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*Controlled-NOT(CX): | *Controlled-NOT(CX): | ||
*Controlled-Phase(CZ): <br/> | *Controlled-Phase(CZ): <br/> | ||
The commutation relations for the above gates are as follows: | The commutation relations for the above gates are as follows:<br/> | ||
XH = HZ, XZ = −ZX<br/> | XH = HZ, XZ = −ZX<br/> | ||
(X ⊗ I)CZ = CZ(X ⊗ Z), (Z ⊗ I)CZ = CZ(Z ⊗ I) 1 <br/> | (X ⊗ I)CZ = CZ(X ⊗ Z), (Z ⊗ I)CZ = CZ(Z ⊗ I) 1 <br/> | ||