  The 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
$\alpha$ (the ratio of the number of stored patterns to the system
size)-$\Delta$ (the strength of the transverse field) phase diagram of this
model in the ground state resembles the $\alpha$-$T$ 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.
