String AI is not a hardware problem. It's not a matter of lack of computational power. It is a software and modeling problem. If you had an AI algorithm and a model, you could still run it on any Turning machine. It would just take a lot longer (perhaps years or decades or more) to compute a single thought on current hardware instead of real time or faster than real time on some super fast future hardware.

There are people (like Roger Penrose) who argued that intelligence and consciousness are not computational in nature (and hence no algorithm can be conscious). Penrose goes all the way down to quantum mechanical effects in the brain. I have not really followed developments on this and where Penrose's argument currently stands.