Fazės vartai (angl. phase gate) – tai kvantiniai vartai, naudojami kvantiniuose kompiuteriuose ir žymimi Z.

Z vartai gaunami nuosekliai išdėsčius Hadamardo vartus, paskui NOT vartus, o paskui vėl Hadamardo vartus:

-H-X-H- = -Z- arba Z=HXH.

${\displaystyle Z|0\rangle =|0\rangle }$.

${\displaystyle Z|1\rangle =-|1\rangle }$.

${\displaystyle H|0\rangle ={\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle )}$.

${\displaystyle X{\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle )={\frac {1}{\sqrt {2}}}(+|0\rangle +|1\rangle )}$.

${\displaystyle H{\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle )=|0\rangle }$.

${\displaystyle H|1\rangle ={\frac {1}{\sqrt {2}}}(|0\rangle -|1\rangle )}$.

${\displaystyle X{\frac {1}{\sqrt {2}}}(|0\rangle -|1\rangle )={\frac {1}{\sqrt {2}}}(-|0\rangle +|1\rangle )=-{\frac {1}{\sqrt {2}}}(|0\rangle -|1\rangle )}$.

${\displaystyle H{\frac {1}{\sqrt {2}}}(-|0\rangle +|1\rangle )=-|1\rangle }$.

ZH=HXHH

${\displaystyle H|0\rangle ={\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle )}$.

${\displaystyle H{\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle )=|0\rangle }$.

${\displaystyle X|0\rangle =|1\rangle }$.

${\displaystyle H|1\rangle ={\frac {1}{\sqrt {2}}}(|0\rangle -|1\rangle )}$.

Taigi:

${\displaystyle Z{\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle )\rightarrow {\frac {1}{\sqrt {2}}}(|0\rangle -|1\rangle )}$.

O ant vieneto superpozicijos:

${\displaystyle Z{\frac {1}{\sqrt {2}}}(|0\rangle -|1\rangle )\rightarrow {\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle )}$.

Hadamardo vartai

CNOT vartai

Kvantiniai NOT vartai

Fazės vartai

Tofolio vartai

• Controlled-Z vartai su fotonais - PDF