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Pattern-recalling processes in quantum Hopfield networks far from saturation

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Title: Pattern-recalling processes in quantum Hopfield networks far from saturation
Authors: Inoue, Jun-ichi Browse this author →KAKEN DB
Issue Date: 2011
Publisher: IOP Publishing
Journal Title: Journal of Physics: Conference Series
Volume: 297
Issue: 1
Start Page: 012012
Publisher DOI: 10.1088/1742-6596/297/1/012012
Abstract: As a mathematical model of associative memories, the Hopfield model was now well-established and a lot of studies to reveal the pattern-recalling process have been done from various different approaches. As well-known, a single neuron is itself an uncertain, noisy unit with a finite unnegligible error in the input-output relation. To model the situation artificially, a kind of ‘heat bath’ that surrounds neurons is introduced. The heat bath, which is a source of noise, is specified by the ‘temperature’. Several studies concerning the pattern-recalling processes of the Hopfield model governed by the Glauber-dynamics at finite temperature were already reported. However, we might extend the ‘thermal noise’ to the quantum-mechanical variant. In this paper, in terms of the stochastic process of quantum-mechanical Markov chain Monte Carlo method (the quantum MCMC), we analytically derive macroscopically deterministic equations of order parameters such as ‘overlap’ in a quantum-mechanical variant of the Hopfield neural networks (let us call quantum Hop eld model or quantum Hop eld networks). For the case in which non-extensive number p of patterns are embedded via asymmetric Hebbian connections, namely, p/N → 0 for the number of neuron N → ∞ (‘far from saturation’), we evaluate the recalling processes for one of the built-in patterns under the influence of quantummechanical noise.
Rights: Published under licence in Journal of Physics: Conference Series by IOP Publishing Ltd.
Type: article
Appears in Collections:情報科学院・情報科学研究院 (Graduate School of Information Science and Technology / Faculty of Information Science and Technology) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 井上 純一

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