Quantum neural network: Difference between revisions

Revision as of 04:23, 26 November 2021

Revision as of 09:26, 27 January 2022

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=== Quantum perceptrons ===

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 paperjournal |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>

=== Quantum networks ===

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At a larger scale, researchers have attempted to generalize neural networks to the quantum setting. One way of constructing a quantum neuron is to first generalise classical neurons and then generalising them further to make unitary gates. Interactions between neurons can be controlled quantumly, with unitary gates, or classically, via measurement of the network states. This high-level theoretical technique can be applied broadly, by taking different types of networks and different implementations of quantum neurons, such as [[Integrated quantum photonics|photonically]] implemented neurons<ref name="WanDKGK16">{{cite journal|last1=Wan|first1=Kwok-Ho|last2=Dahlsten|first2=Oscar|last3=Kristjansson|first3=Hler|last4=Gardner|first4=Robert|last5=Kim|first5=Myungshik|year=2017|title=Quantum generalisation of feedforward neural networks|journal=NPJ Quantum Information|volume=3|pages=36|arxiv=1612.01045|bibcode=2017npjQI...3...36W|doi=10.1038/s41534-017-0032-4|s2cid=51685660}}</ref><ref>{{cite journal |first1=A. |last1=Narayanan |first2=T. |last2=Menneer |title=Quantum artificial neural network architectures and components |journal=Information Sciences |volume=128 |issue= 3–4|pages=231–255 |year=2000 |doi=10.1016/S0020-0255(00)00055-4 }}</ref> and [[quantum reservoir processor]].<ref>{{cite journal |last1=Ghosh |first1=S. |last2=Opala |first2=A. |last3=Matuszewski |first3=M. |last4=Paterek |first4=P. |last5=Liew |first5=T. C. H. |doi=10.1038/s41534-019-0149-8 |title=Quantum reservoir processing |journal=NPJ Quantum Information |volume=5 |pages=35 |year=2019 |arxiv=1811.10335 |bibcode=2019npjQI...5...35G |s2cid=119197635 }}</ref> Most learning algorithms follow the classical model of training an artificial neural network to learn the input-output function of a given [[training set]] and use classical feedback loops to update parameters of the quantum system until they converge to an optimal configuration. Learning as a parameter optimisation problem has also been approached by adiabatic models of quantum computing.<ref>{{cite journal |first1=H. |last1=Neven |display-authors=1 |first2=Vasil S. |last2=Denchev |first3=Geordie |last3=Rose |first4=William G. |last4=Macready |arxiv=0811.0416 |title=Training a Binary Classifier with the Quantum Adiabatic Algorithm |year=2008 }}</ref>

Quantum neural networks can be applied to algorithmic design: given [[qubits]] with tunable mutual interactions, one can attempt to learn interactions following the classical [[backpropagation]] rule from a [[training set]] of desired input-output relations, taken to be the desired output algorithm's behavior.<ref>{{cite journal |first1=J. |last1=Bang |display-authors=1 |first2=Junghee |last2=Ryu |first3=Seokwon |last3=Yoo |first4=Marcin |last4=Pawłowski |first5=Jinhyoung |last5=Lee |doi=10.1088/1367-2630/16/7/073017 |title=A strategy for quantum algorithm design assisted by machine learning |journal=New Journal of Physics |volume=16 |issue= 7|pages=073017 |year=2014 |arxiv=1301.1132 |bibcode=2014NJPh...16g3017B |s2cid=55377982 }}</ref><ref>{{cite journal |first1=E. C. |last1=Behrman |first2=J. E. |last2=Steck |first3=P. |last3=Kumar |first4=K. A. |last4=Walsh |arxiv=0808.1558 |title=Quantum Algorithm design using dynamic learning |journal=Quantum Information and Computation |volume=8 |issue=1–2 |pages=12–29 |year=2008 |doi=10.26421/QIC8.1-2-2 |s2cid=18587557 }}</ref> The quantum network thus ‘learns’ an algorithm.

=== Quantum associative memory ===