Quantum Computation and Quantum Error Prevention

QWiki is up!

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

Let's see, let ${\left\vert {\psi }\right\rangle }=\alpha {\left\vert {0}\right\rangle }+\beta {\left\vert {1}\right\rangle }$ then

${\left\vert {\psi }\right\rangle }\otimes \beta _{00}$ $=(\alpha {\left\vert {0}\right\rangle }+\beta {\left\vert {1}\right\rangle })\left({\frac {1}{\sqrt {2}}}({\left\vert {00}\right\rangle }+{\left\vert {11}\right\rangle })\right)$ $={\frac {1}{\sqrt {2}}}\left(\alpha {\left\vert {0}\right\rangle }({\left\vert {00}\right\rangle }+{\left\vert {11}\right\rangle })+\beta {\left\vert {1}\right\rangle }({\left\vert {00}\right\rangle }+{\left\vert {11}\right\rangle })\right)$ ${\;{{CNOT(1,2)} \atop \longrightarrow }\;}{\frac {1}{\sqrt {2}}}\left(\alpha {\left\vert {0}\right\rangle }({\left\vert {00}\right\rangle }+{\left\vert {11}\right\rangle })+\beta {\left\vert {1}\right\rangle }({\left\vert {10}\right\rangle }+{\left\vert {01}\right\rangle })\right)$ 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 {\;{{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)} $={\frac {1}{2}}\left({\left\vert {00}\right\rangle }(\alpha {\left\vert {0}\right\rangle }+\beta {\left\vert {1}\right\rangle })+{\left\vert {01}\right\rangle }(\alpha {\left\vert {1}\right\rangle }+\beta {\left\vert {0}\right\rangle })+{\left\vert {10}\right\rangle }(\alpha {\left\vert {0}\right\rangle }-\beta {\left\vert {1}\right\rangle })+{\left\vert {11}\right\rangle }(\alpha {\left\vert {1}\right\rangle }-\beta {\left\vert {0}\right\rangle })\right)$ $={\frac {1}{2}}\sum _{b_{1}b_{2}=0}^{1}{\left\vert {b_{1}b_{2}}\right\rangle }(X^{b_{2}}Z^{b_{1}}){\left\vert {\psi }\right\rangle }$