# RZZGate

class RZZGate(theta, label=None)

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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:

$\providecommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{ZZ}(\theta) = \exp\left(-i \th Z{\otimes}Z\right) = \begin{pmatrix} e^{-i \th} & 0 & 0 & 0 \\ 0 & e^{i \th} & 0 & 0 \\ 0 & 0 & e^{i \th} & 0 \\ 0 & 0 & 0 & e^{-i \th} \end{pmatrix}\end{split}$

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

RZZGate.inverse()

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

### power

RZZGate.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.