A lot of proposals attempt to find a quantum equivalent for the [[perceptron]] unit from which neural nets are constructed. A problem is that nonlinear activation functions do not immediately correspond to the mathematical structure of quantum theory, since a quantum evolution is described by linear operations and leads to probabilistic observation. Ideas to imitate the perceptron activation function with a quantum mechanical formalism reach from special measurements <ref>{{cite journal |first=M. |last=Perus |title=Neural Networks as a basis for quantum associative memory |journal=Neural Network World |volume=10 |issue=6 |pages=1001 |year=2000 |citeseerx=10.1.1.106.4583 |url=http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.106.4583&rep=rep1&type=pdf }}</ref><ref>{{cite journal |first1=M. |last1=Zak |first2=C. P. |last2=Williams |title=Quantum Neural Nets |journal=International Journal of Theoretical Physics |volume=37 |issue=2 |pages=651–684 |year=1998 |doi=10.1023/A:1026656110699 |s2cid=55783801 }}</ref> to postulating non-linear quantum operators (a mathematical framework that is disputed).<ref>{{Cite journal | doi=10.1006/jcss.2001.1769| title=Quantum Neural Networks| journal=Journal of Computer and System Sciences| volume=63| issue=3| pages=355–383| year=2001| last1=Gupta| first1=Sanjay| last2=Zia| first2=R.K.P.| arxiv=quant-ph/0201144| s2cid=206569020}}</ref><ref>{{cite journal |first1=J. |last1=Faber |first2=G. A. |last2=Giraldi |title=Quantum Models for Artificial Neural Network |year=2002 |url=http://arquivosweb.lncc.br/pdfs/QNN-Review.pdf }}</ref> A direct implementation of the activation function using the [[quantum circuit|circuit-based model of quantum computation]] has recently been proposed by Schuld, Sinayskiy and Petruccione based on the [[quantum phase estimation algorithm]].<ref>{{cite journal |first1=M. |last1=Schuld |first2=I. |last2=Sinayskiy |first3=F. |last3=Petruccione |title=Simulating a perceptron on a quantum computer |journal=Physics Letters A |arxiv=1412.3635 |year=2014 |volume=379 |issue=7 |pages=660–663 |doi=10.1016/j.physleta.2014.11.061 |s2cid=14288234 }}</ref>
