Note that the CTMQC algorithm, expressed by the equations ( ) and ( ), can be seen as an Ehrenfest scheme corrected by the coupled-trajectory terms where the quantum momentum appears. Specifically, in both equations, the first two terms are identical to the Ehrenfest scheme. The additional contributions allow one to describe decoherence effects, as it has been extensively discussed in the literature . Furthermore, the extra term in the electronic evolution equation ( ) provides a new mechanism for population transfer mediated by the quantum momentum, that has been shown to be key in accurately capturing multi-state processes such as dynamics through a three-state conical intersection .