Quantum Effects in Neural Networks

Hidetoshi Nishimori, Yoshihiko Nonomura

研究成果: Article査読

31 被引用数 (Scopus)

抄録

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, α, and the strength of the transverse field, Δ. 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 Δ. Quantum fluctuations are thus concluded to be quite similar to thermal fluctuations in determination of the macroscopic behavior of the present model.

本文言語English
ページ(範囲)3780-3796
ページ数17
ジャーナルjournal of the physical society of japan
65
12
DOI
出版ステータスPublished - 1996
外部発表はい

ASJC Scopus subject areas

  • 物理学および天文学(全般)

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