Attosecond Entanglement Dynamics and Universal Statistics in Hybrid Quantum Circuits — E8 Intelligence Research

FINDING: Entanglement formation time measured in attoseconds; hybrid quantum circuits show universal statistical laws via random-matrix theory. | MATH: Attosecond scale = 10⁻¹⁸ s; entanglement entropy growth follows S(t) ~ t (linear) for volume-law phases, S(t) ~ log(t) for area-law phases; random-matrix ensembles (GUE/GOE/GSE) with spectral statistics governed by Wigner-Dyson distributions; hybrid circuits parameterized by measurement rate p with phase transition at critical p_c. | CONNECTION: Random-matrix universality classes map to Dyson's threefold way — orthogonal (β=1), unitary (β=2), symplectic (β=4) — which correspond to root systems of Lie algebras (A_n, B_n/C_n, D_n) and crystallographic reflection groups. The critical measurement rate p_c in hybrid circuits often emerges near values consistent with percolation thresholds on lattices (e.g., p_c ≈ 0.5 for 1D, related to golden ratio conjugates in some mappings). | DEPTH: 7 — solid mathematical structure (RMT, phase transition

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com