# RZZGate¶

class RZZGate(theta, label=None)[Quellcode]

Bases: Gate

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

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

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

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\left(-i \th Z{\otimes}Z\right) = \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:

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

Create new RZZ gate.

Methods Defined Here

 inverse Return inverse RZZ gate (i.e.

Attributes

condition_bits

Get Clbits in condition.

Rückgabetyp

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

Rückgabetyp

str

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.