errr, Waltky, Nuclear Submarine usually means that the Sub is running on a Nuclear reactor, not that it's carrying nuke, and the former the Chinese already have for a long time, although they aren't very good once (reputed to be quite noisy , though usually their point isn't to get close to fleets anyway so it's not a huge problem) .
The Chinese have been developing Underwater ICBM for a long time, they actually have older types that theoretically might work, just that its too unreliable.