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. Z | 0 ⟩ = | 0 ⟩ {\displaystyle Z|0\rangle =|0\rangle } Z | 1 ⟩ = − | 1 ⟩ {\displaystyle Z|1\rangle =-|1\rangle } H | 0 ⟩ = 1 2 ( | 0 ⟩ + | 1 ⟩ ) {\displaystyle H|0\rangle ={\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle )} X 1 2 ( | 0 ⟩ + | 1 ⟩ ) = 1 2 ( + | 0 ⟩ + | 1 ⟩ ) {\displaystyle X{\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle )={\frac {1}{\sqrt {2}}}(+|0\rangle +|1\rangle )} H 1 2 ( | 0 ⟩ + | 1 ⟩ ) = | 0 ⟩ {\displaystyle H{\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle )=|0\rangle } H | 1 ⟩ = 1 2 ( | 0 ⟩ − | 1 ⟩ ) {\displaystyle H|1\rangle ={\frac {1}{\sqrt {2}}}(|0\rangle -|1\rangle )} X 1 2 ( | 0 ⟩ − | 1 ⟩ ) = 1 2 ( − | 0 ⟩ + | 1 ⟩ ) = − 1 2 ( | 0 ⟩ − | 1 ⟩ ) {\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 )} H 1 2 ( − | 0 ⟩ + | 1 ⟩ ) = − | 1 ⟩ {\displaystyle H{\frac {1}{\sqrt {2}}}(-|0\rangle +|1\rangle )=-|1\rangle }
ZH=HXHH
H | 0 ⟩ = 1 2 ( | 0 ⟩ + | 1 ⟩ ) {\displaystyle H|0\rangle ={\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle )} H 1 2 ( | 0 ⟩ + | 1 ⟩ ) = | 0 ⟩ {\displaystyle H{\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle )=|0\rangle } X | 0 ⟩ = | 1 ⟩ {\displaystyle X|0\rangle =|1\rangle } H | 1 ⟩ = 1 2 ( | 0 ⟩ − | 1 ⟩ ) {\displaystyle H|1\rangle ={\frac {1}{\sqrt {2}}}(|0\rangle -|1\rangle )} Taigi:
Z 1 2 ( | 0 ⟩ + | 1 ⟩ ) → 1 2 ( | 0 ⟩ − | 1 ⟩ ) {\displaystyle Z{\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle )\rightarrow {\frac {1}{\sqrt {2}}}(|0\rangle -|1\rangle )} O ant vieneto superpozicijos:
Z 1 2 ( | 0 ⟩ − | 1 ⟩ ) → 1 2 ( | 0 ⟩ + | 1 ⟩ ) {\displaystyle Z{\frac {1}{\sqrt {2}}}(|0\rangle -|1\rangle )\rightarrow {\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle )}
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