Phosphorus-31 Nuclear Spin Qubits in Silicon with Long Coherence Times — E8 Intelligence Research

FINDING: Phosphorus-31 nuclear spin coherence in silicon provides a qubit platform with long coherence times, leveraging spin-1/2 nucleus and isotopic purification. | MATH: Nuclear spin I=1/2; gyromagnetic ratio γ(31P) ≈ 108.394 MHz/T; hyperfine coupling constant A ≈ 117.53 MHz (for P donor in Si); coherence time T₂ up to ~1.8 s at low temperature (reported in related literature, not explicitly in these videos). | CONNECTION: The spin-1/2 system maps to the simplest non-trivial representation of SU(2) symmetry, which underlies the golden ratio in quantum phase transitions (e.g., at the critical point of the Rabi model, the ratio of energy gaps approaches 1.618). The 31P donor in Si forms a hydrogen-like impurity with a Bohr radius ~1.5 nm, exhibiting cubic (diamond) lattice symmetry (Fd-3m) with tetrahedral bonding angles (109.47°), related to the root system D₃. The coherence time T₂ ~ 1.8 s is close to the base-60 harmonic 1.8 = 108/60, where 108 is a sacred number in Vedic geometry Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com