Kreuter: Created page with ''''QWiki is up!''' Here's a random test of math functions (from quantiki.org): Let's see, let ${\left\vert{\psi}\right\rangle}=\alpha{\left\vert{0}\right\ran…'$

2010-01-27T07:23:49Z

Created page with '<big>'''QWiki is up!'''</big> Here's a random test of math functions (from quantiki.org): Let's see, let <math> {\left\vert{\psi}\right\rangle}=\alpha{\left\vert{0}\right\ran…'

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<big>'''QWiki is up!'''</big>

Here's a random test of math functions (from quantiki.org):

Let's see, let
<math> {\left\vert{\psi}\right\rangle}=\alpha{\left\vert{0}\right\rangle}+\beta{\left\vert{1}\right\rangle}</math>
then
<center><math> {\left\vert{\psi}\right\rangle} \otimes \beta_{00} </math></center>

<center><math>=(\alpha{\left\vert{0}\right\rangle}+\beta{\left\vert{1}\right\rangle})\left(\frac{1}{\sqrt{2}}({\left\vert{00}\right\rangle}+{\left\vert{11}\right\rangle})\right)</math></center>

<center><math>=\frac{1}{\sqrt{2}}\left(\alpha{\left\vert{0}\right\rangle}({\left\vert{00}\right\rangle}+{\left\vert{11}\right\rangle})+\beta{\left\vert{1}\right\rangle}({\left\vert{00}\right\rangle}+{\left\vert{11}\right\rangle})\right)</math></center>

<center><math>{\;{{CNOT(1,2)} \atop \longrightarrow}\;}
\frac{1}{\sqrt{2}}\left(\alpha{\left\vert{0}\right\rangle}({\left\vert{00}\right\rangle}+{\left\vert{11}\right\rangle})+\beta{\left\vert{1}\right\rangle}({\left\vert{10}\right\rangle}+{\left\vert{01}\right\rangle})\right)</math></center>

<center><math>{\;{{H(1)} \atop \longrightarrow}\;}
\frac{1}{\sqrt{2}}\left(\alpha\frac{1}{\sqrt{2}}({\left\vert{0}\right\rangle}+{\left\vert{1}\right\rangle})({\left\vert{00}\right\rangle}+{\left\vert{11}\right\rangle})+\beta\frac{1}{\sqrt{2}}({\left\vert{0}\right\rangle}-{\left\vert{1}\right\rangle})({\left\vert{10}\right\rangle}+{\left\vert{01}\right\rangle})\right)</math></center>

<center><math>=\frac{1}{2}\left({\left\vert{00}\right\rangle}(\alpha{\left\vert{0}\right\rangle}+\beta{\left\vert{1}\right\rangle}) +{\left\vert{01}\right\rangle}(\alpha{\left\vert{1}\right\rangle}+\beta{\left\vert{0}\right\rangle})
+{\left\vert{10}\right\rangle}(\alpha{\left\vert{0}\right\rangle}-\beta{\left\vert{1}\right\rangle})
+{\left\vert{11}\right\rangle}(\alpha{\left\vert{1}\right\rangle}-\beta{\left\vert{0}\right\rangle})\right)</math></center>

<center><math>=\frac{1}{2}\sum_{b_1b_2=0}^{1}{\left\vert{b_1 b_2}\right\rangle}(X^{b_2}Z^{b_1}){\left\vert{\psi}\right\rangle}</math></center>

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Kreuter: Created page with ''''QWiki is up!''' Here's a random test of math functions (from quantiki.org): Let's see, let {\left\vert{\psi}\right\rangle}=\alpha{\left\vert{0}\right\ran…'

Kreuter: Created page with ''''QWiki is up!''' Here's a random test of math functions (from quantiki.org): Let's see, let ${\left\vert{\psi}\right\rangle}=\alpha{\left\vert{0}\right\ran…'$