China doesn't have any space based missiles. They have some mobile land based intermediate range ballistic missiles which could potentially be used against aircraft carriers. All ballistic missiles are hypersonic when they re-enter the atmosphere. Those missiles don't negate the usefulness of aircraft carriers because the missiles can only hit a target if they get reasonably precise and timely targeting data.
Also carrier escorts carry ABMs which might be able to intercept a limited number of ballistic missiles.
Also carrier escorts carry ABMs which might be able to intercept a limited number of ballistic missiles.