A quantum model of neural network is introduced and its phase structure is
examined. The model is an extension of the classical Z(2) gauged neural network
of learning and recalling to a quantum model by replacing the Z(2) variables,
Si=±1 of neurons and Jij=±1 of synaptic connections, to the U(1)
phase variables, Si=exp(iϕi) and Jij=exp(iθij).
These U(1) variables describe the phase parts of the wave functions (local
order parameters) of neurons and synaptic connections. The model takes the form
similar to the U(1) Higgs lattice gauge theory, the continuum limit of which is
the well known Ginzburg-Landau theory of superconductivity. Its current may
describe the flow of electric voltage along axons and chemical materials
transfered via synaptic connections. The phase structure of the model at finite
temperatures is examined by the mean-field theory, and Coulomb, Higgs and
confinement phases are obtained. By comparing with the result of the Z(2)
model, the quantum effects is shown to weaken the ability of learning and
recalling.Comment: 8 pages, 4 figures: Revised with a new referenc