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In [[quantum computing]], a '''graph state''' is a special type of multi-[[qubit]] state that can be represented by a [[graph (mathematics)|graph]]. Each qubit is represented by a [[Vertex (graph theory)|vertex]] of the graph, and there is an edge between every interacting pair of qubits. In particular, they are a convenient way of representing certain types of [[entangled]] states.
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


Graph states are useful in [[quantum error-correcting code]]s, entanglement measurement and purification and for characterization of computational resources in measurement based quantum computing models.
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


== Formal definition ==
Registered users will be able to choose between the following three rendering modes:


Given a graph ''G'' = (''V'', ''E''), with the set of [[vertex (graph theory)|vertices]] ''V'' and the set of [[Glossary of graph theory#Basics|edges]] ''E'', the corresponding graph state is defined as
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


:<math>{\left| G \right\rangle} =\prod _{(a,b)\in E}U^{\{ a,b\} } {\left| + \right\rangle} ^{\otimes V}</math>
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


where the operator <math>U^{\{ a,b\} }</math> is the [[Quantum_gate#Controlled_gates|controlled-''Z'']] interaction between the two vertices (qubits) ''a'', ''b''
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


:<math> U^{\{ a,b\} } =\left[\begin{array}{cccc} {1} & {0} & {0} & {0} \\ {0} & {1} & {0} & {0} \\ {0} & {0} & {1} & {0} \\ {0} & {0} & {0} & {-1} \end{array}\right]</math>
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


And
==Demos==


:<math>{\left| + \right\rangle} =\frac{{\left| 0 \right\rangle} +{\left| 1 \right\rangle} }{\sqrt{2} } </math>
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


=== Alternative definition ===


An alternative and equivalent definition is the following.
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


Define an operator <math>K_{G}^{(a)}</math> for each vertex ''a'' of ''G'':
==Test pages ==


:<math>K_{G}^{(a)} =\sigma _{x}^{(a)} \prod _{b\in N(a)}\sigma _{z}^{(b)}    </math>
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


where ''N''(''a'') is the neighborhood of ''a'' (that is, the set of all ''b'' such that <math>(a,b)\in E</math>) and <math> \sigma _{x,y,z}</math> are the [[pauli matrices]]. The graph state <math>{\left| G \right\rangle}</math> is then defined as the simultaneous eigenstate of the <math>N=\left|V\right|</math> operators <math> \left\{K_{G}^{(a)} \right\}_{a\in V} </math> with eigenvalue 1:
*[[Inputtypes|Inputtypes (private Wikis only)]]
 
*[[Url2Image|Url2Image (private Wikis only)]]
:<math>K_{G}^{(a)} {\left| G \right\rangle} ={\left| G \right\rangle} </math>
==Bug reporting==
 
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
== See also ==
* [[Entanglement]]
* [[Cluster state]]
 
==References==
* {{cite journal | author=M. Hein, J. Eisert, and H. J. Briegel | title=Multiparty entanglement in graph states| journal=[[Physical Review A]] | year=2004| volume=69 | pages=062311 | doi=10.1103/PhysRevA.69.062311}}
* {{cite journal | author=S. Anders and H. J. Briegel | title=Fast simulation of stabilizer circuits using a graph-state representation| journal=[[Physical Review A]] | year=2006| volume=73 | pages=022334 | doi=10.1103/PhysRevA.73.022334  }}
*[http://xstructure.inr.ac.ru/x-bin/theme3.py?level=1&index1=423009  Graph states on arxiv.org]
 
[[Category:Quantum information science]]
 
 
{{Comp-sci-stub}}

Latest revision as of 23:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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