Neural networks (NNs) are artificial networks based on biological neurons’ models and have been used to solve computational tasks such as artificial intelligence, speech and pattern recognition. Potts-Hopfield NNs show off the feature of associative memory, which is the ability to retrieve from a set of stored network states the one which is closest to the input pattern, allowing to compute incomplete input information. In the last decades, in the light of the success of quantum computation, various efforts aim at harnessing the potential computational power of quantum generalizations of classical NNs.
In this seminar, I will introduce an open quantum generalization of the q-state Potts-Hopfield neural network. The dynamics of this many-body system is formulated in terms of a quantum master equation of Lindblad type, which allows to take into account both probabilistic classical and coherent quantum processes. By means of mean field techniques one can analyze how classical fluctuations, due to temperature, and quantum fluctuations, effectuated by coherent spin rotations, affect the ability of the network to retrieve stored memory patterns.
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