The standard proof of the halting problem might not apply to quantum computers with arbitrary unknown quantum state (I guess it doesn’t, because arbitrary states may encode non determinist advice). But if we stick to the quantum computers that admit a classical description (e.g. the usual ones, as Charlie Steiner and JBlack already mentioned) then no cloning doesn’t apply.
The standard proof of the halting problem might not apply to quantum computers with arbitrary unknown quantum state (I guess it doesn’t, because arbitrary states may encode non determinist advice). But if we stick to the quantum computers that admit a classical description (e.g. the usual ones, as Charlie Steiner and JBlack already mentioned) then no cloning doesn’t apply.