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# XGate

class XGate(label=None)

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The single-qubit Pauli-X gate ($\sigma_x$).

Can be applied to a QuantumCircuit with the x() method.

Matrix Representation:

$\begin{split}X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\end{split}$

Circuit symbol:

     ┌───┐
q_0: ┤ X ├
└───┘

Equivalent to a $\pi$ radian rotation about the X axis.

Note

A global phase difference exists between the definitions of $RX(\pi)$ and $X$.

$\begin{split}RX(\pi) = \begin{pmatrix} 0 & -i \\ -i & 0 \end{pmatrix} = -i X\end{split}$

The gate is equivalent to a classical bit flip.

$\begin{split}|0\rangle \rightarrow |1\rangle \\ |1\rangle \rightarrow |0\rangle\end{split}$

Create new X gate.

## Methods Defined Here

### control

XGate.control(num_ctrl_qubits=1, label=None, ctrl_state=None)

Return a (multi-)controlled-X gate.

One control returns a CX gate. Two controls returns a CCX gate.

Parameters

• num_ctrl_qubits (int) – number of control qubits.
• label (str or None) – An optional label for the gate [Default: None]
• ctrl_state (int or str or None) – control state expressed as integer, string (e.g. ‘110’), or None. If None, use all 1s.

Returns

controlled version of this gate.

Return type

ControlledGate

### inverse

XGate.inverse()

Return inverted X gate (itself).

## Attributes

### condition_bits

Get Clbits in condition.

Return type

List[Clbit]

### decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

### definition

Return definition in terms of other basic gates.

### duration

Get the duration.

### label

Return instruction label

Return type

str

Return the name.

### num_clbits

Return the number of clbits.

### num_qubits

Return the number of qubits.

### params

return instruction params.

### unit

Get the time unit of duration.