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data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Abstract model of quantum computation</div> <p>A <b>quantum cellular automaton</b> (<b>QCA</b>) is an abstract model of <a href="/wiki/Quantum_computation" class="mw-redirect" title="Quantum computation">quantum computation</a>, devised in analogy to conventional models of <a href="/wiki/Cellular_automata" class="mw-redirect" title="Cellular automata">cellular automata</a> introduced by <a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a>. The same name may also refer to <a href="/wiki/Quantum_dot_cellular_automata" class="mw-redirect" title="Quantum dot cellular automata">quantum dot cellular automata</a>, which are a proposed physical implementation of "classical" cellular automata by exploiting <a href="/wiki/Quantum_mechanical" class="mw-redirect" title="Quantum mechanical">quantum mechanical</a> phenomena. QCA have attracted a lot of attention as a result of its extremely small feature size (at the molecular or even atomic scale) and its ultra-low power consumption, making it one candidate for replacing <a href="/wiki/CMOS" title="CMOS">CMOS</a> technology. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Usage_of_the_term">Usage of the term</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_cellular_automaton&action=edit&section=1" title="Edit section: Usage of the term"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the context of models of computation or of physical systems, <i>quantum cellular automaton</i> refers to the merger of elements of both (1) the study of cellular automata in conventional <a href="/wiki/Computer_science" title="Computer science">computer science</a> and (2) the study of <a href="/wiki/Quantum_information_processing" class="mw-redirect" title="Quantum information processing">quantum information processing</a>. In particular, the following are features of models of quantum cellular automata: </p> <ul><li>The computation is considered to come about by parallel operation of multiple computing devices, or <b>cells</b>. The cells are usually taken to be identical, finite-dimensional quantum systems (e.g. each cell is a <a href="/wiki/Qubit" title="Qubit">qubit</a>).</li> <li>Each cell has a neighborhood of other cells. Altogether these form a network of cells, which is usually taken to be regular (e.g. the cells are arranged as a lattice with or without periodic boundary conditions).</li> <li>The evolution of all of the cells has a number of physics-like symmetries. Locality is one: the next state of a cell depends only on its current state and that of its neighbours. Homogeneity is another: the evolution acts the same everywhere, and is independent of time.</li> <li>The state space of the cells, and the operations performed on them, should be motivated by principles of quantum mechanics.</li></ul> <p>Another feature that is often considered important for a model of quantum cellular automata is that it should be <a href="/wiki/Universal_computation" class="mw-redirect" title="Universal computation">universal</a> for quantum computation (i.e. that it can efficiently simulate <a href="/wiki/Quantum_Turing_machine" title="Quantum Turing machine">quantum Turing machines</a>,<sup id="cite_ref-WQCA_1-0" class="reference"><a href="#cite_note-WQCA-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-LUQCA_2-0" class="reference"><a href="#cite_note-LUQCA-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> some arbitrary <a href="/wiki/Quantum_circuit" title="Quantum circuit">quantum circuit</a><sup id="cite_ref-SFWQCA_3-0" class="reference"><a href="#cite_note-SFWQCA-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> or simply all other quantum cellular automata<sup id="cite_ref-AFQCA_4-0" class="reference"><a href="#cite_note-AFQCA-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-AGQCA_5-0" class="reference"><a href="#cite_note-AGQCA-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>). </p><p>Models which have been proposed recently impose further conditions, e.g. that quantum cellular automata should be reversible and/or locally unitary, and have an easily determined global transition function from the rule for updating individual cells.<sup id="cite_ref-LUQCA_2-1" class="reference"><a href="#cite_note-LUQCA-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Recent results show that these properties can be derived axiomatically, from the symmetries of the global evolution.<sup id="cite_ref-SWQCA_6-0" class="reference"><a href="#cite_note-SWQCA-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ANWQCA1_7-0" class="reference"><a href="#cite_note-ANWQCA1-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ANWQCA2_8-0" class="reference"><a href="#cite_note-ANWQCA2-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Models">Models</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_cellular_automaton&action=edit&section=2" title="Edit section: Models"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Early_proposals">Early proposals</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_cellular_automaton&action=edit&section=3" title="Edit section: Early proposals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1982, <a href="/wiki/Richard_Feynman" title="Richard Feynman">Richard Feynman</a> suggested an initial approach to quantizing a model of cellular automata.