quantum gate directory
Pauli-X
Symbol
$X$
Description:
Bit-flip gate that swaps $|0\rangle$ and $|1\rangle$.
Alternate notations:
- $X$
- $\sigma_x$
- $\sigma^x$
- $\sigma_1$
- $\mathrm{NOT}$
SDK Support
| SDK | Name |
|---|---|
| Qiskit |
qiskit.circuit.library.XGate
|
| PennyLane |
pennylane.PauliX
|
| Cirq |
cirq.X
|
| Q# | — |
| PyQuil | — |
| Braket | — |
| BQSKit | — |
Groups
This gate is contained in the following groups:
The Pauli-$X$ gate is the quantum analog of a classical NOT.
$$ X = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} $$
Properties
- Hermitian and self-inverse: $X^\dagger = X$ and $X^2 = I$.
- Equivalent to a $R_x(\pi)$ up to global phase.
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