Phosphorus-31 Spin Qubits in Silicon: A Leading Quantum Computing Platform — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Phosphorus-31 (³¹P) is a spin-½ nucleus (I = 1/2) with 15 protons and 16 neutrons, stable, and its coherence in silicon is a leading platform for quantum computing via electron-nuclear spin coupling. | MATH: Nuclear spin I = 1/2 → two-level system (Hilbert space dimension 2); ³¹P has gyromagnetic ratio γ ≈ 17.235 MHz/T (for ¹H reference, γ(³¹P)/γ(¹H) ≈ 0.4048); nuclear Zeeman Hamiltonian H = −γℏB·I; hyperfine coupling A (contact term) between electron and nucleus in Si:P ~ 117 MHz (bulk) — this sets the clock for coherent oscillations. | CONNECTION: The ratio γ(³¹P)/γ(¹H) ≈ 0.4048 is close to 0.404 — not a golden ratio, but note 0.4048 ≈ 0.382 + 0.0228 (off by ~6%). More striking: the hyperfine coupling A ≈ 117 MHz and the electron Zeeman frequency at B = 0.3 T (~8.4 GHz) give a ratio ~71.8 — no direct golden link. However, the spin-½ system maps to the Bloch sphere (SU(2) symmetry), whose equatorial plane exhibits the golden-angle-like rotations for optimal pulse sequences (e Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214096184