# RZZGate¶

class RZZGate(theta, label=None)[ソース]

A parametric 2-qubit $$Z \otimes Z$$ interaction (rotation about ZZ).

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

Circuit Symbol:

q_0: ───■────
│zz(θ)
q_1: ───■────


Matrix Representation:

\begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{ZZ}(\theta) = exp(-i \th Z{\otimes}Z) = \begin{pmatrix} e^{-i \th} & 0 & 0 & 0 \\ 0 & e^{i \th} & 0 & 0 \\ 0 & 0 & e^{i \th} & 0 \\ 0 & 0 & 0 & e^{-i \th} \end{pmatrix}\end{split}\end{aligned}\end{align}

This is a direct sum of RZ rotations, so this gate is equivalent to a uniformly controlled (multiplexed) RZ gate:

$\begin{split}R_{ZZ}(\theta) = \begin{pmatrix} RZ(\theta) & 0 \\ 0 & RZ(-\theta) \end{pmatrix}\end{split}$

Examples:

$R_{ZZ}(\theta = 0) = I$
$R_{ZZ}(\theta = 2\pi) = -I$
$R_{ZZ}(\theta = \pi) = - Z \otimes Z$
$\begin{split}R_{ZZ}(\theta = \frac{\pi}{2}) = \frac{1}{\sqrt{2}} \begin{pmatrix} 1-i & 0 & 0 & 0 \\ 0 & 1+i & 0 & 0 \\ 0 & 0 & 1+i & 0 \\ 0 & 0 & 0 & 1-i \end{pmatrix}\end{split}$

Create new RZZ gate.

Methods Defined Here

 inverse Return inverse RZZ gate (i.e.

Attributes

condition_bits

Get Clbits in condition.

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

str

params

return instruction params.

unit

Get the time unit of duration.