Supplemental Materiel

This Supplemental Material gives the detailed HEOM equations with the different artificial modes (TM-HEOM, FP-HEOM and D-HEOM). It gathers the parameters of the two-pole Lorentzian Tannor-Meier functions fitting the spectral densities used in the simulations. Parameters of the exponential functions fitting the contribution of the Matsubara terms to the bath correlation functions C(t) are also reported. Finally, we illustrate the convergence of the number of discrete modes used in D-HEOM and T-TEDOPA in the pure dephasing qubit.