I heard once that the main problem is how to do radiation simulation to test the best shape of the components so that the emitted X-rays from the fission reaction initiate the fusion reaction. Supposedly this involves the use of lenses to focus the X-rays.
I have heard the numerical simulation can be done with Monte Carlo methods but I do not know how accurate that is.
The US also has laboratories which operate fusion reactors like the National Ignition Facility and the Z Pulsed Power Facility which supposedly can replicate these conditions in tests to calibrate models. France has the Laser Megajoule. I do not know which facilities Russia or China do have for this.