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Authors: V. Ahufinger, M. Pons, C. Wunderlich, A. Sanpera and M. Lewenstein Neural networks (NN) are a prototype model of parallel distributed information processing [1,2], and have been intensively studied by physicists since the famous paper by Hopfield [3]. These disordered systems with long range interactions typically have a large number of metastable (free) energy minima, like in spin glasses [2]. These states can be used to store information distributed over the whole system. The patterns stored by the network have large basins of attraction in the thermodynamical sense which means that even fuzzy patterns are recognized as perfect ones. For this reason, attractive NN's can be used as associative memory. At the same time, NN are robust, so that destroying even a large part of the network does not necessarily diminish the network performance. The above listed properties make NN's interesting for studying distributed quantum information processing. Recently it has been shown that the Hamiltonian describing a linear chain of harmonically trapped ions exposed to a magnetic field gradient [4] or interacting with convenient laser fields [5] can be transformed into an effective spin-spin Hamiltonian with long range interactions mediated by the collective motion of the ions. Taking advantage of the similarities of the latter Hamiltonian with the Hopfield model, we demonstrate the possibility of realizing a neural network in a chain of trapped ions with induced long range interactions. We show that the storage capacity of such network, which depends on the phonon spectrum of the system, can be controlled by changing the external trapping potential and/or by applying longitudinal local magnetic fields [6]. [1] D.J. Amit, Modeling Brain Function, (Cambridge University Press, 1989). [2] M. Mézard, G. Parisi, and M.A. Virasoro, Spin Glass and Beyond (World Scientific, Singapour, 1987). [3] J.J. Hopfield, Proc. Natl. Acad. Sci. USA Vol. 81, pp. 3088-3092 (1984). [4]F. Mintert and C. Wunderlich, Phys. Rev. Lett. 87, 257904 (2001); C. Wunderlich, in Laser Physics at the Limit (Springer Verlag, Heidelberg, 2002), pp. 261--271; also available as quant-ph/0111158. [5] D. Porras and J.I. Cirac, Phys. Rev. Lett. 92, 207901 (2004). [6] M. Pons,V. Ahufinger, C. Wunderlich, A. Sanpera and M. Lewenstein, cond-mat/0512606, submitted to Phys. Rev. Lett. |
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