# RXXGate

class RXXGate(theta, label=None)

GitHub

A parametric 2-qubit $X \otimes X$ interaction (rotation about XX).

This gate is symmetric, and is maximally entangling at $\theta = \pi/2$.

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

Circuit Symbol:

     ┌─────────┐
q_0: ┤1        ├
│  Rxx(ϴ) │
q_1: ┤0        ├
└─────────┘

Matrix Representation:

$\providecommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{XX}(\theta) = \exp\left(-i \th X{\otimes}X\right) = \begin{pmatrix} \cos\left(\th\right) & 0 & 0 & -i\sin\left(\th\right) \\ 0 & \cos\left(\th\right) & -i\sin\left(\th\right) & 0 \\ 0 & -i\sin\left(\th\right) & \cos\left(\th\right) & 0 \\ -i\sin\left(\th\right) & 0 & 0 & \cos\left(\th\right) \end{pmatrix}\end{split}$

Examples:

$R_{XX}(\theta = 0) = I$ $R_{XX}(\theta = \pi) = i X \otimes X$ $\begin{split}R_{XX}\left(\theta = \frac{\pi}{2}\right) = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 0 & 0 & -i \\ 0 & 1 & -i & 0 \\ 0 & -i & 1 & 0 \\ -i & 0 & 0 & 1 \end{pmatrix}\end{split}$

Create new RXX gate.

## Methods Defined Here

### inverse

RXXGate.inverse()

Return inverse RXX gate (i.e. with the negative rotation angle).

### power

RXXGate.power(exponent)

Raise gate to a power.

## 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.