Quantum Computation and Quantum Error Prevention

QWiki is up!

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

Let's see, let <left>Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\left\vert{\psi}\right\rangle}=\alpha{\left\vert{0}\right\rangle}+\beta{\left\vert{1}\right\rangle}} </left> then

${\left\vert {\psi }\right\rangle }\otimes \beta _{00}$ $=(\alpha {\left\vert {0}\right\rangle }+\beta {\left\vert {1}\right\rangle })\left({\frac {1}{\sqrt {2}}}({\left\vert {00}\right\rangle }+{\left\vert {11}\right\rangle })\right)$ $={\frac {1}{\sqrt {2}}}\left(\alpha {\left\vert {0}\right\rangle }({\left\vert {00}\right\rangle }+{\left\vert {11}\right\rangle })+\beta {\left\vert {1}\right\rangle }({\left\vert {00}\right\rangle }+{\left\vert {11}\right\rangle })\right)$ ${\;{{CNOT(1,2)} \atop \longrightarrow }\;}{\frac {1}{\sqrt {2}}}\left(\alpha {\left\vert {0}\right\rangle }({\left\vert {00}\right\rangle }+{\left\vert {11}\right\rangle })+\beta {\left\vert {1}\right\rangle }({\left\vert {10}\right\rangle }+{\left\vert {01}\right\rangle })\right)$ ${\;{{H(1)} \atop \longrightarrow }\;}{\frac {1}{\sqrt {2}}}\left(\alpha {\frac {1}{\sqrt {2}}}({\left\vert {0}\right\rangle }+{\left\vert {1}\right\rangle })({\left\vert {00}\right\rangle }+{\left\vert {11}\right\rangle })+\beta {\frac {1}{\sqrt {2}}}({\left\vert {0}\right\rangle }-{\left\vert {1}\right\rangle })({\left\vert {10}\right\rangle }+{\left\vert {01}\right\rangle })\right)$ $={\frac {1}{2}}\left({\left\vert {00}\right\rangle }(\alpha {\left\vert {0}\right\rangle }+\beta {\left\vert {1}\right\rangle })+{\left\vert {01}\right\rangle }(\alpha {\left\vert {1}\right\rangle }+\beta {\left\vert {0}\right\rangle })+{\left\vert {10}\right\rangle }(\alpha {\left\vert {0}\right\rangle }-\beta {\left\vert {1}\right\rangle })+{\left\vert {11}\right\rangle }(\alpha {\left\vert {1}\right\rangle }-\beta {\left\vert {0}\right\rangle })\right)$ Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle =\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}}