  We develop the statistical mechanics of the Hopfield model in a transverse
field to investigate how quantum fluctuations affect the macroscopic behavior
of neural networks. When the number of embedded patterns is finite, the Trotter
decomposition reduces the problem to that of a random Ising model. It turns out
that the effects of quantum fluctuations on macroscopic variables play the same
roles as those of thermal fluctuations. For an extensive number of embedded
patterns, we apply the replica method to the Trotter-decomposed system. The
result is summarized as a ground-state phase diagram drawn in terms of the
number of patterns per site, $\alpha$, and the strength of the transverse
field, $\Delta$. The phase diagram coincides very accurately with that of the
conventional classical Hopfield model if we replace the temperature T in the
latter model by $\Delta$. Quantum fluctuations are thus concluded to be quite
similar to thermal fluctuations in determination of the macroscopic behavior of
the present model.
