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The supposition is that if you can hold coherence you can basically try every solution to a problem at once.
The point is that if you can hold entanglement long enough, then you can do simultaneous operations in (2N)! - 1 dimensions with N qubits (if I remember by <bra|ket> algebra right - it's been a while).
And since the factorial scales faster than exponentially, you have just reduced whole classes of problems from taking an exponential number of bits to only taking a polynomial number of bits.
Which is awesome, but only tangentially related to sentience.
As for neurons and consciousness, Penrose famously thinks consciousness is a quantum process. I'm not sure we have a good enough model of how neurons actually work to say if he's right. (Probably not, but it's too early to tell.)
It is not categorically impossible, but the scale argues against it. Biologists do not routinely use quantum mechanics to describe inter-cellular interactions (or even, AFAIK, most intra-cellular interactions).
Which, of course, is not to say that quantum computing won't be useful for building AIs - natural human locomotion does not use steel or aluminium, but that does not prevent them from being useful in building trains.
Friends come and go. Enemies accumulate.
E.g. when using Turing machines for video processing, you have to calculate each bit in the frame sequentially. That doesn't make it impossible to do associative recognition and processing, but it's inherently different - theoretically and practically - to working with entire frames, and using an associative memory that can retrieve relevant pattern information in a single operation.
You can fake associative processing sequentially, but certain kinds of processing remain impractical. With associative processing, they may not be.
So it becomes a game changer. Potentially you can't just do things more quickly, you can do entirely new things.
Biologists do not routinely use quantum mechanics to describe inter-cellular interactions
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