151 lines
4.3 KiB
Plaintext
151 lines
4.3 KiB
Plaintext
---
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title: XXMinusYYGate
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description: API reference for qiskit.circuit.library.XXMinusYYGate
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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.XXMinusYYGate
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---
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# XXMinusYYGate
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<Class id="qiskit.circuit.library.XXMinusYYGate" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.20/qiskit/circuit/library/standard_gates/xx_minus_yy.py" signature="XXMinusYYGate(theta, beta=0, label='{XX-YY}')" modifiers="class">
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Bases: `qiskit.circuit.gate.Gate`
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XX-YY interaction gate.
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A 2-qubit parameterized XX-YY interaction. Its action is to induce a coherent rotation by some angle between $|00\rangle$ and $|11\rangle$.
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**Circuit Symbol:**
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```python
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┌───────────────┐
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q_0: ┤0 ├
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│ {XX-YY}(θ,β) │
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q_1: ┤1 ├
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└───────────────┘
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```
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**Matrix Representation:**
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$$
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\begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{XX-YY}(\theta, \beta) q_0, q_1 =
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RZ_1(\beta) \cdot exp(-i \frac{\theta}{2} \frac{XX-YY}{2}) \cdot RZ_1(-\beta) =
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\begin{pmatrix}
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\cos(\th) & 0 & 0 & -i\sin(\th)e^{-i\beta} \\
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0 & 1 & 0 & 0 \\
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0 & 0 & 1 & 0 \\
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-i\sin(\th)e^{i\beta} & 0 & 0 & \cos(\th)
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\end{pmatrix}\end{split}\end{aligned}\end{align}
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$$
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<Admonition title="Note" type="note">
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In Qiskit’s convention, higher qubit indices are more significant (little endian convention). In the above example we apply the gate on (q\_0, q\_1) which results in adding the (optional) phase defined by $beta$ on q\_1. Instead, if we apply it on (q\_1, q\_0), the phase is added on q\_0. If $beta$ is set to its default value of $0$, the gate is equivalent in big and little endian.
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```python
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┌───────────────┐
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q_0: ┤1 ├
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│ {XX-YY}(θ,β) │
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q_1: ┤0 ├
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└───────────────┘
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```
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$$
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\begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{XX-YY}(\theta, \beta) q_1, q_0 =
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RZ_0(\beta) \cdot exp(-i \frac{\theta}{2} \frac{XX-YY}{2}) \cdot RZ_0(-\beta) =
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\begin{pmatrix}
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\cos(\th) & 0 & 0 & -i\sin(\th)e^{i\beta} \\
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0 & 1 & 0 & 0 \\
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0 & 0 & 1 & 0 \\
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-i\sin(\th)e^{-i\beta} & 0 & 0 & \cos(\th)
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\end{pmatrix}\end{split}\end{aligned}\end{align}
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$$
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</Admonition>
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Create new XX-YY gate.
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**Parameters**
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* **theta** (`Union`\[`ParameterExpression`, `float`]) – The rotation angle.
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* **beta** (`Union`\[`ParameterExpression`, `float`]) – The phase angle.
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* **label** (`Optional`\[`str`]) – The label of the gate.
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## Methods Defined Here
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### inverse
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<Function id="qiskit.circuit.library.XXMinusYYGate.inverse" signature="XXMinusYYGate.inverse()">
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Inverse gate.
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</Function>
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## Attributes
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### condition\_bits
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<Attribute id="qiskit.circuit.library.XXMinusYYGate.condition_bits">
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Get Clbits in condition.
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**Return type**
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`List`\[`Clbit`]
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</Attribute>
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### decompositions
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<Attribute id="qiskit.circuit.library.XXMinusYYGate.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.XXMinusYYGate.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.XXMinusYYGate.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.XXMinusYYGate.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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### name
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<Attribute id="qiskit.circuit.library.XXMinusYYGate.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.XXMinusYYGate.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.XXMinusYYGate.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.XXMinusYYGate.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.XXMinusYYGate.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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