Quantum – Circuits – CZ

CZ Gate

The quantum CZ gate, the controlled Z gate,  phase-flips the second qubit in a multipart qubit whenever the first qubit is j^v and the second qubit is j^v. The first qubit is the control and the CZ gate works as follows:

• CZ|j^{^}j^{^}> =    
  • = |j^{^}j^{^}>

• CZ|j^vj^{^}> =    
  • = |j^vj^{^}>

• CZ|j^vj^v> =    
  • = |j^{^-}j^{^}> = ^–|j^{^}j^{^}>

Note that all gates are unitary and as such the quantum CZ gate is reversible.

• CZ^–|j^vj^v> =    
  • = |j^vj^v>

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