$X$
Paulis & basics 1 qubit
Pauli-X
Bit-flip gate that swaps $|0\rangle$ and $|1\rangle$.
Open in Quirk ↗
hermitian
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.
The unitary, drawn
Every entry of the matrix as a disc. The area is the transition probability $|U_{jk}|^2$; the colour and the hand are the phase. Rows are outputs $\langle j|$, columns inputs $|k\rangle$, in the computational basis.
Phase
Disc area $= |U_{jk}|^2$. Hover an entry for its value, or take the JSON.
SDK support
How to call this gate in each framework. Hover a ⓘ for a note; the support matrix compares every gate at once.
| SDK | Name |
|---|---|
| Qiskit | qiskit.circuit.library.XGate |
| PennyLane | pennylane.PauliX |
| Cirq | cirq.X |
| Q# | Std.Intrinsic.X |
| PyQuil | pyquil.gates.X |
| Braket | braket.circuits.gates.X |
| BQSKit | bqskit.ir.gates.XGate |
| Qibo | qibo.gates.X |
| pytket | pytket.circuit.OpType.X |
| Stim | X |
| OpenQASM | stdgates.inc: x |