in Silicon: A Key Qubit Platform for Quantum Error Correction — E8 Intelligence Research

FINDING: Phosphorus-31 (³¹P) in silicon is a leading qubit platform; its nuclear spin-½ coherence is central to quantum error correction and magnetic-field-controlled spin manipulation. MATH: - ³¹P: Z=15, N=16, A=31 → odd-odd nucleus → nuclear spin I = 1/2 (from unpaired proton in 3p³ subshell, [Ne]3s²3p³). - Gyromagnetic ratio γ(³¹P) ≈ 17.235 MHz/T (from NMR data). - Zeeman splitting: ΔE = ħγB₀ → for B₀ = 1 T, ν ≈ 17.235 MHz. - Hyperfine coupling (P donor in Si): A ≈ 117 MHz (bulk) — key for electron-nuclear entanglement. - Coherence time T₂ (nuclear spin) can exceed 1 s at mK temperatures; electron spin T₂ ~ 0.5–1 ms. - Magnetic-field control: Rabi frequency Ω = γB₁ (for nuclear spin) — linear in RF field amplitude. CONNECTION: - Spin-½ is the simplest nontrivial representation of SU(2) — its Bloch sphere is a 2-sphere with intrinsic curvature. - The ratio of hyperfine to Zeeman energy at typical fields (e.g., 0.1–1 T) spans 0.1–1 — near the golden ratio conjugate Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com