Communism is bad for innovation for two major, connected, reasons. First, there is very little, if any, competition. Most innovation comes from trying to beat the other guy and there just isn't any competition in a system that wants the state to run everything. Second, entrepreneur's are non-existent because there is no way for them to make money off of their inventions outside of cozying up with the State.
Also, your point about them moving from a medieval society to a modern one is ironic considering the USSR's pathetic technology. Outside of military applications they were failing in almost every single way. Just read some stories about the East Germans trying to flee to West Germany or the USSR's Olympic team visiting the US and thinking that our grocery stores were fake because of all of the food.