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> In 1985, <a href="/wiki/David_Deutsch" title="David Deutsch">David Deutsch</a> presented a formal development of the subject.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Later, Gerhard Grössing and <a href="/wiki/Anton_Zeilinger" title="Anton Zeilinger">Anton Zeilinger</a> introduced the term "quantum cellular automata" to refer to a model they defined in 1988,<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> although their model had very little in common with the concepts developed by Deutsch and so has not been developed significantly as a model of computation. </p> <div class="mw-heading mw-heading3"><h3 id="Models_of_universal_quantum_computation">Models of universal quantum computation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_cellular_automaton&action=edit&section=4" title="Edit section: Models of universal quantum computation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The first formal model of quantum cellular automata to be researched in depth was that introduced by <a href="/wiki/John_Watrous_(computer_scientist)" title="John Watrous (computer scientist)">John Watrous</a>.<sup id="cite_ref-WQCA_1-1" class="reference"><a href="#cite_note-WQCA-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> This model was developed further by Wim van Dam,<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> as well as Christoph Dürr, Huong LêThanh, and Miklos Santha,<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Jozef Gruska.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> and Pablo Arrighi.<sup id="cite_ref-AQCA_16-0" class="reference"><a href="#cite_note-AQCA-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> However it was later realised that this definition was too loose, in the sense that some instances of it allow superluminal signalling.<sup id="cite_ref-SWQCA_6-1" class="reference"><a href="#cite_note-SWQCA-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ANWQCA1_7-1" class="reference"><a href="#cite_note-ANWQCA1-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> A second wave of models includes those of Susanne Richter and Reinhard Werner,<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> of Benjamin Schumacher and Reinhard Werner,<sup id="cite_ref-SWQCA_6-2" class="reference"><a href="#cite_note-SWQCA-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> of Carlos Pérez-Delgado and Donny Cheung,<sup id="cite_ref-LUQCA_2-2" class="reference"><a href="#cite_note-LUQCA-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> and of Pablo Arrighi, Vincent Nesme and Reinhard Werner.<sup id="cite_ref-ANWQCA1_7-2" class="reference"><a href="#cite_note-ANWQCA1-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ANWQCA2_8-1" class="reference"><a href="#cite_note-ANWQCA2-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> These are all closely related, and do not suffer any such locality issue. In the end one can say that they all agree to picture quantum cellular automata as just some large quantum circuit, infinitely repeating across time and space. Recent reviews of the topic are available here.<sup id="cite_ref-OverQCA_18-0" class="reference"><a href="#cite_note-OverQCA-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-RevQCA_19-0" class="reference"><a href="#cite_note-RevQCA-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Models_of_physical_systems">Models of physical systems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_cellular_automaton&action=edit&section=5" title="Edit section: Models of physical systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Models of quantum cellular automata have been proposed by David Meyer,<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Bruce_M._Boghosian" title="Bruce M. Boghosian">Bruce Boghosian</a> and Washington Taylor,<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> and Peter Love and Bruce Boghosian<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> as a means of simulating quantum lattice gases, motivated by the use of "classical" cellular automata to model classical physical phenomena such as gas dispersion.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> Criteria determining when a quantum cellular automaton (QCA) can be described as quantum lattice gas automaton (QLGA) were given by Asif Shakeel and Peter Love.