CNOT Gate (CX) | Controlled-NOT Entanglement Generator
Quick Technical Answer:
The CNOT (Controlled-NOT or CX) gate is a fundamental 2-qubit entangling gate. If the control qubit is |1⟩, it flips the target qubit via Pauli-X; if the control is |0⟩, the target qubit remains unchanged.
Formula / Unitary:
CX = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{pmatrix}, \quad CX|c, t\rangle = |c, c \oplus t\rangle
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Bell State & Maximal Entanglement Generation
When a CNOT gate is preceded by a Hadamard gate on the control qubit (H on q0, CX from q0 to q1), it creates the maximally entangled Bell state (|00⟩ + |11⟩)/√2, proving Einstein-Podolsky-Rosen (EPR) quantum correlation.
CNOT 2-Qubit Truth Table
| Input |Control, Target⟩ | Output |Control, Target⟩ | Action on Target |
|---|---|---|
| |00⟩ | |00⟩ | No Flip (Control is 0) |
| |01⟩ | |01⟩ | No Flip (Control is 0) |
| |10⟩ | |11⟩ | Flipped 0 → 1 (Control is 1) |
| |11⟩ | |10⟩ | Flipped 1 → 0 (Control is 1) |
Frequently Asked Questions
Can CNOT be reversed if control and target are swapped?
Swapping control and target can be achieved by placing Hadamard gates on both qubits before and after the CNOT: (H ⊗ H) · CX · (H ⊗ H) = CX_reversed.