  Multitime quantum correlation functions are central objects in physical
science, offering a direct link between experimental observables and the
dynamics of an underlying model. While experiments such as 2D spectroscopy and
quantum control can now measure such quantities, the accurate simulation of
such responses remains computationally expensive and sometimes impossible,
depending on the system's complexity. A natural tool to employ is the
generalized quantum master equation (GQME), which can offer computational
savings by extending reference dynamics at a comparatively trivial cost.
However, dynamical methods that can tackle chemical systems with atomistic
resolution, such as those in the semiclassical hierarchy, often suffer from
poor accuracy, limiting the credence one might lend to their results. By
combining work on the accuracy-boosting formulation of semiclassical memory
kernels with recent work on the multitime GQME, here we show for the first time
that one can exploit a multitime semiclassical GQME to dramatically improve
both the accuracy of coarse mean-field Ehrenfest dynamics and obtain orders of
magnitude efficiency gains.
