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{{short description|Quantum Mechanics in Neural Networks}}
[[File:Neural Network - basic scheme with legends.png|thumb|Sample model of a feed forward neural network. For a deep learning network, increase the number of hidden layers.]]
'''Quantum neural networks''' are [[Neural network (machine learning)|computational neural network]] models which are based on the principles of [[quantum mechanics]]. The first ideas on quantum neural computation were published independently in 1995 by [[Subhash Kak]] and Ron Chrisley,<ref>{{cite journal |first=S. |last=Kak |title=On quantum neural computing |journal=Advances in Imaging and Electron Physics |volume=94 |pages=259–313 |year=1995 |doi=10.1016/S1076-5670(08)70147-2 |isbn=9780120147366 }}</ref><ref>{{cite book |first=R. |last=Chrisley |chapter=Quantum Learning |title=New directions in cognitive science: Proceedings of the international symposium, Saariselka, 4–9 August 1995, Lapland, Finland |editor-first=P. |editor-last=Pylkkänen |editor2-first=P. |editor2-last=Pylkkö |publisher=Finnish Association of Artificial Intelligence |___location=Helsinki |pages=77–89 |year=1995 |isbn=951-22-2645-6 }}</ref> engaging with the theory of [[quantum mind]], which posits that quantum effects play a role in cognitive function. However, typical research in quantum neural networks involves combining classical [[artificial neural network]] models (which are widely used in machine learning for the important task of pattern recognition) with the advantages of [[quantum information]] in order to develop more efficient algorithms.<ref>{{cite journal|last1=da Silva|first1=Adenilton J.|last2=Ludermir|first2=Teresa B.|last3=de Oliveira|first3=Wilson R.|year=2016|title=Quantum perceptron over a field and neural network architecture selection in a quantum computer|journal=Neural Networks|volume=76|pages=55–64|arxiv=1602.00709|bibcode=2016arXiv160200709D|doi=10.1016/j.neunet.2016.01.002|pmid=26878722|s2cid=15381014}}</ref><ref>{{cite journal|last1=Panella|first1=Massimo|last2=Martinelli|first2=Giuseppe|year=2011|title=Neural networks with quantum architecture and quantum learning|journal=[[International Journal of Circuit Theory and Applications]]|volume=39|pages=61–77|doi=10.1002/cta.619|s2cid=3791858 }}</ref><ref>{{cite journal |first1=M. |last1=Schuld |first2=I. |last2=Sinayskiy |first3=F. |last3=Petruccione |arxiv=1408.7005 |title=The quest for a Quantum Neural Network |journal=Quantum Information Processing |volume=13 |issue=11 |pages=2567–2586 |year=2014 |doi=10.1007/s11128-014-0809-8 |bibcode=2014QuIP...13.2567S |s2cid=37238534 }}</ref> One important motivation for these investigations is the difficulty to train classical neural networks, especially in [[Big data|big data applications]]. The hope is that features of [[quantum computing]] such as [[quantum parallelism]] or the effects of [[quantum interference|interference]] and [[Quantum entanglement|entanglement]] can be used as resources. Since the technological implementation of a quantum computer is still in a premature stage, such quantum neural network models are mostly theoretical proposals that await their full implementation in physical experiments.
Most Quantum neural networks are developed as [[Feedforward neural network|feed-forward]] networks. Similar to their classical counterparts, this structure intakes input from one layer of qubits, and passes that input onto another layer of qubits. This layer of qubits evaluates this information and passes on the output to the next layer. Eventually the path leads to the final layer of qubits.<ref name=":0">{{Cite journal|last1=Beer|first1=Kerstin|last2=Bondarenko|first2=Dmytro|last3=Farrelly|first3=Terry|last4=Osborne|first4=Tobias J.|last5=Salzmann|first5=Robert|last6=Scheiermann|first6=Daniel|last7=Wolf|first7=Ramona|date=2020-02-10|title=Training deep quantum neural networks|url= |journal=Nature Communications|language=en|volume=11|issue=1|pages=808|doi=10.1038/s41467-020-14454-2|issn=2041-1723|pmc=7010779|pmid=32041956|arxiv=1902.10445|bibcode=2020NatCo..11..808B}}</ref><ref name="WanDKGK16" /> The layers do not have to be of the same width, meaning they don't have to have the same number of qubits as the layer before or after it. This structure is trained on which path to take similar to classical [[artificial neural network]]s. This is discussed in a lower section. Quantum neural networks refer to three different categories: Quantum computer with classical data, classical computer with quantum data, and quantum computer with quantum data.<ref name=":0" />
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