141 lines
3.7 KiB
Plaintext
141 lines
3.7 KiB
Plaintext
---
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title: RXXGate
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description: API reference for qiskit.circuit.library.RXXGate
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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.RXXGate
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---
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# RXXGate
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<Class id="qiskit.circuit.library.RXXGate" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.25/qiskit/circuit/library/standard_gates/rxx.py" signature="qiskit.circuit.library.RXXGate(theta, label=None)" modifiers="class">
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Bases: [`Gate`](qiskit.circuit.Gate "qiskit.circuit.gate.Gate")
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A parametric 2-qubit $X \otimes X$ interaction (rotation about XX).
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This gate is symmetric, and is maximally entangling at $\theta = \pi/2$.
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Can be applied to a [`QuantumCircuit`](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit") with the [`rxx()`](qiskit.circuit.QuantumCircuit#rxx "qiskit.circuit.QuantumCircuit.rxx") method.
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**Circuit Symbol:**
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```python
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┌─────────┐
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q_0: ┤1 ├
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│ Rxx(ϴ) │
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q_1: ┤0 ├
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└─────────┘
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```
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**Matrix Representation:**
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$$
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\begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{XX}(\theta) = \exp\left(-i \th X{\otimes}X\right) =
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\begin{pmatrix}
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\cos\left(\th\right) & 0 & 0 & -i\sin\left(\th\right) \\
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0 & \cos\left(\th\right) & -i\sin\left(\th\right) & 0 \\
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0 & -i\sin\left(\th\right) & \cos\left(\th\right) & 0 \\
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-i\sin\left(\th\right) & 0 & 0 & \cos\left(\th\right)
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\end{pmatrix}\end{split}\end{aligned}\end{align}
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$$
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**Examples:**
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> $$
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> R_{XX}(\theta = 0) = I
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> $$
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>
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> $$
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> R_{XX}(\theta = \pi) = i X \otimes X
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> $$
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>
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> $$
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> \begin{split}R_{XX}\left(\theta = \frac{\pi}{2}\right) = \frac{1}{\sqrt{2}}
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> \begin{pmatrix}
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> 1 & 0 & 0 & -i \\
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> 0 & 1 & -i & 0 \\
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> 0 & -i & 1 & 0 \\
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> -i & 0 & 0 & 1
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> \end{pmatrix}\end{split}
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> $$
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Create new RXX gate.
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## Attributes
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### condition\_bits
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<Attribute id="qiskit.circuit.library.RXXGate.condition_bits">
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Get Clbits in condition.
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</Attribute>
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### decompositions
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<Attribute id="qiskit.circuit.library.RXXGate.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.RXXGate.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.RXXGate.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.RXXGate.label">
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Return instruction label
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</Attribute>
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### name
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<Attribute id="qiskit.circuit.library.RXXGate.name">
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Return the name.
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</Attribute>
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### num\_clbits
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<Attribute id="qiskit.circuit.library.RXXGate.num_clbits">
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Return the number of clbits.
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</Attribute>
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### num\_qubits
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<Attribute id="qiskit.circuit.library.RXXGate.num_qubits">
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Return the number of qubits.
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</Attribute>
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### params
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<Attribute id="qiskit.circuit.library.RXXGate.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.RXXGate.unit">
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Get the time unit of duration.
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</Attribute>
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## Methods
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### inverse
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<Function id="qiskit.circuit.library.RXXGate.inverse" signature="inverse()">
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Return inverse RXX gate (i.e. with the negative rotation angle).
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</Function>
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### power
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<Function id="qiskit.circuit.library.RXXGate.power" signature="power(exponent)">
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Raise gate to a power.
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</Function>
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</Class>
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