Quantum Annealing with Antiferromagnetic Transverse Interactions for the Hopfield Model

Abstract

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.