Optimal Gain Balancing in Continuous-Time Quantum Error Correction — E8 Intelligence Research

FINDING: Continuous-time quantum error correction (CTQEC) via weak measurements and feedback yields a fidelity threshold governed by a stochastic master equation (SME), with optimal gain balancing measurement back-action against correction drive. | MATH: The SME for CTQEC takes the form \( dρ = -i[H,ρ]dt + D[√]ρ\,dt + √ηγ\,H[L]ρ\,dW \), where \(D\) is the Lindblad dissipator, \(H\) is the measurement back-action superoperator, \(η\) is detection efficiency, \(γ\) is measurement strength, and \(dW\) is a Wiener increment. The steady-state fidelity \(F_∞\) obeys \( F_∞ = 1 - {γeff}{γcorr} + O(γeff^2/γcorr^2) \), with \(γcorr\) the correction rate. The threshold condition is \(γcorr > γeff · (1 + 2/η)\), and the optimal feedback gain \(g^*\) satisfies \( g^* = √{γ_{ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com