There is a lot of excitement around AI recently, but AI is also the field that has historically over promised and under delivered. Quantum computing on the other hand is making concrete progress, consistently, for years. Which one do you think will become practical first? Quantum computers in every home or strong AI bots everywhere? My vote is for quantum computing.
"Strong AI" is a not a very well-defined problem. People will disagree on whether something is a strong AI -- to the point that any solved problem will no longer be considered strong AI, as soon as it has been solved. Quantum computing is much more well-defined, and thus we'll likely have a quantum computer before a strong AI. That being said, I would also expect some very major advances in the wider field of AI before we get to large scale quantum computers.
I think quantum computing will optimize certain AI tasks, so in a nutshell theory you will need quantum computing to establish strong(est) AI ... and forget about the bots, I don't even consider them a task in this, more on the automated planning side.