# RZZGate¶

class RZZGate(theta)[source]

A parameteric 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.

Attributes

 RZZGate.decompositions Get the decompositions of the instruction from the SessionEquivalenceLibrary. RZZGate.definition Return definition in terms of other basic gates. RZZGate.label Return gate label RZZGate.params return instruction params.

Methods

 RZZGate.add_decomposition(decomposition) Add a decomposition of the instruction to the SessionEquivalenceLibrary. Assemble a QasmQobjInstruction RZZGate.broadcast_arguments(qargs, cargs) Validation and handling of the arguments and its relationship. RZZGate.c_if(classical, val) Add classical condition on register classical and value val. RZZGate.control([num_ctrl_qubits, label, …]) Return controlled version of gate. RZZGate.copy([name]) Copy of the instruction. Return inverse RZZ gate (i.e. Return True .IFF. For a composite instruction, reverse the order of sub-gates. RZZGate.power(exponent) Creates a unitary gate as gate^exponent. Return a default OpenQASM string for the instruction. Creates an instruction with gate repeated n amount of times. Return a Numpy.array for the gate unitary matrix.