  We consider a system of two-level quantum quasi-spins and gauge bosons put on
a 3+1D lattice. As a model of neural network of the brain functions, these
spins describe neurons quantum-mechanically, and the gauge bosons describes
weights of synaptic connections. It is a generalization of the Hopfield model
to a quantum network with dynamical synaptic weights. At the microscopic level,
this system becomes a model of quantum brain dynamics proposed by Umezawa et
al., where spins and gauge field describe water molecules and photons,
respectively. We calculate the phase diagram of this system under quantum and
thermal fluctuations, and find that there are three phases; confinement,
Coulomb, and Higgs phases. Each phase is classified according to the ability to
learn patterns and recall them. By comparing the phase diagram with that of
classical networks, we discuss the effect of quantum fluctuations and thermal
fluctuations (noises in signal propagations) on the brain functions.
