According to the paper by Koch and Hepp The relation between quantum mechanics and higher brain functions: Lessons from quantum computation and neurobiology from 2007, quantum mechanics and its indeterminism is not relevant to explain consciousness.
The interaction of neurons – "a 300 Kelvin wet and warm tissue strongly coupled to its environment" - is governed by classical physics.
On the other hand, a minority of neurobiologists and physicists maintains "that quantum mechanics is important for understanding higher brain functions, e.g. for the generation of voluntary movements (free will), for high-level perception and for consciousness.”
What is the state-of-the-art concerning the question from the heading?
In particular, it would be helpful to learn the assessment from users who are familiar with both fields, quantum mechanics and neuroscience.
Note: My question is triggered by several comments from @Double Knot.