157 lines
3.8 KiB
Plaintext
157 lines
3.8 KiB
Plaintext
---
|
|
title: RZZGate
|
|
description: API reference for qiskit.circuit.library.RZZGate
|
|
in_page_toc_min_heading_level: 1
|
|
python_api_type: class
|
|
python_api_name: qiskit.circuit.library.RZZGate
|
|
---
|
|
|
|
# RZZGate
|
|
|
|
<Class id="qiskit.circuit.library.RZZGate" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.24/qiskit/circuit/library/standard_gates/rzz.py" signature="RZZGate(theta, label=None)" modifiers="class">
|
|
Bases: [`Gate`](qiskit.circuit.Gate "qiskit.circuit.gate.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`](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit") with the [`rzz()`](qiskit.circuit.QuantumCircuit#rzz "qiskit.circuit.QuantumCircuit.rzz") method.
|
|
|
|
**Circuit Symbol:**
|
|
|
|
```python
|
|
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
|
|
|
|
<span id="qiskit-circuit-library-rzzgate-inverse" />
|
|
|
|
### inverse
|
|
|
|
<Function id="qiskit.circuit.library.RZZGate.inverse" signature="RZZGate.inverse()">
|
|
Return inverse RZZ gate (i.e. with the negative rotation angle).
|
|
</Function>
|
|
|
|
<span id="qiskit-circuit-library-rzzgate-power" />
|
|
|
|
### power
|
|
|
|
<Function id="qiskit.circuit.library.RZZGate.power" signature="RZZGate.power(exponent)">
|
|
Raise gate to a power.
|
|
</Function>
|
|
|
|
## Attributes
|
|
|
|
### condition\_bits
|
|
|
|
<Attribute id="qiskit.circuit.library.RZZGate.condition_bits">
|
|
Get Clbits in condition.
|
|
</Attribute>
|
|
|
|
### decompositions
|
|
|
|
<Attribute id="qiskit.circuit.library.RZZGate.decompositions">
|
|
Get the decompositions of the instruction from the SessionEquivalenceLibrary.
|
|
</Attribute>
|
|
|
|
### definition
|
|
|
|
<Attribute id="qiskit.circuit.library.RZZGate.definition">
|
|
Return definition in terms of other basic gates.
|
|
</Attribute>
|
|
|
|
### duration
|
|
|
|
<Attribute id="qiskit.circuit.library.RZZGate.duration">
|
|
Get the duration.
|
|
</Attribute>
|
|
|
|
### label
|
|
|
|
<Attribute id="qiskit.circuit.library.RZZGate.label">
|
|
Return instruction label
|
|
</Attribute>
|
|
|
|
### name
|
|
|
|
<Attribute id="qiskit.circuit.library.RZZGate.name">
|
|
Return the name.
|
|
</Attribute>
|
|
|
|
### num\_clbits
|
|
|
|
<Attribute id="qiskit.circuit.library.RZZGate.num_clbits">
|
|
Return the number of clbits.
|
|
</Attribute>
|
|
|
|
### num\_qubits
|
|
|
|
<Attribute id="qiskit.circuit.library.RZZGate.num_qubits">
|
|
Return the number of qubits.
|
|
</Attribute>
|
|
|
|
### params
|
|
|
|
<Attribute id="qiskit.circuit.library.RZZGate.params">
|
|
return instruction params.
|
|
</Attribute>
|
|
|
|
### unit
|
|
|
|
<Attribute id="qiskit.circuit.library.RZZGate.unit">
|
|
Get the time unit of duration.
|
|
</Attribute>
|
|
</Class>
|
|
|