RXXGate¶

class RXXGate(theta, label=None)[source]¶

Bases: Gate

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:

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

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`	Return inverse RXX gate (i.e.
`power`	Raise gate to a power.

Attributes

condition_bits¶: Get Clbits in condition.

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

name¶: 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.