Fugitive Sisyphus
Escape Artist
The reason a new AI would require a quantum computer is because there is only so much you can program on a classical computer. While quantum computers are most famous for being faster, that is not the only benefit. There are some methods of programming that simply cannot be done on current computers. It is suggested that consciousness is linked to quantum mechanics, which if true, means that you need quantum processes for intelligence.
Other than that, there is no reason why a better AI would need a new engine. The AI code is in CvGameCore.dll (the SDK). The engine is just graphics.
That is not true. Everything that can be done on a quantum computer is already possible on a your basic personal computer.