quantum gate directory
Controlled Not
Symbol
$\mathrm{C}X$
Description:
Flips the target qubit when the control qubit is in the $|1\rangle$ state.
Alternate notations:
- $\mathrm{C}X$
- $\mathrm{CNOT}$
- $\mathrm{CNOT}_{ij}$
- $\text{controlled-}X$
- $\Lambda(X)$
- $\mathrm{XOR}[i, j]$
SDK Support
| SDK | Name |
|---|---|
| Qiskit |
qiskit.circuit.library.CXGate
|
| PennyLane |
pennylane.CNOT
|
| Cirq |
cirq.CNOT
|
| Q# |
Std.Intrinsic.CNOT
|
| PyQuil |
pyquil.gates.CNOT
|
| Braket | — |
| BQSKit | — |
Groups
This gate is contained in the following groups:
The controlled-NOT (CNOT) gate is a two-qubit entangling gate that conditionally applies $X$ to the target.
$$ \mathrm{C}X = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{bmatrix} $$
Properties
- Self-inverse and Hermitian: $\mathrm{CNOT}^\dagger = \mathrm{CNOT}$.
- Equivalent to a controlled-$Z$ up to Hadamards on the target: $\mathrm{CNOT} = (I \otimes H),\mathrm{CZ},(I \otimes H)$.
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