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Quantum_dot_cellular_automata">Quantum dot cellular automata</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_cellular_automaton&action=edit&section=6" title="Edit section: Quantum dot cellular automata"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A proposal for implementing <i>classical</i> cellular automata by systems designed with <a href="/wiki/Quantum_dots" class="mw-redirect" title="Quantum dots">quantum dots</a> has been proposed under the name "quantum cellular automata" by <a href="/wiki/Paul_Douglas_Tougaw" title="Paul Douglas Tougaw">Doug Tougaw</a> and Craig Lent,<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> as a replacement for classical computation using CMOS technology. In order to better differentiate between this proposal and models of cellular automata which perform quantum computation, many authors working on this subject now refer to this as a <a href="/wiki/Quantum_dot_cellular_automaton" title="Quantum dot cellular automaton">quantum dot cellular automaton</a>. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_cellular_automaton&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Quantum_finite_automata" class="mw-redirect" title="Quantum finite automata">Quantum finite automata</a> – Quantum analog of probabilistic automata<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span></li> <li><a href="/wiki/Quantum_Hall_effect" title="Quantum Hall effect">Quantum Hall effect</a> – Electromagnetic effect in physics</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_cellular_automaton&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-WQCA-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-WQCA_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-WQCA_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFWatrous1995" class="citation cs2"><a href="/wiki/John_Watrous_(computer_scientist)" title="John Watrous (computer scientist)">Watrous, John</a> (1995), "On one-dimensional quantum cellular automata", <a href="/wiki/Symposium_on_Foundations_of_Computer_Science" title="Symposium on Foundations of Computer Science"><i>Proc. 36th Annual Symposium on Foundations of Computer Science (Milwaukee, WI, 1995)</i></a>, Los Alamitos, CA: IEEE Comput. Soc. Press, pp. 528–537, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FSFCS.1995.492583">10.1109/SFCS.1995.492583</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8186-7183-1" title="Special:BookSources/0-8186-7183-1"><bdi>0-8186-7183-1</bdi></a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1619103">1619103</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:7441203">7441203</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=On+one-dimensional+quantum+cellular+automata&rft.btitle=Proc.+36th+Annual+Symposium+on+Foundations+of+Computer+Science+%28Milwaukee%2C+WI%2C+1995%29&rft.place=Los+Alamitos%2C+CA&rft.pages=528-537&rft.pub=IEEE+Comput.+Soc.+Press&rft.date=1995&rft_id=info%3Adoi%2F10.1109%2FSFCS.1995.492583&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1619103%23id-name%3DMR&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A7441203%23id-name%3DS2CID&rft.isbn=0-8186-7183-1&rft.aulast=Watrous&rft.aufirst=John&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuantum+cellular+automaton" class="Z3988"></span>.</span> </li> <li id="cite_note-LUQCA-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-LUQCA_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-LUQCA_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-LUQCA_2-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">C. Pérez-Delgado and D. Cheung, "Local Unitary Quantum Cellular Automata", Phys. Rev. A 76, 032320, 2007. See also <a rel="nofollow" class="external text" href="http://www.arxiv.org/abs/0709.0006">arXiv:0709.0006 (quant-ph)</a></span> </li> <li id="cite_note-SFWQCA-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-SFWQCA_3-0">^</a></b></span> <span class="reference-text"> D.J. Shepherd, T. Franz, R.F. Werner: Universally programmable Quantum Cellular Automaton. Phys. Rev. Lett. 97, 020502 (2006)</span> </li> <li id="cite_note-AFQCA-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-AFQCA_4-0">^</a></b></span> <span class="reference-text">P. Arrighi, R. Fargetton, Z. Wang, Intrinsically universal one-dimensional quantum cellular automata in two flavours, Fundamenta Informaticae Vol.91, No.2, pp.197-230, (2009). See also <a rel="nofollow" class="external text" href="https://arxiv.org/abs/0704.3961">(quant-ph)</a></span> </li> <li id="cite_note-AGQCA-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-AGQCA_5-0">^</a></b></span> <span class="reference-text">P. Arrighi, J. Grattage, A quantum Game of Life, Proceedings of JAC 2010, Turku, December 2010. TUCS Lecture Notes 13, 31-42, (2010). See also <a rel="nofollow" class="external text" href="https://arxiv.org/abs/arXiv:1010.3120">(quant-ph)</a> and <a rel="nofollow" class="external text" href="http://www.grattage.co.uk/jon/3DQCA">(Companion Website)</a></span> </li> <li id="cite_note-SWQCA-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-SWQCA_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-SWQCA_6-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-SWQCA_6-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">B. Schumacher