125 lines
2.9 KiB
Plaintext
125 lines
2.9 KiB
Plaintext
---
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title: RZZGate
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description: API reference for qiskit.circuit.library.RZZGate
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in_page_toc_min_heading_level: 1
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python_api_type: class
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python_api_name: qiskit.circuit.library.RZZGate
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---
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# RZZGate
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<Class id="qiskit.circuit.library.RZZGate" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.18/qiskit/circuit/library/standard_gates/rzz.py" signature="RZZGate(theta)" modifiers="class">
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Bases: `qiskit.circuit.gate.Gate`
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A parametric 2-qubit $Z \otimes Z$ interaction (rotation about ZZ).
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This gate is symmetric, and is maximally entangling at $\theta = \pi/2$.
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**Circuit Symbol:**
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```python
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q_0: ───■────
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│zz(θ)
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q_1: ───■────
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```
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**Matrix Representation:**
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$$
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\begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{ZZ}(\theta) = exp(-i \th Z{\otimes}Z) =
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\begin{pmatrix}
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e^{-i \th} & 0 & 0 & 0 \\
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0 & e^{i \th} & 0 & 0 \\
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0 & 0 & e^{i \th} & 0 \\
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0 & 0 & 0 & e^{-i \th}
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\end{pmatrix}\end{split}\end{aligned}\end{align}
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$$
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This is a direct sum of RZ rotations, so this gate is equivalent to a uniformly controlled (multiplexed) RZ gate:
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$$
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\begin{split}R_{ZZ}(\theta) =
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\begin{pmatrix}
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RZ(\theta) & 0 \\
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0 & RZ(-\theta)
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\end{pmatrix}\end{split}
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$$
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**Examples:**
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> $$
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> R_{ZZ}(\theta = 0) = I
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> $$
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>
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> $$
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> R_{ZZ}(\theta = 2\pi) = -I
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> $$
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>
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> $$
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> R_{ZZ}(\theta = \pi) = - Z \otimes Z
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> $$
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>
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> $$
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> \begin{split}R_{ZZ}(\theta = \frac{\pi}{2}) = \frac{1}{\sqrt{2}}
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> \begin{pmatrix}
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> 1-i & 0 & 0 & 0 \\
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> 0 & 1+i & 0 & 0 \\
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> 0 & 0 & 1+i & 0 \\
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> 0 & 0 & 0 & 1-i
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> \end{pmatrix}\end{split}
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> $$
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Create new RZZ gate.
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## Methods Defined Here
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### inverse
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<Function id="qiskit.circuit.library.RZZGate.inverse" signature="RZZGate.inverse()">
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Return inverse RZZ gate (i.e. with the negative rotation angle).
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</Function>
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## Attributes
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### decompositions
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<Attribute id="qiskit.circuit.library.RZZGate.decompositions">
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Get the decompositions of the instruction from the SessionEquivalenceLibrary.
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</Attribute>
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### definition
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<Attribute id="qiskit.circuit.library.RZZGate.definition">
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Return definition in terms of other basic gates.
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</Attribute>
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### duration
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<Attribute id="qiskit.circuit.library.RZZGate.duration">
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Get the duration.
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</Attribute>
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### label
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<Attribute id="qiskit.circuit.library.RZZGate.label">
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Return instruction label
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**Return type**
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`str`
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</Attribute>
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### params
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<Attribute id="qiskit.circuit.library.RZZGate.params">
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return instruction params.
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</Attribute>
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### unit
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<Attribute id="qiskit.circuit.library.RZZGate.unit">
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Get the time unit of duration.
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</Attribute>
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</Class>
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