151 lines
4.9 KiB
Plaintext
151 lines
4.9 KiB
Plaintext
---
|
||
title: XXPlusYYGate
|
||
description: API reference for qiskit.circuit.library.XXPlusYYGate
|
||
in_page_toc_min_heading_level: 1
|
||
python_api_type: class
|
||
python_api_name: qiskit.circuit.library.XXPlusYYGate
|
||
---
|
||
|
||
# XXPlusYYGate
|
||
|
||
<Class id="qiskit.circuit.library.XXPlusYYGate" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.21/qiskit/circuit/library/standard_gates/xx_plus_yy.py" signature="XXPlusYYGate(theta, beta=0, label='{XX+YY}')" modifiers="class">
|
||
Bases: [`qiskit.circuit.gate.Gate`](qiskit.circuit.Gate "qiskit.circuit.gate.Gate")
|
||
|
||
XX+YY interaction gate.
|
||
|
||
A 2-qubit parameterized XX+YY interaction, also known as an XY gate. Its action is to induce a coherent rotation by some angle between $|01\rangle$ and $|10\rangle$.
|
||
|
||
**Circuit Symbol:**
|
||
|
||
```python
|
||
┌───────────────┐
|
||
q_0: ┤0 ├
|
||
│ {XX+YY}(θ,β) │
|
||
q_1: ┤1 ├
|
||
└───────────────┘
|
||
```
|
||
|
||
**Matrix Representation:**
|
||
|
||
$$
|
||
\begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{XX+YY}(\theta, \beta)\ q_0, q_1 =
|
||
RZ_0(-\beta) \cdot \exp\left(-i \frac{\theta}{2} \frac{XX+YY}{2}\right) \cdot RZ_0(\beta) =
|
||
\begin{pmatrix}
|
||
1 & 0 & 0 & 0 \\
|
||
0 & \cos\left(\th\right) & -i\sin\left(\th\right)e^{-i\beta} & 0 \\
|
||
0 & -i\sin\left(\th\right)e^{i\beta} & \cos\left(\th\right) & 0 \\
|
||
0 & 0 & 0 & 1
|
||
\end{pmatrix}\end{split}\end{aligned}\end{align}
|
||
$$
|
||
|
||
<Admonition title="Note" type="note">
|
||
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\_0. Instead, if we apply it on (q\_1, q\_0), the phase is added on q\_1. If $beta$ is set to its default value of $0$, the gate is equivalent in big and little endian.
|
||
|
||
```python
|
||
┌───────────────┐
|
||
q_0: ┤1 ├
|
||
│ {XX+YY}(θ,β) │
|
||
q_1: ┤0 ├
|
||
└───────────────┘
|
||
```
|
||
</Admonition>
|
||
|
||
$$
|
||
\begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{XX+YY}(\theta, \beta)\ q_0, q_1 =
|
||
RZ_1(-\beta) \cdot \exp\left(-i \frac{\theta}{2} \frac{XX+YY}{2}\right) \cdot RZ_1(\beta) =
|
||
\begin{pmatrix}
|
||
1 & 0 & 0 & 0 \\
|
||
0 & \cos\left(\th\right) & -i\sin\left(\th\right)e^{i\beta} & 0 \\
|
||
0 & -i\sin\left(\th\right)e^{-i\beta} & \cos\left(\th\right) & 0 \\
|
||
0 & 0 & 0 & 1
|
||
\end{pmatrix}\end{split}\end{aligned}\end{align}
|
||
$$
|
||
|
||
Create new XX+YY gate.
|
||
|
||
**Parameters**
|
||
|
||
* **theta** (`Union`\[[`ParameterExpression`](qiskit.circuit.ParameterExpression "qiskit.circuit.parameterexpression.ParameterExpression"), `float`]) – The rotation angle.
|
||
* **beta** (`Union`\[[`ParameterExpression`](qiskit.circuit.ParameterExpression "qiskit.circuit.parameterexpression.ParameterExpression"), `float`]) – The phase angle.
|
||
* **label** (`Optional`\[`str`]) – The label of the gate.
|
||
|
||
## Methods Defined Here
|
||
|
||
### inverse
|
||
|
||
<Function id="qiskit.circuit.library.XXPlusYYGate.inverse" signature="XXPlusYYGate.inverse()">
|
||
Return inverse XX+YY gate (i.e. with the negative rotation angle and same phase angle).
|
||
</Function>
|
||
|
||
## Attributes
|
||
|
||
### condition\_bits
|
||
|
||
<Attribute id="qiskit.circuit.library.XXPlusYYGate.condition_bits">
|
||
Get Clbits in condition.
|
||
|
||
**Return type**
|
||
|
||
`List`\[[`Clbit`](qiskit.circuit.Clbit "qiskit.circuit.classicalregister.Clbit")]
|
||
</Attribute>
|
||
|
||
### decompositions
|
||
|
||
<Attribute id="qiskit.circuit.library.XXPlusYYGate.decompositions">
|
||
Get the decompositions of the instruction from the SessionEquivalenceLibrary.
|
||
</Attribute>
|
||
|
||
### definition
|
||
|
||
<Attribute id="qiskit.circuit.library.XXPlusYYGate.definition">
|
||
Return definition in terms of other basic gates.
|
||
</Attribute>
|
||
|
||
### duration
|
||
|
||
<Attribute id="qiskit.circuit.library.XXPlusYYGate.duration">
|
||
Get the duration.
|
||
</Attribute>
|
||
|
||
### label
|
||
|
||
<Attribute id="qiskit.circuit.library.XXPlusYYGate.label">
|
||
Return instruction label
|
||
|
||
**Return type**
|
||
|
||
`str`
|
||
</Attribute>
|
||
|
||
### name
|
||
|
||
<Attribute id="qiskit.circuit.library.XXPlusYYGate.name">
|
||
Return the name.
|
||
</Attribute>
|
||
|
||
### num\_clbits
|
||
|
||
<Attribute id="qiskit.circuit.library.XXPlusYYGate.num_clbits">
|
||
Return the number of clbits.
|
||
</Attribute>
|
||
|
||
### num\_qubits
|
||
|
||
<Attribute id="qiskit.circuit.library.XXPlusYYGate.num_qubits">
|
||
Return the number of qubits.
|
||
</Attribute>
|
||
|
||
### params
|
||
|
||
<Attribute id="qiskit.circuit.library.XXPlusYYGate.params">
|
||
return instruction params.
|
||
</Attribute>
|
||
|
||
### unit
|
||
|
||
<Attribute id="qiskit.circuit.library.XXPlusYYGate.unit">
|
||
Get the time unit of duration.
|
||
</Attribute>
|
||
</Class>
|
||
|