The brain is a deterministic system. We understand the dynamics of deterministic systems from the study of physics, so what is free will in terms of a system with an already decided outcome?
Possibly it's a chaotic deterministic system, which means it can't be precisely predicted by any means short of a full simulation.
As I wrote in a comment below I guess the feeling of a free will is just the observation that nobody else and not even oneself kan predict ones decision until it is made even because the decision process is chaotic.
If you really believed that you wouldn't say things like "we understand". Because if you really believe there's no free will then all human understanding is a sham.
Quantum Physics has perfectly random outcomes
In QM, you may teleport into the sun, but it was never registered for de-coherent macro objects, even for few millimeters. A brain is macro, neurons and their signals are pretty macro. Why should a brain or its parts even slightly depend on QM effects? Modern CPUs which have much smaller parts can work for years and not experience QM randomness bugs. Nothing is deterministic or “the same” at quantum level, but at the classical scale it doesn’t matter, because chances to observe any difference or randomness in an usual object lifetime are essentially zero.
QM does have some impact on functional biochemistry, but I highly doubt its enough to make the system nondeterministic at any appreciable level. Not to mention, do we truly know that any part of QM is nondeterministic? Perhaps the nondeterministic appearance of QM is just our lack of understanding combined with our limited perspective.
That is debatable. QM is deterministic at the quantum level, and deterministic at the classic level, randomness only (seems to) appear at the cross between them. There are even interpretation such as MWI that don't involve any randomness at a fundamental level.