RZZGate#

class qiskit.circuit.library.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.

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.

Methods

inverse()[Quellcode]#: Return inverse RZZ gate (i.e. with the negative rotation angle).

power(exponent)[Quellcode]#

Raise gate to a power.