Quantum Mechanics is sometimes taken to have something interesting to say on the subject of free will. For meaningful definitions of free will, it does not. Issues of free will, as with so many questions in philosophy, simply dissolve once you bother to properly define your terms. It isn't even necessary to say one definition is right, though investigating various cases may reveal some definitions to be more useful than others.

Some take 'free will' to mean non-determinism. In that case, yes, quantum mechanics is relevant. One may think that since quantum mechanics is normally used for things that are very small, it should not be - this application of the correspondence principle is a red herring. Certainly quantum instabilities are capable of cascading up to conscious levels - they do not cancel out, they merely become impractical to measure. But if one does resort to quantum mechanics as a source of indeterminism, the answer is more confusing than informative. Quantum mechanics does not in itself say the universe is nondeterministic. That's one interpretation. Another is that the universe is deterministic, and the randomness is purely subjective. You can think of the universe as a contingency table, and our subjective viewpoints traverse it... but all of the branches are equally real.

Regardless, I do not believe that simple non-determinism is sufficient for a reasonable definition of free will. If I were to randomly violate my principles, that would not seem to me to be a very meaningful expression of free will. And that is just what quantum randomness would tend to do.

If, on the other hand, we take free will to be a property of systems that model themselves and their environments and have motivations that are not modified except through application of said motivations... then we can speak of deviations from free will via environmental factors like inexperience, misinformation, addiction, brain probes, or duress - the usual factors when normal people refer to failures of free will. Referring to questions of determinism simply doesn't come up... except for the issue that the rules must be sufficiently close to deterministic that the system's properties can be maintained. No version of quantum mechanics introduces enough randomness to contradict that.

The only remaining relevance of quantum mechanics is a dualistic model in which the selection of which branch to traverse in that cosmic contingency table is due to a matter of will. Setting aside how prima facie daft this sounds (the contingency table is an approximation, not a first-order ontological entity, setting even further aside the issue of first-order ontological wills), it doesn't really begin to answer the question - it just shunts it off another layer. What makes this new will-y-force-thing decide what it decides? Is it determined by something? If so, how is that not deterministic? If not, then why should we call that deviation from determination 'free will' instead of 'interference'? These are exactly the same questions we had on the first layer, only we've denied ourselves access to anything that could possibly shine any light on the situation.