Quantum neural network: Difference between revisions

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=== Quantum associative memory ===

The first 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. AnAs advantagesuch, liesthis inis thenot exponentiala storagefully capacity ofcontent-addressable memory states, howeversince theonly questionincomplete remains whether the model has significance regarding the initial purpose of Hopfield models as a demonstration of how simplified artificial neural networkspatterns can simulate features of thebe brainretrieved.

The first truly content-addressable quantum memory, which can retrieve patterns also from corrupted inputs, was proposed by Carlo A. Trugenberger<ref>{{Cite journal |last=Trugenberger |first=C. A. |date=2001-07-18 |title=Probabilistic Quantum Memories |url=http://dx.doi.org/10.1103/physrevlett.87.067901 |journal=Physical Review Letters |volume=87 |issue=6 |doi=10.1103/physrevlett.87.067901 |issn=0031-9007}}</ref><ref name=":2">{{Cite journal |last=Trugenberger |first=Carlo A. |date=2002 |title=Quantum Pattern Recognition |journal=Quantum Information Processing |volume=1 |issue=6 |pages=471-493}}</ref><ref>{{Cite journal |last=Trugenberger |first=C. A. |date=2002-12-19 |title=Phase Transitions in Quantum Pattern Recognition |url=http://dx.doi.org/10.1103/physrevlett.89.277903 |journal=Physical Review Letters |volume=89 |issue=27 |doi=10.1103/physrevlett.89.277903 |issn=0031-9007}}</ref>. Both memories can store an exponential (in terms of n qubits) number of patterns but can be used only once due to the no-cloning theorem and their destruction upon measurement.

Trugenberger<ref name=":2" />, however, has shown that his proababilistic model of quantum associative memory can be efficiently implemented and re-used multiples times for any polynomial number of stored patterns, a large advantage with respect to classical associative memories.

=== Classical neural networks inspired by quantum theory ===