Phase diagram of quantum generalized PottsHopfield neural networks
Abstract
We introduce and analyze an open quantum generalization of the qstate PottsHopfield neural network, which is an associative memory model based on multilevel classical spins. The dynamics of this manybody system is formulated in terms of a Markovian master equation of Lindblad type, which allows to incorporate both probabilistic classical and coherent quantum processes on an equal footing. By employing a mean field description we investigate 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. We construct the corresponding phase diagram, which in the low temperature regime displays pattern retrieval in analogy to the classical PottsHopfield neural network. When increasing quantum fluctuations, however, a limit cycle phase emerges, which has no classical counterpart. This shows that quantum effects can qualitatively alter the structure of the stationary state manifold with respect to the classical model, and potentially allow one to encode and retrieve novel types of patterns.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.10140
 Bibcode:
 2021arXiv210910140F
 Keywords:

 Quantum Physics;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 15 pages, 8 figures