Thank you for your interest! :) I'd recommend skimming some of the papers cited by this working group I'm in called DISARM:SIMC4; we've tried to collect the most relevant papers here in one place:
In response to your question:
At a high level, the academic consensus is that combining AI with nuclear command & control does not increase deterrence, and yet it increases the risk of accidents, and increases the chances that terrorists can "catalyze" a great-power conflict.
So, there is no upside to be had, and there's significant downside, both in terms of increasing accidents and empowering fundamentalist terrorists (e.g. the Islamic State) which would be happy to utilize a chance to wipe the US, China, and Russia all off the map and create a "clean slate" for a new Caliphate to rule the world's ashes.
There is no reason at all to connect AI to NC3 except that AI is "the shiny new thing". Not all new things are useful in a given application.