  We study the quantum simulation of mixed quantum-semiclassical (MQS) systems,
of fundamental interest in many areas of physics, such as molecular scattering
and gravitational backreaction. A basic question for these systems is whether
quantum algorithms of MQS systems would be valuable at all, when one could
instead study the full quantum-quantum system. We study MQS simulations in the
context where a semiclassical system is encoded in a Koopman-von Neumann (KvN)
Hamiltonian and a standard quantum Hamiltonian describes the quantum system. In
this case, because KvN and quantum Hamiltonians are constructed with the same
operators on a Hilbert space, standard theorems guaranteeing simulation
efficiency apply. We show that, in this context, $\textit{many-body}$ MQS
particle simulations give only nominal improvements in qubit resources over
quantum-quantum simulations due to logarithmic scaling in the ratio, $S_q/S_c$,
of actions between quantum and semiclassical systems. However, $\textit{field}$
simulations can give improvements proportional to the ratio of quantum to
semiclassical actions, $S_q/S_c$. Of particular note, due to the ratio $S_q/S_c
\sim 10^{-18}$ of particle and gravitational fields, this approach could be
important for semiclassical gravity. We demonstrate our approach in a model of
gravitational interaction, where a harmonic oscillator mediates the interaction
between two spins. In particular, we demonstrate a lack of distillable
entanglement generation between spins due to classical mediators, a distinct
difference in dynamics relative to the fully quantum case.
