where P (Φ) is the probability distribution of the random phase Φ, δ(Φ) is the Dirac delta distribution, and RN is a random number in the range of RN ∈ [0, 1]. The "+R" relaxation stage of the Ehrenfest+R approach is summarized in Eq. A27a, Eq. A27b, and Eq. A28. This provides an effective Poisson process for incorporating decoherence. Generalizing this approach to multiple state has been proposed and tested as well , where the coefficients {c j,ξ } for |j⟩ / ∈ {|0⟩, |1⟩} are not changed by the Lindbladian time evolution, such that c j,ξ (t + dt) = c j,ξ (t).