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Pattern-recalling processes in quantum Hopfield networks far from saturation
| 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. |
| Relation: | http://iopscience.iop.org/1742-6596/297/1/012012 |
| Type: | article |
| URI: | http://hdl.handle.net/2115/47173 |
| 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)
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Submitter: 井上 純一
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