and R. Werner, "Reversible quantum cellular automata", <a rel="nofollow" class="external text" href="http://www.arxiv.org/abs/quant-ph/0405174">quant-ph/0405174</a></span> </li> <li id="cite_note-ANWQCA1-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-ANWQCA1_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ANWQCA1_7-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-ANWQCA1_7-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">Pablo Arrighi, Vincent Nesme, Reinhard Werner, One-dimensional quantum cellular automata over finite, unbounded configurations. See also <a rel="nofollow" class="external text" href="https://arxiv.org/abs/0711.3517">(quant-ph)</a></span> </li> <li id="cite_note-ANWQCA2-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-ANWQCA2_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ANWQCA2_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Pablo Arrighi, Vincent Nesme, Reinhard Werner, N-dimensional quantum cellular automata. See also <a rel="nofollow" class="external text" href="https://arxiv.org/abs/0711.3975">(quant-ph)</a></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">R. Feynman, "Simulating physics with computers", Int. J. Theor. Phys. <b>21</b>, 1982: pp. 467–488.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">D. Deutsch, "Quantum theory, the Church-Turing principle and the universal quantum computer" Proceedings of the Royal Society of London A 400 (1985), pp. 97–117.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">G. Grossing and A. Zeilinger, "Quantum cellular automata", Complex Systems 2 (2), 1988: pp. 197–208 and 611–623.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">W. van Dam, "Quantum cellular automata", Master Thesis, Computer Science Nijmegen, Summer 1996.</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">C. Dürr and M. Santha, "A decision procedure for unitary linear quantum cellular automata", <a rel="nofollow" class="external text" href="http://www.arxiv.org/abs/quant-ph/9604007">quant-ph/9604007 </a>.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">C. Dürr, H. LêTanh, M. Santha, "A decision procedure for well-formed linear quantum cellular automata", Rand. Struct. Algorithms 11, 1997: pp. 381–394. See also <a rel="nofollow" class="external text" href="http://www.arxiv.org/abs/cs.DS/9906024">cs.DS/9906024</a>.</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">J. Gruska, "Quantum Computing", McGraw-Hill, Cambridge 1999: Section 4.3.</span> </li> <li id="cite_note-AQCA-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-AQCA_16-0">^</a></b></span> <span class="reference-text">Pablo Arrighi, An algebraic study of unitary one dimensional quantum cellular automata, Proceedings of MFCS 2006, LNCS 4162, (2006), pp122-133. See also <a rel="nofollow" class="external text" href="https://arxiv.org/abs/quant-ph/0512040">quant-ph/0512040</a></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">S. Richter and R.F. Werner, "Ergodicity of quantum cellular automata", J. Stat. Phys. 82, 1996: pp. 963–998. 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See also <a rel="nofollow" class="external text" href="http://www.arxiv.org/abs/quant-ph/9604003">quant-ph/9604003</a>.</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text">D. Meyer, "On the absence of homogeneous scalar unitary cellular automata'", Physics Letters A 223, 1996: pp. 337–340. See also <a rel="nofollow" class="external text" href="http://www.arxiv.org/abs/quant-ph/9604011">quant-ph/9604011</a>.</span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text">B. Boghosian and W. Taylor, "Quantum lattice-gas model for the many-particle Schrödinger equation in d dimensions", Physical Review E 57, 1998: pp. 54–66.</span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text">P. Love and B. Boghosian, "From Dirac to Diffusion: Decoherence in Quantum Lattice Gases", Quantum Information Processing 4, 2005, pp. 335–354.</span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text">B. Chophard and M. Droz, "Cellular Automata modeling of Physical Systems", Cambridge University Press, 1998.</span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShakeelLove2013" class="citation journal cs1">Shakeel, Asif; Love, Peter J. (2013-09-01). "When is a quantum cellular automaton (QCA) a quantum lattice gas automaton (QLGA)?". <i>Journal of Mathematical Physics</i>. <b>54</b> (9): 092203. