Quantum Annealing with Antiferromagnetic Transverse Interactions for the Hopfield Model

TL;DR

This paper explores how antiferromagnetic transverse interactions can improve quantum annealing in the Hopfield model, avoiding first-order phase transitions in some cases, thus enhancing the efficiency of quantum optimization in certain random systems.

Contribution

It demonstrates that antiferromagnetic transverse interactions can help avoid first-order transitions in quantum annealing for specific Hopfield models, extending previous findings to random systems.

Findings

Avoidance of first-order transitions for finite patterns with 5 ≤ k ≤ 21.

Avoidance of first-order transitions for extensive patterns with k=4 and 5.

First-order transitions cannot be avoided for finite patterns with k=3 and extensive patterns with k=2 and 3.

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.