We discuss the efficiency of quantum annealing with antiferromagnetic fluctuations for mean-field models (the infinite-range ferromagnetic model and the Hopfield model) by analyzing those phase diagrams. The phase diagrams are obtained by using the Suzuki-Trotter formula, the static anzats, and the saddle-point method. The results for the ferromagnetic model show that the antiferromagnetic fluctuations let the system evolve only through second-order transitions when the order of interactions is a finite value greater than 3. The results for the Hopfield model with finite patterns are the same as those for the ferromagnetic model. In contrast, the antiferromagnetic fluctuations cannot avoid first-order transitions of the Hopfield model with many patterns, which is a spin-glass model. We thus conclude that the antiferromagnetic fluctuations are not effective for NP-hard problems.
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