Quantum noise does not give you the ability to choose, because you don't control or choose the quantum noise. So in terms of free will, there's no possibility of help from quantum noise. And once you're above that level, then it's determinism, not just in the sense of "not free will", but also in the sense of "not random".
Ascribing human intelligence to quantum noise seems to me like physics woo - we can't figure out where else it comes from, so we'll say "quantum" and hope that that somehow explains the inexplicable. Or did you have an actual mechanism in mind, rather than just a fond hope?
But as for the rest of it - "in the materialist view, you cannot have any free will or any kind of ability to make a non-determined choice". This is what I disagree with. Non-determinism arises through (for example) shot noise, and as for free will... The effects of randomness on a system and the effects of "free will" on a system are equivalent. There is no way to tell if a particular decision was randomly decided or if it was the result of a decision by a sentience. Entropy of a signal is at its maximum either when something is random noise or if it is perfectly compressed data - and perfectly compressed data is indistinguishable from noise.
[1] http://math.ucr.edu/home/baez/physics/Quantum/see_a_photon.h...
[2] http://www.extremetech.com/extreme/123485-mit-discovers-the-...
[3] https://en.wikipedia.org/wiki/Neural_coding#Temporal_coding
Why? Quantum mechanics has randomness all over the place - and we already know that human brains are chaotic in that small amounts of noise are amplified. It is not unreasonable to posit that QM noise effects us on the macroscopic scale.
Or, to put it another way, materialism does not imply determinism, unlike what you said.
Personally, my pet theory is that human brains are quantum noise feedback loops. Or to put it another way, the bit that makes us sentient is quantum noise, and our brains are "just" IO / amplifiers / etc.