2002/07/31 by Yukari Fujita, Tetsuo Matsui
Physics and Astronomy · #cond-mat.dis-nn #hep-lat #quant-ph
published as Proceedings of 9th International Conference on Neural Information Processing, ed. by L.Wang et al. (2002)1360-1367. · 8 pages, 4 figures: Revised with a new reference
arxiv created 2002/10/16 · arxiv updated 2009/11/30
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.