Someone on research gate said the answer was no
Our brain is a neural network with a very complex connectome. Any system is in a sense a computer adhering quantum mechanics, but what is known about human brain doesn’t tell us it uses quantum-mechanical effects such as entangled states and superposition states as en essential element of computation.
So the human brain is more like a classical computer Or is the brain not like a Turing machine?
There is evidence that quantum coherence and it's role in chemical reactivity is responsible for the magnetic field sensing in migratory birds, the so called avian compass, https://arxiv.org/abs/1206.5946v1.
Similar quantum effects and chemistry could very well be occuring and playing a role in the brain, though as far as I know there isn't anything published in that direction. And even if there is a role for quantum coherent effects, it is likely a far cry from how we think about quantum computing.
As far as we know - and I know, so correct me anyone if there's research to the contrary - the neuron interactions in the brain are well within the classical regime.
