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'''Continuous-variable quantum computation''', also called '''continuous quantum computation''', is the area of [[quantum computation]] that makes use of [[Observable|physical observables]], like the strength of an [[electromagnetic field]], whose numerical values belong to [[List of continuity-related mathematical topics|continuous]] [[Interval (mathematics)|intervals]].<ref>{{Cite journal|last=Lloyd|first=Seth|last2=Braunstein|first2=Samuel L.|date=1999-01-01|title=Quantum Computation over Continuous Variables|url=https://link.aps.org/doi/10.1103/PhysRevLett.82.1784|journal=Physical Review Letters|volume=82|issue=8|pages=1784–1787|arxiv=quant-ph/9810082|doi=10.1103/PhysRevLett.82.1784}}</ref><ref>{{Cite journal|last=Bartlett|first=Stephen D.|last2=Sanders|first2=Barry C.|date=2002-01-01|title=Universal continuous-variable quantum computation: Requirement of optical nonlinearity for photon counting|url=https://link.aps.org/doi/10.1103/PhysRevA.65.042304|journal=Physical Review A|volume=65|issue=4|pages=|arxiv=quant-ph/0110039|doi=10.1103/PhysRevA.65.042304}}</ref><ref>{{Cite journal|last=Menicucci|first=Nicolas C.|last2=van Loock|first2=Peter|last3=Gu|first3=Mile|last4=Weedbrook|first4=Christian|last5=Ralph|first5=Timothy C.|last6=Nielsen|first6=Michael A.|date=2006-09-13|title=Universal Quantum Computation with Continuous-Variable Cluster States|url=https://link.aps.org/doi/10.1103/PhysRevLett.97.110501|journal=Physical Review Letters|volume=97|issue=11|pages=110501|arxiv=quant-ph/0605198|doi=10.1103/PhysRevLett.97.110501}}</ref><ref>{{Cite journal|last=Tasca|first=D. S.|last2=Gomes|first2=R. M.|last3=Toscano|first3=F.|last4=Souto Ribeiro|first4=P. H.|last5=Walborn|first5=S. P.|date=2011-01-01|title=Continuous-variable quantum computation with spatial degrees of freedom of photons|url=https://link.aps.org/doi/10.1103/PhysRevA.83.052325|journal=Physical Review A|volume=83|issue=5|pages=|arxiv=1106.3049|doi=10.1103/PhysRevA.83.052325}}</ref> In a sense, continuous-variable quantum computation is "analogue," while quantum computation using [[Qubit|qubits]] is "digital." In more technical terms, the former makes use of [[Hilbert space|Hilbert spaces]] that are [[Dimension|infinite-dimensional]], while the Hilbert spaces for systems comprising collections of qubits are finite-dimensional.<ref>{{Cite book|url=|title=Quantum Information with Continuous Variables|last=Braunstein|first=S. L.|last2=Pati|first2=A. K.|date=2012-12-06|publisher=Springer Science & Business Media|year=|isbn=9789401512589|___location=|pages=|language=en|doi=10.1007/978-94-015-1258-9}}</ref><ref>{{Cite journal|last=Braunstein|first=Samuel L.|last2=van Loock|first2=Peter|date=2005-06-29|title=Quantum information with continuous variables|url=https://link.aps.org/doi/10.1103/RevModPhys.77.513|journal=Reviews of Modern Physics|volume=77|issue=2|pages=513–577|arxiv=quant-ph/0410100|doi=10.1103/RevModPhys.77.513}}</ref> One major motivation for studying continuous-variable quantum computation is that many scientific problems have mathematical formulations that are naturally continuous in character. Another motivation is to understand in what ways quantum computers are more capable or more powerful than classical computers.<ref>{{Cite journal|last=Adesso|first=Gerardo|last2=Ragy|first2=Sammy|last3=Lee|first3=Antony R.|date=2014-03-12|title=Continuous Variable Quantum Information: Gaussian States and Beyond|url=http://www.worldscientific.com/doi/abs/10.1142/S1230161214400010|journal=Open Systems & Information Dynamics|volume=21|issue=01n02|pages=1440001|arxiv=1401.4679|doi=10.1142/S1230161214400010|issn=1230-1612}}</ref>
== Applications ==
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