The quantum mind theory is a belief that large-scale quantum coherence is necessary to understand the mind and brain.
This is very much a minority opinion, although it does have the support of the well-known mathematical physicist Roger Penrose. Other proponents include Stuart Hameroff, Subhash Kak, Karl Pribram, and Henry Stapp. The argument for the quantum mind is that classical mechanics cannot explain consciousness.
It also has the support of Brian Flanagan and Michael Lockwood.
The main argument against the quantum mind is that the brain is warm, wet and noisy and that the structures of the brain are much too large for quantum mechanics to be important. Consequently, it is difficult for coherent quantum states to form for very long in the brain, and impossible for them to exist at scales on the order of the size of neurons. These issues have led Penrose to argue that consciousness is not a consequence of interactions between neurons in the brain but arises as from microtubules within cells, which are much smaller and for which quantum effects could be significant. This was originally the theory of Stuart Hameroff.
On the other hand, a system does not cease to be quantum because it is wet and noisy. And then, what was previously dismissed as "noise" in the brain has recently been discovered to be complex signals.
Then again, if the brain is fractal in character, it may well exhibit sensitive dependence on initial (quantum) conditions. Given the fractal character of dendritic arborizations, brain function may depend on self-similar processes at lower spatio-temporal scales. Or, neural form follows quantum function. If all matter consists of quantum fields, as Dyson makes explicit in his Scientific American article on "Field Theory," (reference?) then the brain is a collection of such fields.
This view is very different from conventional views of how the brain works, in which neurons communicate via electric impulses which trigger the release of neurotransmitters in the synapses. In the conventional view of brain function, microtubules play no significant role in brain function other than to provide structural support to the neurons. The theory of the quantum mind has been criticized on a number of grounds. For one, it fails to explain how chemicals and physical processes which affect neuron functioning would cause generally predictable changes in consciousness, whereas the conventional theory provides an explanation for how psychoactive substances work and how the brain would react to injury.
Lockwood, Stapp, and Flanagan have argued that the rich state space of quantum theory easily accommodates the variety of perceptual state spaces, whereas classical theory cannot.
Also, decoherence mechanisms such as emission of thermal radiation appear to apply to large molecules such as microtubule protein subunits and synaptic vesicle proteins, making quantum coherence on the scale proposed for quantum mind theories unlikely.
Quantum theories of mind are among the few classes of theories acceptable in the philosophical stances of pseudonomenalism and mind/brain identity theory.
There is another type of quantum theory of mind called the many-minds interpretation that is invoked as a conservative version of the many-worlds interpretation of quantum theory and does not involve collapse of the QM wave function.