Quantum learning for neural associative memories

• Published in: Fuzzy sets and systems Vol. 157; no. 13; pp. 1797 - 1813
• Main Authors: Rigatos, G.G., Tzafestas, S.G.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2006; Elsevier
• Subjects: Applied sciences; Associative memories; Circuit properties; Computer science; control theory; systems; Control theory. Systems; Digital circuits; Eigenstructure analysis; Electric, optical and optoelectronic circuits; Electronic circuits; Electronics; Exact sciences and technology; Hebbian learning; Information, signal and communications theory; Mathematical methods; Miscellaneous; Quantum learning; Strong fuzzy partition; System theory; Telecommunications and information theory; Theoretical computing; Unitary rotations; Associative memories; Hebbian learning; Strong fuzzy partition; Quantum learning; Unitary rotations; Eigenstructure analysis; Human; Fuzzy system; Fuzzy set; Attractor; Learning; Engineering; Vector space; Quantum mechanics; Information processing; Learning algorithm
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2006.02.012

Quantum information processing in neural structures results in an exponential increase of patterns storage capacity and can explain the extensive memorization and inferencing capabilities of humans. An example can be found in neural associative memories if the synaptic weights are taken to be fuzzy variables. In that case, the weights’ update is carried out with the use of a fuzzy learning algorithm which satisfies basic postulates of quantum mechanics. The resulting weight matrix can be decomposed into a superposition of associative memories. Thus, the fundamental memory patterns (attractors) can be mapped into different vector spaces which are related to each other via unitary rotations. Quantum learning increases the storage capacity of associative memories by a factor of 2 N , where N is the number of neurons.