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.

本补充材料详细阐述了不同人工模式下的HEOM方程（包括TM-HEOM、FP-HEOM和D-HEOM）。其中收集了用于模拟中的光谱密度拟合的双极洛伦兹Tannor-Meier函数的参数。同时，还报告了拟合Matsubara项对浴相关函数C(t)贡献的指数函数的参数。最后，我们展示了在纯去相干量子比特中，D-HEOM和T-TEDOPA所使用的离散模式的数量收敛性。