Editing Theoretical computer science (section)

===Quantum computation===
{{main|Quantum computation}}
A [[quantum computer]] is a [[computation]] system that makes direct use of [[quantum mechanics|quantum-mechanical]] [[phenomena]], such as [[quantum superposition|superposition]] and [[quantum entanglement|entanglement]], to perform [[Instruction (computer science)|operations]] on [[data]].<ref>"[http://cba.mit.edu/docs/papers/98.06.sciqc.pdf Quantum Computing with Molecules]" article in ''[[Scientific American]]'' by [[Neil Gershenfeld]] and [[Isaac L. Chuang]]</ref> Quantum computers are different from digital computers based on [[transistor]]s. Whereas digital computers require data to be encoded into binary digits ([[bit]]s), each of which is always in one of two definite states (0 or 1), quantum computation uses [[qubits]] (quantum bits), which can be in [[quantum superposition|superpositions]] of states. A theoretical model is the [[quantum Turing machine]], also known as the universal quantum computer.  Quantum computers share theoretical similarities with [[Non-deterministic Turing machine|non-deterministic]] and [[probabilistic automaton|probabilistic computers]]; one example is the ability to be in more than one state simultaneously.  The field of quantum computing was first introduced by [[Yuri Manin]] in 1980<ref name="manin1980vychislimoe">{{cite book| author=Manin, Yu. I.| title=Vychislimoe i nevychislimoe| trans-title=Computable and Noncomputable| year=1980| publisher=Sov.Radio| url=http://publ.lib.ru/ARCHIVES/M/MANIN_Yuriy_Ivanovich/Manin_Yu.I._Vychislimoe_i_nevychislimoe.(1980).%5Bdjv%5D.zip| pages=13–15| language=ru| access-date=4 March 2013| url-status=dead| archive-url=https://web.archive.org/web/20130510173823/http://publ.lib.ru/ARCHIVES/M/MANIN_Yuriy_Ivanovich/Manin_Yu.I._Vychislimoe_i_nevychislimoe.(1980).%5Bdjv%5D.zip| archive-date=10 May 2013}}</ref> and [[Richard Feynman]] in 1982.<ref name="Feynman82">{{cite journal |last=Feynman |first=R. P. |title=Simulating physics with computers |journal=[[International Journal of Theoretical Physics]] |year=1982 |volume=21 |issue=6 |pages=467–488 |doi=10.1007/BF02650179 |bibcode=1982IJTP...21..467F |citeseerx=10.1.1.45.9310 |s2cid=124545445 }}</ref><ref>{{cite journal |title=Quantum computation |author-link=David Deutsch |first=David |last=Deutsch |journal=Physics World |date=1992-01-06 |volume=5 |issue=6 |pages=57–61 |doi=10.1088/2058-7058/5/6/38 }}</ref> A quantum computer with spins as quantum bits was also formulated for use as a quantum [[space–time]] in 1968.<ref>{{cite book |first=David |last=Finkelstein |chapter=Space-Time Structure in High Energy Interactions |title=Fundamental Interactions at High Energy |editor1-first=T. |editor1-last=Gudehus |editor2-first=G. |editor2-last=Kaiser |location=New York |publisher=Gordon & Breach |year=1968 }}</ref>

Experiments have been carried out in which quantum computational operations were executed on a very small number of qubits.<ref>{{cite web|url=http://phys.org/news/2013-01-qubit-bodes-future-quantum.html|title=New qubit control bodes well for future of quantum computing|access-date=26 October 2014}}</ref> Both practical and theoretical research continues, and many national governments and military funding agencies support quantum computing research to develop quantum [[computer]]s for both civilian and national security purposes, such as [[cryptanalysis]].<ref>[http://qist.lanl.gov/qcomp_map.shtml Quantum Information Science and Technology Roadmap] for a sense of where the research is heading.</ref>