  We apply a numerical method based on multi-configurational Ehrenfest tra
jectories, and demonstrate converged results for the Choi fidelity of an
entangling quantum gate between two two-level systems interacting through a set
of bosonic modes. We consider both spin-boson and rotating wave Hamiltonians,
for various numbers of mediating modes (from 1 to 100), and extend our
treatment to include finite temperatures. Our results apply to two-level
impurities interacting with the same band of a photonic crystal, or to two
distant ions interacting with the same set of motional degrees of freedom.
