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=== Quantum associative memory ===
The quantum associative memory algorithm was introduced by Dan Ventura and Tony Martinez in 1999.<ref>{{cite journal |first1=D. |last1=Ventura |first2=T. |last2=Martinez |url=https://pdfs.semanticscholar.org/d46f/e04b57b75a7f9c57f25d03d1c56b480ab755.pdf |archive-url=https://web.archive.org/web/20170911115617/https://pdfs.semanticscholar.org/d46f/e04b57b75a7f9c57f25d03d1c56b480ab755.pdf |url-status=dead |archive-date=2017-09-11 |title=A quantum associative memory based on Grover's algorithm |journal=Proceedings of the International Conference on Artificial Neural Networks and Genetics Algorithms |pages=22–27 |year=1999 |doi=10.1007/978-3-7091-6384-9_5 |isbn=978-3-211-83364-3 |s2cid=3258510 }}</ref> The authors do not attempt to translate the structure of artificial neural network models into quantum theory, but propose an algorithm for a [[quantum circuit|circuit-based quantum computer]] that simulates [[associative memory (psychology)|associative memory]]. The memory states (in [[Hopfield neural network]]s saved in the weights of the neural connections) are written into a superposition, and a [[Grover search algorithm|Grover-like quantum search algorithm]] retrieves the memory state closest to a given input. An advantage lies in the exponential storage capacity of memory states, however the question remains whether the model has significance regarding the initial purpose of Hopfield models as a demonstration of how simplified artificial neural networks can simulate features of the brain.
=== Classical neural networks inspired by quantum theory ===
A substantial amount of interest has been given to a “quantum-inspired” model that uses ideas from quantum theory to implement a neural network based on [[fuzzy logic]].<ref>{{cite journal |first1=G. |last1=Purushothaman |first2=N. |last2=Karayiannis |url=https://pdfs.semanticscholar.org/fe11/93d386f42358e7cf9b1f71bf33e7ddd945b5.pdf |archive-url=https://web.archive.org/web/20170911115935/https://pdfs.semanticscholar.org/fe11/93d386f42358e7cf9b1f71bf33e7ddd945b5.pdf |url-status=dead |archive-date=2017-09-11 |title=Quantum Neural Networks (QNN's): Inherently Fuzzy Feedforward Neural Networks |journal=IEEE Transactions on Neural Networks |volume=8 |issue=3 |pages=679–93 |year=1997 |doi=10.1109/72.572106 |pmid=18255670 |s2cid=1634670 }}</ref>
== Training ==
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