where Λ is the eigenvalues matrix (the diagonal form of ĤQ ), and Û is the eigenvector matrix, satisfying ĤQ Û = Λ Û . The evolution of any vector can now be obtained by operating Eq. B1 on the vector. To test the accuracy of the different propagators, we generated N = 10 6 samples of random state vectors by randomly selecting the coefficients in Eq. 26 (in the complex plane) while keeping it properly normalized. For each configuration, the bath fluctuation term ν C n,ν R n,ν in ĤQ (see Eq. 27) is also randomly sampled, based on the Wigner distribution (Eq. 72). For each value of the uncertainty parameter z, we compute the error of the propagator by comparing it against the exact evolution by