Quantum – Circuits – CNOT

CNOT  Gate 

The quantum CNOT gate, controlled not, inverts the second qubit in a multipart qubit whenever the first qubit is j^v. The first qubit is the control.

Examples of Quantum CNOT Gate

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

• CNOT |j^{^}j^v> =  
  • = |j^{^}j^v>

• CNOT |j^vj^{^}> =    
  • = |j^vj^v>

• CNOT |j^vj^v> =    
  • = |j^vj^{^}> 

• CNOT ^–|j^vj^{^}> =    
  • = ^–|j^vj^v>

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

• CNOT ^–|j^vj^v> =    
  • = ^–|j^vj^{^}>

See the Bellagio circuit for examples of the CNOT gate.

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Quantum CNOT Gate in Dirac State Format

• CNOT |j^{^}j^{^}> =  |j^{^}j^{^}>
• CNOT |j^{^}j^v> = |j^{^}j^v>
• CNOT |j^vj^{^}> = |j^vj^v >
• CNOT |j^vj^v> = |j^vj^{^}>
• CNOT ^–|j^vj^{^}> = ^–|j^vj^v >
• CNOT ^–|j^vj^v> = ^–|j^vj^{^}>

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