  We investigate quantum annealing with antiferromagnetic transverse
interactions for the generalized Hopfield model with $k$-body interactions. The
goal is to study the effectiveness of antiferromagnetic interactions, which
were shown to help us avoid problematic first-order quantum phase transitions
in pure ferromagnetic systems, in random systems. We estimate the efficiency of
quantum annealing by analyzing phase diagrams for two cases where the number of
embedded patterns is finite or extensively large. The phase diagrams of the
model with finite patterns show that there exist annealing paths that avoid
first-order transitions at least for $5 \le k \le 21$. The same is true for the
extensive case with $k=4$ and $5$. In contrast, it is impossible to avoid
first-order transitions for the case of finite patterns with $k=3$ and the case
of extensive number of patterns with $k=2$ and $3$. The spin-glass phase
hampers the quantum annealing process in the case of $k=2$ and extensive
patterns. These results indicate that quantum annealing with antiferromagnetic
transverse interactions is efficient also for certain random spin systems.
