Source-verifiedLevel 2
CNOT Gate
The CNOT (Controlled-NOT) gate is a two-qubit gate that flips the target qubit if and only if the control qubit is |1⟩, serving as the fundamental entangling gate in quantum computing.
What it means
The CNOT gate is the most important two-qubit gate.It applies a Pauli-X (NOT) to the target qubit conditioned on the control qubit being in state |1⟩.Its truth table is: |00⟩→|00⟩, |01⟩→|01⟩, |10⟩→|11⟩, |11⟩→|10⟩.When the control qubit is in superposition, CNOT creates entanglement: H|0⟩⊗|0⟩ followed by CNOT produces the Bell state (|00⟩+|11⟩)/√2.CNOT is part of the universal gate set {H, T, CNOT} and is essential for quantum error correction, teleportation, and virtually all quantum algorithms.Everyday analogy
The CNOT gate is like a conditional light switch -- if the master switch (control) is ON, the secondary switch (target) toggles; if the master is OFF, nothing happens.
Think of it as a quantum XOR gate -- the target qubit becomes the XOR of the control and target inputs.
Common misconceptions
- CNOT is NOT symmetric -- swapping control and target gives a different operation (though they are related by Hadamard conjugation).
- CNOT alone cannot create entanglement -- the control qubit must be in a superposition state for entanglement to occur.
Key takeaways
- CNOT flips the target qubit conditioned on the control qubit being |1⟩.
- CNOT + superposition = entanglement; it is the primary entangling gate.
- Part of the universal gate set {H, T, CNOT}.
Check your understanding
What is the output of CNOT applied to |10⟩ (control=|1⟩, target=|0⟩)?
- A.|10⟩
- B.|11⟩
- C.|00⟩
- D.|01⟩
Show the answer
Answer: B. |11⟩
Why: Since the control is |1⟩, the target is flipped from |0⟩ to |1⟩, giving |11⟩.
Builds on
Primary source: Barenco et al., Phys. Rev. A 52, 3457 (1995), doi:10.1103/PhysRevA.52.3457
Learn it hands-on
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