  We present a framework for simulating the open dynamics of spin-boson systems
by combing variational non-Gaussian states with a quantum trajectories
approach. We apply this method to a generic spin-boson Hamiltonian that has
both Tavis-Cummings and Holstein type couplings, and which has broad
applications to a variety of quantum simulation platforms, polaritonic physics,
and quantum chemistry. Additionally, we discuss how the recently developed
truncated Wigner approximation for open quantum systems can be applied to the
same Hamiltonian. We benchmark the performance of both methods and identify the
regimes where each method is best suited to. Finally we discuss strategies to
improve each technique.
