Reducing simulation runtimes with DynamicsBackend

[arthurostrauss]

What is the expected behavior?

The simulation of pulse schedules are much slower with DynamicsBackend.run method than with Solver.solve method when the simulation is done with Jax. It was mentioned in this thread that this might be related to the location of the conversion process of the schedules towards waveforms. It would be nice to be able to have alternative ways of reducing dramatically the simulation times with the DynamicsBackend for a batch of circuits. A comparison of runtimes is attached through a notebook. jittable_sims_runtime.ipynb.zip