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# XXMinusYYGate

class XXMinusYYGate(theta, beta=0, label='{XX-YY}')

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XX-YY interaction gate.

A 2-qubit parameterized XX-YY interaction. Its action is to induce a coherent rotation by some angle between $|00\rangle$ and $|11\rangle$.

Circuit Symbol:

     ┌───────────────┐
q_0: ┤0              ├
│  {XX-YY}(θ,β) │
q_1: ┤1              ├
└───────────────┘

Matrix Representation:

$\providecommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{XX-YY}(\theta, \beta) q_0, q_1 = RZ_1(\beta) \cdot \exp\left(-i \frac{\theta}{2} \frac{XX-YY}{2}\right) \cdot RZ_1(-\beta) = \begin{pmatrix} \cos\left(\th\right) & 0 & 0 & -i\sin\left(\th\right)e^{-i\beta} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ -i\sin\left(\th\right)e^{i\beta} & 0 & 0 & \cos\left(\th\right) \end{pmatrix}\end{split}$
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_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.

     ┌───────────────┐
q_0: ┤1              ├
│  {XX-YY}(θ,β) │
q_1: ┤0              ├
└───────────────┘
$\providecommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{XX-YY}(\theta, \beta) q_1, q_0 = RZ_0(\beta) \cdot \exp\left(-i \frac{\theta}{2} \frac{XX-YY}{2}\right) \cdot RZ_0(-\beta) = \begin{pmatrix} \cos\left(\th\right) & 0 & 0 & -i\sin\left(\th\right)e^{i\beta} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ -i\sin\left(\th\right)e^{-i\beta} & 0 & 0 & \cos\left(\th\right) \end{pmatrix}\end{split}$

Create new XX-YY gate.

Parameters

## Methods Defined Here

### inverse

XXMinusYYGate.inverse()

Inverse gate.

### power

XXMinusYYGate.power(exponent)

Raise gate to a power.

## Attributes

### condition_bits

Get Clbits in condition.

Return type

List[Clbit]

### decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

### definition

Return definition in terms of other basic gates.

### duration

Get the duration.

### label

Return instruction label

Return type

str

Return the name.

### num_clbits

Return the number of clbits.

### num_qubits

Return the number of qubits.

### params

return instruction params.

### unit

Get the time unit of duration.