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1209.5367">1209.5367</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013JMP....54i2203S">2013JMP....54i2203S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.4821640">10.1063/1.4821640</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0022-2488">0022-2488</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:2351651">2351651</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Mathematical+Physics&rft.atitle=When+is+a+quantum+cellular+automaton+%28QCA%29+a+quantum+lattice+gas+automaton+%28QLGA%29%3F&rft.volume=54&rft.issue=9&rft.pages=092203&rft.date=2013-09-01&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A2351651%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2013JMP....54i2203S&rft_id=info%3Aarxiv%2F1209.5367&rft.issn=0022-2488&rft_id=info%3Adoi%2F10.1063%2F1.4821640&rft.aulast=Shakeel&rft.aufirst=Asif&rft.au=Love%2C+Peter+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuantum+cellular+automaton" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text">P. Tougaw, C. Lent, "Logical devices implemented using quantum cellular automata", J. Appl. Phys. 75, 1994: pp. 1818–1825</span> </li> </ol></div></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · 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href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Quantum_mechanics_topics" title="Template:Quantum mechanics topics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Quantum_mechanics_topics" title="Template talk:Quantum mechanics topics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Quantum_mechanics_topics" title="Special:EditPage/Template:Quantum mechanics topics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Quantum_mechanics" style="font-size:114%;margin:0 4em"><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Background</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Introduction_to_quantum_mechanics" title="Introduction to quantum mechanics">Introduction</a></li> <li><a href="/wiki/History_of_quantum_mechanics" title="History of quantum mechanics">History</a> <ul><li><a href="/wiki/Timeline_of_quantum_mechanics" title="Timeline of quantum mechanics">Timeline</a></li></ul></li> <li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a></li> <li><a href="/wiki/Old_quantum_theory" title="Old quantum theory">Old quantum theory</a></li> <li><a href="/wiki/Glossary_of_elementary_quantum_mechanics" title="Glossary of elementary quantum mechanics">Glossary</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Fundamentals</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Born_rule" title="Born rule">Born rule</a></li> <li><a href="/wiki/Bra%E2%80%93ket_notation" title="Bra–ket notation">Bra–ket notation</a></li> <li><a href="/wiki/Complementarity_(physics)" title="Complementarity (physics)"> Complementarity</a></li> <li><a href="/wiki/Density_matrix" title="Density matrix">Density matrix</a></li> <li><a href="/wiki/Energy_level" title="Energy level">Energy level</a> <ul><li><a href="/wiki/Ground_state" title="Ground state">Ground state</a></li> <li><a href="/wiki/Excited_state" title="Excited state">Excited state</a></li> <li><a href="/wiki/Degenerate_energy_levels" title="Degenerate energy levels">Degenerate levels</a></li> <li><a href="/wiki/Zero-point_energy" title="Zero-point energy">Zero-point energy</a></li></ul></li> <li><a href="/wiki/Quantum_entanglement" title="Quantum entanglement">Entanglement</a></li> <li><a href="/wiki/Hamiltonian_(quantum_mechanics)" title="Hamiltonian (quantum mechanics)">Hamiltonian</a></li> <li><a href="/wiki/Wave_interference" title="Wave interference">Interference</a></li> <li><a href="/wiki/Quantum_decoherence" title="Quantum decoherence">Decoherence</a></li> <li><a href="/wiki/Measurement_in_quantum_mechanics" title="Measurement in quantum mechanics">Measurement</a></li> <li><a href="/wiki/Quantum_nonlocality" title="Quantum nonlocality">Nonlocality</a></li> <li><a href="/wiki/Quantum_state" title="Quantum state">Quantum state</a></li> <li><a href="/wiki/Quantum_superposition" title="Quantum superposition">Superposition</a></li> <li><a href="/wiki/Quantum_tunnelling" title="Quantum tunnelling">Tunnelling</a></li> <li><a href="/wiki/Scattering_theory" class="mw-redirect" title="Scattering theory">Scattering theory</a></li> <li><a href="/wiki/Symmetry_in_quantum_mechanics" title="Symmetry in quantum mechanics">Symmetry in quantum mechanics</a></li> <li><a href="/wiki/Uncertainty_principle" title="Uncertainty principle">Uncertainty</a></li> <li><a href="/wiki/Wave_function" title="Wave function">Wave function</a> <ul><li><a href="/wiki/Wave_function_collapse" title="Wave function collapse">Collapse</a></li> <li><a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">Wave–particle duality</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Formulations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mathematical_formulation_of_quantum_mechanics" title="Mathematical formulation of quantum mechanics">Formulations</a></li> <li><a href="/wiki/Heisenberg_picture" title="Heisenberg picture">Heisenberg</a></li> <li><a href="/wiki/Interaction_picture" title="Interaction picture">Interaction</a></li> <li><a href="/wiki/Matrix_mechanics" title="Matrix mechanics">Matrix mechanics</a></li> <li><a href="/wiki/Schr%C3%B6dinger_picture" title="Schrödinger picture">Schrödinger</a></li> <li><a href="/wiki/Path_integral_formulation" title="Path integral formulation">Path integral formulation</a></li> <li><a href="/wiki/Phase-space_formulation" title="Phase-space formulation">Phase