=== Reservoir computing and quantum reservoir computing===
In reservoir computing a sparse recurrent neural network with fixed weights equipped of fading memory and echo state property is followed by a trainable output layer. Its universality has been demonstrated separately for what concerns networks of rate neurons <ref>{{Cite journal |lastlast1=MaassGrigoryeva |firstfirst1=WolfgangL. |last2=MarkramOrtega |first2=Henry J.-P. |date=20042018 |title=OnEcho thestate computationalnetworks powerare ofuniversal circuits|journal=Neural ofNetworks spiking neurons|volume=108 |urlissue=http://www.igi.tugraz.at/maass/psfiles/135.pdf1 |journalpages=Journal of computer and system sciences495–508 |volumearxiv=691806.00797 |pagesdoi=593–61610.1016/j.neunet.2018.08.025}}</ref> and spiking neurons, respectively. <ref>{{Cite journal |last1last=GrigoryevaMaass |first1first=L.Wolfgang |last2=OrtegaMarkram |first2=J.-P.Henry |date=20182004 |title=EchoOn statethe networkscomputational arepower universalof |journal=Neuralcircuits Networksof |volume=108spiking neurons |issueurl=1http://www.igi.tugraz.at/maass/psfiles/135.pdf |pagesjournal=495–508Journal of computer and system sciences |arxivvolume=1806.0079769 |doipages=10.1016/j.neunet.2018.08.025593–616}}</ref> In 2024, the framework has been generalized and extended to quantum reservoirs where the reservoir is based on qubits defined over Hilbert spaces. <ref>{{cite arXiv |last1=Monzani |first1=Francesco |title=Universality conditions of unified classical and quantum reservoir computing |date=2024|eprint=2401.15067 |last2=Prati |first2=Enrico |class=quant-ph }}</ref>
