Quantum Error Correction Thresholds: Noise Bounds, Not Golden-Ratio Constants — E8 Intelligence Research

FINDING: Quantum error correction thresholds are noise-rate bounds, not golden-ratio constants; the Fibonacci Turaev-Viro code links topological order to Fibonacci numbers, but no direct golden-ratio threshold emerges from these abstracts. | MATH: Threshold theorems (e.g., \(\epsilon_{\text{th}} > 0\) for fault tolerance); Pauli noise estimation via process tomography (Kliesch: sample complexity \(\mathcal{O}(n^2/\epsilon^2)\) for \(n\)-qubit noise channels); Fibonacci Turaev-Viro code: anyon fusion rules \(1 \times \tau = \tau\), \(\tau \times \tau = 1 + \tau\), with quantum dimension \(d_\tau = \phi = (1+\sqrt{5})/2 \approx 1.618\); Rydberg erasure thresholds: biased noise reduces effective threshold by factor \(\eta = p_{\text{erasure}}/p_{\text{total}}\). | CONNECTION: Fibonacci anyons have quantum dimension \(\phi = 1.618\) — the golden ratio appears as a *topological charge dimension*, not as a threshold value. The Turaev-Viro invariant is a state-sum over triangulations, linking Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com