space</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Equations</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Klein%E2%80%93Gordon_equation" title="Klein–Gordon equation">Klein–Gordon</a></li> <li><a href="/wiki/Dirac_equation" title="Dirac equation">Dirac</a></li> <li><a href="/wiki/Weyl_equation" title="Weyl equation">Weyl</a></li> <li><a href="/wiki/Majorana_equation" title="Majorana equation">Majorana</a></li> <li><a href="/wiki/Rarita%E2%80%93Schwinger_equation" title="Rarita–Schwinger equation">Rarita–Schwinger</a></li> <li><a href="/wiki/Pauli_equation" title="Pauli equation">Pauli</a></li> <li><a href="/wiki/Rydberg_formula" title="Rydberg formula">Rydberg</a></li> <li><a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Interpretations_of_quantum_mechanics" title="Interpretations of quantum mechanics">Interpretations</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_Bayesianism" title="Quantum Bayesianism">Bayesian</a></li> <li><a href="/wiki/Consistent_histories" title="Consistent histories">Consistent histories</a></li> <li><a href="/wiki/Copenhagen_interpretation" title="Copenhagen interpretation">Copenhagen</a></li> <li><a href="/wiki/De_Broglie%E2%80%93Bohm_theory" title="De Broglie–Bohm theory">de Broglie–Bohm</a></li> <li><a href="/wiki/Ensemble_interpretation" title="Ensemble interpretation">Ensemble</a></li> <li><a href="/wiki/Hidden-variable_theory" title="Hidden-variable theory">Hidden-variable</a> <ul><li><a href="/wiki/Local_hidden-variable_theory" title="Local hidden-variable theory">Local</a> <ul><li><a href="/wiki/Superdeterminism" title="Superdeterminism">Superdeterminism</a></li></ul></li></ul></li> <li><a href="/wiki/Many-worlds_interpretation" title="Many-worlds interpretation">Many-worlds</a></li> <li><a href="/wiki/Objective-collapse_theory" title="Objective-collapse theory">Objective collapse</a></li> <li><a href="/wiki/Quantum_logic" title="Quantum logic">Quantum logic</a></li> <li><a href="/wiki/Relational_quantum_mechanics" title="Relational quantum mechanics">Relational</a></li> <li><a href="/wiki/Transactional_interpretation" title="Transactional interpretation">Transactional</a></li> <li><a href="/wiki/Von_Neumann%E2%80%93Wigner_interpretation" title="Von Neumann–Wigner interpretation">Von Neumann–Wigner</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Experiments</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bell_test" title="Bell test">Bell test</a></li> <li><a href="/wiki/Davisson%E2%80%93Germer_experiment" title="Davisson–Germer experiment">Davisson–Germer</a></li> <li><a href="/wiki/Delayed-choice_quantum_eraser" title="Delayed-choice quantum eraser">Delayed-choice quantum eraser</a></li> <li><a href="/wiki/Double-slit_experiment" title="Double-slit experiment">Double-slit</a></li> <li><a href="/wiki/Franck%E2%80%93Hertz_experiment" title="Franck–Hertz experiment">Franck–Hertz</a></li> <li><a href="/wiki/Mach%E2%80%93Zehnder_interferometer" title="Mach–Zehnder interferometer">Mach–Zehnder interferometer</a></li> <li><a href="/wiki/Elitzur%E2%80%93Vaidman_bomb_tester" title="Elitzur–Vaidman bomb tester">Elitzur–Vaidman</a></li> <li><a href="/wiki/Popper%27s_experiment" title="Popper's experiment">Popper</a></li> <li><a href="/wiki/Quantum_eraser_experiment" title="Quantum eraser experiment">Quantum eraser</a></li> <li><a href="/wiki/Stern%E2%80%93Gerlach_experiment" title="Stern–Gerlach experiment">Stern–Gerlach</a></li> <li><a href="/wiki/Wheeler%27s_delayed-choice_experiment" title="Wheeler's delayed-choice experiment">Wheeler's delayed choice</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_nanoscience" class="mw-redirect" title="Quantum nanoscience">Science</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_biology" title="Quantum biology">Quantum biology</a></li> <li><a href="/wiki/Quantum_chemistry" title="Quantum chemistry">Quantum chemistry</a></li> <li><a href="/wiki/Quantum_chaos" title="Quantum chaos">Quantum chaos</a></li> <li><a href="/wiki/Quantum_cosmology" title="Quantum cosmology">Quantum cosmology</a></li> <li><a href="/wiki/Quantum_differential_calculus" title="Quantum differential calculus">Quantum differential calculus</a></li> <li><a href="/wiki/Quantum_dynamics" title="Quantum dynamics">Quantum dynamics</a></li> <li><a href="/wiki/Quantum_geometry" title="Quantum geometry">Quantum geometry</a></li> <li><a href="/wiki/Measurement_problem" title="Measurement problem">Quantum measurement problem</a></li> <li><a href="/wiki/Quantum_mind" title="Quantum mind">Quantum mind</a></li> <li><a href="/wiki/Quantum_stochastic_calculus" title="Quantum stochastic calculus">Quantum stochastic calculus</a></li> <li><a href="/wiki/Quantum_spacetime" title="Quantum spacetime">Quantum spacetime</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_technology" class="mw-redirect" title="Quantum technology">Technology</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_algorithm" title="Quantum algorithm">Quantum algorithms</a></li> <li><a href="/wiki/Quantum_amplifier" title="Quantum