To perform the γ-SQC dynamics, we need to sample the initial condition for the quantum subsystem. In this work, we sample the action-angle variables {ε b , θ b } and subsequently transform them to the mapping variables{p b , q b } using Eq. 27. The action variables {ε b } are sampled according to the window function in Eq. 29, and the angle variables {θ b } are randomly sampled from [0, 2π). The triangle window is used in this work, although the square window generates similar results.