Fig. presents the profile of the resonant VSC rate constant enhancement k/k 0 as a function of cavity frequency ω c with different light-matter coupling strengths η c (color-coded with the legend in panel (a)). Fig. presents the results obtained from the exact HEOM simulations, and Fig. presents the results obtained from γ-SQC. The most important feature of the γ-SQC is that it successfully reproduces the correct resonance condition (Eq. 1), maximizing the rate constant at the frequency ω c ≈ ω 0 , and exhibiting a sharp peak that is semi-quantitatively similar to the HEOM results in panel (a). More importantly, it is not relevant to the barrier frequency ω b . Thus, the current simulation using γ-SQC provides a significant improvement in terms of predicting the correct resonance VSC behavior compared to the previous RPMD simulations which predict an incorrect resonance condition at ω c ≈ ω b (see Fig. of Ref. 15). On the other hand, the magnitude of the k/k 0 from the γ-SQC simulations seems to be three to four times larger than the corresponding values of HEOM. Despite being less ideal in terms of predicting the precise value of the k/k 0 , it is encouraging to see that by treating |ν L ⟩ and |ν ′ L ⟩ as quantum states in the MQC simulation (and even treat cavity mode as part of the classical DOFs), one can still recover the correct VSC resonance condition.