amplifier">Quantum amplifier</a></li> <li><a href="/wiki/Quantum_bus" title="Quantum bus">Quantum bus</a></li> <li><a class="mw-selflink selflink">Quantum cellular automata</a> <ul><li><a href="/wiki/Quantum_finite_automaton" title="Quantum finite automaton">Quantum finite automata</a></li></ul></li> <li><a href="/wiki/Quantum_channel" title="Quantum channel">Quantum channel</a></li> <li><a href="/wiki/Quantum_circuit" title="Quantum circuit">Quantum circuit</a></li> <li><a href="/wiki/Quantum_complexity_theory" title="Quantum complexity theory">Quantum complexity theory</a></li> <li><a href="/wiki/Quantum_computing" title="Quantum computing">Quantum computing</a> <ul><li><a href="/wiki/Timeline_of_quantum_computing_and_communication" title="Timeline of quantum computing and communication">Timeline</a></li></ul></li> <li><a href="/wiki/Quantum_cryptography" title="Quantum cryptography">Quantum cryptography</a></li> <li><a href="/wiki/Quantum_electronics" class="mw-redirect" title="Quantum electronics">Quantum electronics</a></li> <li><a href="/wiki/Quantum_error_correction" title="Quantum error correction">Quantum error correction</a></li> <li><a href="/wiki/Quantum_imaging" title="Quantum imaging">Quantum imaging</a></li> <li><a href="/wiki/Quantum_image_processing" title="Quantum image processing">Quantum image processing</a></li> <li><a href="/wiki/Quantum_information" title="Quantum information">Quantum information</a></li> <li><a href="/wiki/Quantum_key_distribution" title="Quantum key distribution">Quantum key distribution</a></li> <li><a href="/wiki/Quantum_logic" title="Quantum logic">Quantum logic</a></li> <li><a href="/wiki/Quantum_logic_gate" title="Quantum logic gate">Quantum logic gates</a></li> <li><a href="/wiki/Quantum_machine" title="Quantum machine">Quantum machine</a></li> <li><a href="/wiki/Quantum_machine_learning" title="Quantum machine learning">Quantum machine learning</a></li> <li><a href="/wiki/Quantum_metamaterial" title="Quantum metamaterial">Quantum metamaterial</a></li> <li><a href="/wiki/Quantum_metrology" title="Quantum metrology">Quantum metrology</a></li> <li><a href="/wiki/Quantum_network" title="Quantum network">Quantum network</a></li> <li><a href="/wiki/Quantum_neural_network" title="Quantum neural network">Quantum neural network</a></li> <li><a href="/wiki/Quantum_optics" title="Quantum optics">Quantum optics</a></li> <li><a href="/wiki/Quantum_programming" title="Quantum programming">Quantum programming</a></li> <li><a href="/wiki/Quantum_sensor" title="Quantum sensor">Quantum sensing</a></li> <li><a href="/wiki/Quantum_simulator" title="Quantum simulator">Quantum simulator</a></li> <li><a href="/wiki/Quantum_teleportation" title="Quantum teleportation">Quantum teleportation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Extensions</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_fluctuation" title="Quantum fluctuation">Quantum fluctuation</a></li> <li><a href="/wiki/Casimir_effect" title="Casimir effect">Casimir effect</a></li> <li><a href="/wiki/Quantum_statistical_mechanics" title="Quantum statistical mechanics">Quantum statistical mechanics</a></li> <li><a href="/wiki/Quantum_field_theory" title="Quantum field theory">Quantum field theory</a> <ul><li><a href="/wiki/History_of_quantum_field_theory" title="History of quantum field theory">History</a></li></ul></li> <li><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></li> <li><a href="/wiki/Relativistic_quantum_mechanics" title="Relativistic quantum mechanics">Relativistic quantum mechanics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Schr%C3%B6dinger%27s_cat" title="Schrödinger's cat">Schrödinger's cat</a> <ul><li><a href="/wiki/Schr%C3%B6dinger%27s_cat_in_popular_culture" title="Schrödinger's cat in popular culture">in popular culture</a></li></ul></li> <li><a href="/wiki/Wigner%27s_friend" title="Wigner's friend">Wigner's friend</a></li> <li><a href="/wiki/Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox" title="Einstein–Podolsky–Rosen paradox">EPR paradox</a></li> <li><a href="/wiki/Quantum_mysticism" title="Quantum mysticism">Quantum mysticism</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Quantum_mechanics" title="Category:Quantum mechanics">Category</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Richard_Feynman" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Richard_Feynman" title="Template:Richard Feynman"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Richard_Feynman" title="Template talk:Richard Feynman"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Richard_Feynman" title="Special:EditPage/Template:Richard Feynman"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Richard_Feynman" style="font-size:114%;margin:0 4em"><a href="/wiki/Richard_Feynman" title="Richard Feynman">Richard Feynman</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Career</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Feynman_diagram" title="Feynman diagram">Feynman diagram</a></li> <li><a