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Quantum Hopfield Model

Yoshihiko Nonomura·Hidetoshi Nishimori
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Abstract

The Hopfield model in a transverse field is investigated in order to clarify how quantum fluctuations affect the macroscopic behavior of neural networks. Using the Trotter decomposition and the replica method, we find that the $α$ (the ratio of the number of stored patterns to the system size)-$Δ$ (the strength of the transverse field) phase diagram of this model in the ground state resembles the $α$-$T$ phase diagram of the Hopfield model quantitatively, within the replica-symmetric and static approximations. This fact suggests that quantum fluctuations play quite similar roles to thermal fluctuations in neural networks as long as macroscopic properties are concerned.

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Yoshihiko Nonomura, Hidetoshi Nishimori. 1996-03-07. Quantum Hopfield Model. https://arxiv.org/abs/cond-mat/9512142

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