RXXGate

class RXXGate(theta)

Bases: qiskit.circuit.gate.Gate

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

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

Circuit Symbol:

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

Matrix Representation:

\[ \begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{XX}(\theta) = exp(-i \th X{\otimes}X) = \begin{pmatrix} \cos(\th) & 0 & 0 & -i\sin(\th) \\ 0 & \cos(\th) & -i\sin(\th) & 0 \\ 0 & -i\sin(\th) & \cos(\th) & 0 \\ -i\sin(\th) & 0 & 0 & \cos(\th) \end{pmatrix}\end{split}\end{aligned}\end{align} \]

Examples:

\[R_{XX}(\theta = 0) = I\]

\[R_{XX}(\theta = \pi) = i X \otimes X\]

\[\begin{split}R_{XX}(\theta = \frac{\pi}{2}) = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 0 & 0 & -i \\ 0 & 1 & -i & 0 \\ 0 & -i & 1 & 0 \\ -i & 0 & 0 & 1 \end{pmatrix}\end{split}\]

Create new RXX gate.

Methods Defined Here

inverse

Return inverse RXX gate (i.e.

Attributes

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

params

return instruction params.

unit

Get the time unit of duration.