href="/wiki/Feynman%E2%80%93Kac_formula" title="Feynman–Kac formula">Feynman–Kac formula</a></li> <li><a href="/wiki/Wheeler%E2%80%93Feynman_absorber_theory" title="Wheeler–Feynman absorber theory">Wheeler–Feynman absorber theory</a></li> <li><a href="/wiki/Bethe%E2%80%93Feynman_formula" title="Bethe–Feynman formula">Bethe–Feynman formula</a></li> <li><a href="/wiki/Hellmann%E2%80%93Feynman_theorem" title="Hellmann–Feynman theorem">Hellmann–Feynman theorem</a></li> <li><a href="/wiki/Feynman_slash_notation" title="Feynman slash notation">Feynman slash notation</a></li> <li><a href="/wiki/Feynman_parametrization" title="Feynman parametrization">Feynman parametrization</a></li> <li><a href="/wiki/Path_integral_formulation" title="Path integral formulation">Path integral formulation</a></li> <li><a href="/wiki/Parton_(particle_physics)" title="Parton (particle physics)">Parton model</a></li> <li><a href="/wiki/Sticky_bead_argument" title="Sticky bead argument">Sticky bead argument</a></li> <li><a href="/wiki/One-electron_universe" title="One-electron universe">One-electron universe</a></li> <li><a class="mw-selflink selflink">Quantum cellular automaton</a></li> <li><a href="/wiki/Rogers_Commission_Report" title="Rogers Commission Report">Rogers Commission Report</a></li> <li><a href="/wiki/Feynman_checkerboard" title="Feynman checkerboard">Feynman checkerboard</a></li> <li><a href="/wiki/Feynman_sprinkler" title="Feynman sprinkler">Feynman sprinkler</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Works</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>"<a href="/wiki/There%27s_Plenty_of_Room_at_the_Bottom" title="There's Plenty of Room at the Bottom">There's Plenty of Room at the Bottom</a>" <span style="font-size:85%;">(1959)</span></li> <li><i><a href="/wiki/The_Feynman_Lectures_on_Physics" title="The Feynman Lectures on Physics">The Feynman Lectures on Physics</a></i> <span style="font-size:85%;">(1964)</span></li> <li><i><a href="/wiki/The_Character_of_Physical_Law" title="The Character of Physical Law">The Character of Physical Law</a></i> <span style="font-size:85%;">(1965)</span></li> <li><i><a href="/wiki/QED:_The_Strange_Theory_of_Light_and_Matter" title="QED: The Strange Theory of Light and Matter">QED: The Strange Theory of Light and Matter</a></i> <span style="font-size:85%;">(1985)</span></li> <li><i><a href="/wiki/Surely_You%27re_Joking,_Mr._Feynman!" title="Surely You're Joking, Mr. Feynman!">Surely You're Joking, Mr. Feynman!</a></i> <span style="font-size:85%;">(1985)</span></li> <li><i><a href="/wiki/What_Do_You_Care_What_Other_People_Think%3F" title="What Do You Care What Other People Think?">What Do You Care What Other People Think?</a></i> <span style="font-size:85%;">(1988)</span></li> <li><i><a href="/wiki/Feynman%27s_Lost_Lecture" title="Feynman's Lost Lecture">Feynman's Lost Lecture: The Motion of Planets Around the Sun</a></i> <span style="font-size:85%;">(1997)</span></li> <li><i><a href="/wiki/The_Meaning_of_It_All" title="The Meaning of It All">The Meaning of It All</a></i> <span style="font-size:85%;">(1999)</span></li> <li><i><a href="/wiki/The_Pleasure_of_Finding_Things_Out" title="The Pleasure of Finding Things Out">The Pleasure of Finding Things Out</a></i> <span style="font-size:85%;">(1999)</span></li> <li><i><a href="/wiki/Perfectly_Reasonable_Deviations_from_the_Beaten_Track" title="Perfectly Reasonable Deviations from the Beaten Track">Perfectly Reasonable Deviations from the Beaten Track</a></i> <span style="font-size:85%;">(2005)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Family</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Joan_Feynman" title="Joan Feynman">Joan Feynman</a> <span style="font-size:85%;">(sister)</span></li> <li><a href="/wiki/Charles_Hirshberg" title="Charles Hirshberg">Charles Hirshberg</a> <span style="font-size:85%;">(nephew)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_things_named_after_Richard_Feynman" title="List of things named after Richard Feynman">Namesakes</a></li> <li><a href="/wiki/Cargo_cult_science" class="mw-redirect" title="Cargo cult science">Cargo cult science</a></li> <li><i><a href="/wiki/Quantum_Man:_Richard_Feynman%27s_Life_in_Science" title="Quantum Man: Richard Feynman's Life in Science">Quantum Man: Richard Feynman's Life in Science</a></i></li> <li><i><a href="/wiki/Tuva_or_Bust!" title="Tuva or Bust!">Tuva or Bust!</a></i></li> <li><a href="/wiki/Feynman_Prize_in_Nanotechnology" title="Feynman Prize in Nanotechnology">Feynman Prize in Nanotechnology</a></li> <li><a href="/wiki/Infinity_(1996_film)" title="Infinity (1996 film)"><i>Infinity</i> <small>(1996 film)</small></a></li> <li><a href="/wiki/QED_(play)" title="QED (play)"><i>QED</i> <span style="font-size:85%;">(2001 play)</span></a></li> <li><a href="/wiki/The_Challenger_Disaster" title="The Challenger Disaster"><i>The Challenger Disaster</i> <small>(2013 film)</small></a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: 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