due to the matrix elements of Eq. 24 that involve states {|j⟩}. The equation of motion for the coefficients {c a,ξ (t)} governed by the evolution of ĤQ + ĤQC (or e L Ĥ dt in Eq. 27) can be computed based on the simple MFE approach in Eq. 15. The rest of the derivation will be focused on updating the coefficients to match these jump operator dynamics, separate from any Hamiltonian dynamics (as Eq. 27 allows us to do).