2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147552The Hopfield model in a transverse field is investigated in order to clarify how quantum fluctuations affect the macroscopic behavior of neural networks. Using the Trotter decomposition and the replica method, we find that the $α$ (the ratio of the number of stored patterns to the system size)-$Δ$ (the strength of the transverse field) phase diagram of this model in the ground state resembles the $α$-$T$ phase diagram of the Hopfield model quantitatively, within the replica-symmetric and static approximations. This fact suggests that quantum fluctuations play quite similar roles to thermal fluctuations in neural networks as long as macroscopic properties are concerned.11 pages, 1 compressed/uuencoded postscript figure, revtexCondensed Mattertext